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Chapter 5. Reading and Manipulating Grids FLUENT can import many different types of grids from various sources. You can modify the grid by translating or scaling node coordinates, par- titioning the cells for parallel processing, reordering the cells in the do- main to decrease bandwidth, and merging or separating zones. You can also obtain diagnostic information on the grid, including memory usage and simplex, topological, and domain information. You can find out the number of nodes, faces, and cells in the grid, determine the minimum and maximum cell volumes in the domain, and check for the proper numbers of nodes and faces per cell. These and other capabilities are described in the following sections. Section 5.1: Grid Topologies Section 5.2: Grid Requirements and Considerations Section 5.3: Grid Import Section 5.4: Non-Conformal Grids Section 5.5: Checking the Grid Section 5.6: Reporting Grid Statistics Section 5.7: Modifying the Grid See Chapter 23 for information about adapting the grid based on solution data and related functions, and Section 28.4 for details on partitioning the grid for parallel processing. c Fluent Inc. November 28, 2001 5-1

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  • Chapter 5. Reading and Manipulating

    Grids

    FLUENT can import many dierent types of grids from various sources.You can modify the grid by translating or scaling node coordinates, par-titioning the cells for parallel processing, reordering the cells in the do-main to decrease bandwidth, and merging or separating zones. You canalso obtain diagnostic information on the grid, including memory usageand simplex, topological, and domain information. You can nd out thenumber of nodes, faces, and cells in the grid, determine the minimum andmaximum cell volumes in the domain, and check for the proper numbersof nodes and faces per cell. These and other capabilities are describedin the following sections.

    Section 5.1: Grid Topologies Section 5.2: Grid Requirements and Considerations Section 5.3: Grid Import Section 5.4: Non-Conformal Grids Section 5.5: Checking the Grid Section 5.6: Reporting Grid Statistics Section 5.7: Modifying the Grid

    See Chapter 23 for information about adapting the grid based on solutiondata and related functions, and Section 28.4 for details on partitioningthe grid for parallel processing.

    c Fluent Inc. November 28, 2001 5-1

  • Reading and Manipulating Grids

    5.1 Grid Topologies

    Since FLUENT is an unstructured solver, it uses internal data structuresto assign an order to the cells, faces, and grid points in a mesh and tomaintain contact between adjacent cells. It does not, therefore, requirei,j,k indexing to locate neighboring cells. This gives you the flexibility touse the grid topology that is best for your problem, since the solverdoes not force an overall structure or topology on the grid. In 2D,quadrilateral and triangular cells are accepted, and in 3D, hexahedral,tetrahedral, pyramid, and wedge cells can be used. (Figure 5.1.1 depictseach of these cell types.) Both single-block and multi-block structuredmeshes are acceptable, as well as hybrid meshes containing quadrilateraland triangular cells or hexahedral, tetrahedral, pyramid, and wedge cells.In addition, FLUENT also accepts grids with hanging nodes (i.e., nodeson edges and faces that are not vertices of all the cells sharing thoseedges or faces). See Section 23.2.2 for details. Grids with non-conformalboundaries (i.e., grids with multiple subdomains in which the grid nodelocations at the internal subdomain boundaries are not identical) arealso acceptable. See Section 5.4 for details.

    Some examples of grids that are valid for FLUENT are presented in Sec-tion 5.1.1. Section 5.1.2 explains how to choose the grid type that is bestsuited for your problem.

    5.1.1 Examples of Acceptable Grid Topologies

    As mentioned above, FLUENT can solve problems on a wide variety ofgrids. Figures 5.1.2{5.1.12 show examples of grids that are valid for FLU-ENT. O-type grids, grids with zero-thickness walls, C-type grids, confor-mal block-structured grids, multiblock structured grids, non-conformalgrids, and unstructured triangular, tetrahedral, quadrilateral, and hexa-hedral grids are all acceptable. Note that while FLUENT does not requirea cyclic branch cut in an O-type grid, it will accept a grid that containsone.

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  • 5.1 Grid Topologies

    Tetrahedron Hexahedron

    Prism/Wedge Pyramid

    Triangle Quadrilateral

    2D Cell Types

    3D Cell Types

    Figure 5.1.1: Cell Types

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  • Reading and Manipulating Grids

    Figure 5.1.2: Structured Quadrilateral Grid for an Airfoil

    Figure 5.1.3: Unstructured Quadrilateral Grid

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  • 5.1 Grid Topologies

    Figure 5.1.4: Multiblock Structured Quadrilateral Grid

    Figure 5.1.5: O-Type Structured Quadrilateral Grid

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  • Reading and Manipulating Grids

    Figure 5.1.6: Parachute Modeled With Zero-Thickness Wall

    Branch Cut

    Figure 5.1.7: C-Type Structured Quadrilateral Grid

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  • 5.1 Grid Topologies

    Figure 5.1.8: 3D Multiblock Structured Grid

    Figure 5.1.9: Unstructured Triangular Grid for an Airfoil

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  • Reading and Manipulating Grids

    Figure 5.1.10: Unstructured Tetrahedral Grid

    Figure 5.1.11: Hybrid Triangular/Quadrilateral Grid with HangingNodes

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  • 5.1 Grid Topologies

    Figure 5.1.12: Non-Conformal Hybrid Grid for a Rotor-Stator Geometry

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  • Reading and Manipulating Grids

    5.1.2 Choosing the Appropriate Grid Type

    FLUENT can use grids comprised of triangular or quadrilateral cells (ora combination of the two) in 2D, and tetrahedral, hexahedral, pyramid,or wedge cells (or a combination of these) in 3D. The choice of whichmesh type to use will depend on your application. When choosing yourmesh type, you should consider the following issues:

    Setup time Computational expense Numerical diusion

    To clarify the trade-os inherent in your choice of mesh type, these issuesare discussed further.

    Setup Time

    Many flow problems solved in engineering practice involve complex ge-ometries. The creation of structured or block-structured grids (consist-ing of quadrilateral or hexahedral elements) for such problems can beextremely time-consuming, if not impossible. Setup time for complexgeometries is, therefore, the major motivation for using unstructuredgrids employing triangular or tetrahedral cells. If your geometry is rela-tively simple, however, there may be no clear saving in setup time witheither approach.

    If you already have a mesh created for a structured code such as FLUENT4, it would clearly save you time to use this mesh in FLUENT rather thanregenerate it. This might be a strong motivation for using quadrilateralor hexahedral cells in your FLUENT simulation. Note that FLUENT hasa range of lters that allow you to import structured meshes from othercodes, including FLUENT 4 (see Section 5.3).

    Computational Expense

    When geometries are complex or the range of length scales of the flow islarge, a triangular/tetrahedral mesh can often be created with far fewer

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  • 5.1 Grid Topologies

    cells than the equivalent mesh consisting of quadrilateral/hexahedralelements. This is because a triangular/tetrahedral mesh allows cellsto be clustered in selected regions of the flow domain, whereas struc-tured quadrilateral/hexahedral meshes will generally force cells to beplaced in regions where they are not needed. Unstructured quadrilat-eral/hexahedral meshes oer many of the advantages of triangular/tetra-hedral meshes for moderately-complex geometries.

    One characteristic of quadrilateral/hexahedral elements that might makethem more economical in some situations is that they permit a muchlarger aspect ratio than triangular/tetrahedral cells. A large aspect ratioin a triangular/tetrahedral cell will invariably aect the skewness of thecell, which is undesirable as it may impede accuracy and convergence.Therefore, if you have a relatively simple geometry in which the flowconforms well to the shape of the geometry, such as a long thin duct, youcan use a mesh of high-aspect-ratio quadrilateral/hexahedral cells. Themesh is likely to have far fewer cells than if you use triangular/tetrahedralcells.

    Numerical Diusion

    A dominant source of error in multidimensional situations is numeri-cal diusion, also termed false diusion. (The term \false diusion" isused because the diusion is not a real phenomenon, yet its eect ona flow calculation is analogous to that of increasing the real diusioncoecient.)

    The following points can be made about numerical diusion:

    Numerical diusion is most noticeable when the real diusion issmall, that is, when the situation is convection-dominated.

    All practical numerical schemes for solving fluid flow contain anite amount of numerical diusion. This is because numericaldiusion arises from truncation errors that are a consequence ofrepresenting the fluid flow equations in discrete form.

    The second-order discretization scheme used in FLUENT can helpreduce the eects of numerical diusion on the solution.

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  • Reading and Manipulating Grids

    The amount of numerical diusion is inversely related to the reso-lution of the mesh. Therefore, one way of dealing with numericaldiusion is to rene the mesh.

    Numerical diusion is minimized when the flow is aligned with themesh.

    The last point is the most relevant to the choice of the grid. It isclear that if you use a triangular/tetrahedral mesh the flow can neverbe aligned with the grid. On the other hand, if you use a quadrilat-eral/hexahedral mesh this situation might occur, but not for complexflows. It is only in a simple flow, such as the flow through a long duct,in which you can rely on a quadrilateral/hexahedral mesh to minimizenumerical diusion. In such situations, there might be some advan-tage to using a quadrilateral/hexahedral mesh, since you will be able toget a better solution with fewer cells than if you were using a triangu-lar/tetrahedral mesh.

    5.2 Grid Requirements and Considerations

    This section contains information about special geometry/grid require-ments and general comments on mesh quality.

    5.2.1 Geometry/Grid Requirements

    You should be aware of the following geometry setup and grid construc-tion requirements at the beginning of your problem setup:

    Axisymmetric geometries must be dened such that the axis ofrotation is the x axis of the Cartesian coordinates used to denethe geometry (Figure 5.2.1).

    FLUENT allows you to set up periodic boundaries using either con-formal or non-conformal periodic zones. For conformal periodicboundaries, the periodic zones must have identical grids. The con-formal periodic boundaries can be created in GAMBIT or TGridwhen you are generating the volume mesh. (See the GAMBIT Mod-eling Guide or the TGrid Users Guide for more information about

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  • 5.2 Grid Requirements and Considerations

    y

    x CLFigure 5.2.1: Setup of Axisymmetric Geometries with the x Axis as theCenterline

    creating periodic boundaries in GAMBIT or TGrid.) Alternatively,you can create the conformal periodic boundaries in FLUENT usingthe make-periodic text command (see Section 5.7.5 for details).

    Although GAMBIT and TGrid can produce true periodic bound-aries, most CAD packages do not. If your mesh was created insuch a package, you can create the periodic boundaries using thenon-conformal periodic option in FLUENT (see Section 5.7.5 fordetails). This option, however, is recommended only for periodiczones that are planar.

    5.2.2 Mesh Quality

    The quality of the mesh plays a signicant role in the accuracy andstability of the numerical computation. The attributes associated withmesh quality are node point distribution, smoothness, and skewness.

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  • Reading and Manipulating Grids

    Node Density and Clustering

    Since you are discretely dening a continuous domain, the degree towhich the salient features of the flow (such as shear layers, separatedregions, shock waves, boundary layers, and mixing zones) are resolveddepends on the density and distribution of nodes in the mesh. In manycases, poor resolution in critical regions can dramatically alter the flowcharacteristics. For example, the prediction of separation due to an ad-verse pressure gradient depends heavily on the resolution of the boundarylayer upstream of the point of separation.

    Resolution of the boundary layer (i.e., mesh spacing near walls) alsoplays a signicant role in the accuracy of the computed wall shear stressand heat transfer coecient. This is particularly true in laminar flowswhere the grid adjacent to the wall should obey

    yp

    ru1x

    1 (5.2-1)

    where yp = distance to the wall from the adjacent cell centroidu1 = free-stream velocity = kinematic viscosity of the fluidx = distance along the wall from the starting point

    of the boundary layer

    Equation 5.2-1 is based upon the Blasius solution for laminar flow overa flat plate at zero incidence [203].

    Proper resolution of the mesh for turbulent flows is also very important.Due to the strong interaction of the mean flow and turbulence, the nu-merical results for turbulent flows tend to be more susceptible to griddependency than those for laminar flows. In the near-wall region, dif-ferent mesh resolutions are required depending on the near-wall modelbeing used. See Section 10.9 for detailed guidelines.

    In general, no flow passage should be represented by fewer than 5 cells.Most cases will require many more cells to adequately resolve the pas-sage. In regions of large gradients, as in shear layers or mixing zones, thegrid should be ne enough to minimize the change in the flow variables

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  • 5.2 Grid Requirements and Considerations

    from cell to cell. Unfortunately, it is usually very dicult to determinein advance the locations of important flow features. Moreover, the gridresolution in most complicated three-dimensional flow elds will be con-strained by CPU time and computer resource limitations (i.e., memoryand disk space). Although accuracy increases with larger grids, the CPUand memory requirements to compute the solution and postprocess theresults also increase. Solution-adaptive grid renement can be used toincrease and/or decrease grid density based on the evolving flow eld,and thus provides the potential for more economical use of grid points(and, hence, reduced time and resource requirements). See Chapter 23for more information on solution adaption.

    Smoothness

    Rapid changes in cell volume between adjacent cells translate into largertruncation errors. Truncation error is the dierence between the partialderivatives in the governing equations and their discrete approximations.FLUENT provides the capability to improve the smoothness by reningthe mesh based on the change in cell volume or the gradient of cellvolume. See Sections 23.4 and 23.7 for more information on rening thegrid based on change in cell volume.

    Cell Shape

    The shape of the cell (including its skewness and aspect ratio) also has asignicant impact on the accuracy of the numerical solution. Skewnesscan be dened as the dierence between the cells shape and the shape ofan equilateral cell of equivalent volume. Highly skewed cells can decreaseaccuracy and destabilize the solution. For example, optimal quadrilat-eral meshes will have vertex angles close to 90 degrees, while triangularmeshes should preferably have angles of close to 60 degrees and have allangles less than 90 degrees.

    Aspect ratio is a measure of the stretching of the cell. As discussed inSection 5.1.2, for highly anisotropic flows, extreme aspect ratios mayyield accurate results with fewer cells. However, a general rule of thumbis to avoid aspect ratios in excess of 5:1.

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  • Reading and Manipulating Grids

    Flow-Field Dependency

    The eect of resolution, smoothness and cell shape on the accuracy andstability of the solution process is strongly dependent on the flow eldbeing simulated. For example, very skewed cells can be tolerated inbenign flow regions, but can be very damaging in regions with strong flowgradients. Since the locations of strong flow gradients generally cannotbe determined a priori, you should strive to achieve a high-quality meshover the entire flow domain.

    5.3 Grid Import

    Since FLUENT can handle a number of dierent grid topologies, there aremany sources from which you can obtain a grid to be used in your simu-lation. You can generate a grid using GAMBIT, TGrid, GeoMesh, preBFC,ICEMCFD, I-DEAS, NASTRAN, PATRAN, ARIES, ANSYS, or other pre-processors, or use the grid contained in a FLUENT/UNS, RAMPANT,or FLUENT 4 case le. You can also prepare multiple mesh les andcombine them to create a single mesh.

    5.3.1 GAMBIT Grid Files

    You can use GAMBIT to create 2D and 3D structured/unstructured/hybridgrids. To create any of these meshes for FLUENT, follow the proceduredescribed in the GAMBIT Modeling Guide, and export your mesh in FLU-ENT 5/6 format. All such meshes can be imported directly into FLUENTusing the File/Read/Case... menu item, as described in Section 3.2.

    5.3.2 GeoMesh Grid Files

    You can use GeoMesh to create complete 2D quadrilateral or triangulargrids, 3D hexahedral grids, and triangular surface grids for 3D tetra-hedral grids. To create any of these meshes for FLUENT, follow theprocedure described in the GeoMesh Users Guide. To complete the gen-eration of a 3D tetrahedral mesh, you must read the surface mesh intoTGrid and generate the volume mesh there. All other meshes, however,can be imported directly into FLUENT using the File/Read/Case... menuitem, as described in Section 3.2.

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  • 5.3 Grid Import

    5.3.3 TGrid Grid Files

    You can use TGrid to create 2D and 3D unstructured triangular/tetrahe-dral grids from boundary or surface grids. Follow the meshing proce-dure described in the TGrid Users Guide, and save your mesh using theFile/Write/Mesh... menu item. To import the grid into FLUENT, use theFile/Read/Case... menu item, as described in Section 3.2.

    5.3.4 preBFC Grid Files

    You can use preBFC to create two dierent types of grids for FLUENT:structured quadrilateral/hexahedral and unstructured triangular/tetrahe-dral. The procedure for generating and importing each is outlined below.

    Structured Grid Files

    To generate a structured 2D or 3D grid, follow the procedure describedin the preBFC Users Guide (Chapters 6 and 7). The resulting grid willcontain quadrilateral (2D) or hexahedral (3D) elements. Remember tospecify no more than 70 wall zones and no more than 35 inlet zones.

    To import the grid, use the File/Import/preBFC Structured Mesh... menuitem, as described in Section 3.2.4.

    To manually convert a le in preBFC format to a mesh le suitable forFLUENT, enter the following command:

    utility fl42seg input-lename output-lename

    The output le produced can be read into FLUENT using theFile/Read/Case... menu item, as described in Section 3.2.

    Unstructured Triangular and Tetrahedral Grid Files

    To generate an unstructured 2D grid, follow the procedure described inthe preBFC Users Guide (Chapter 8), and save your mesh le in theRAMPANT format using the MESH-RAMPANT/TGRID command. Note thatthe current FLUENT format is the same as the RAMPANT format. The

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  • Reading and Manipulating Grids

    resulting grid will contain triangular elements. To import the grid, usethe File/Read/Case... menu item, as described in Section 3.2.

    To generate a 3D unstructured tetrahedral grid, follow the procedure de-scribed in Chapter 8 of the preBFC Users Guide for generating a surfacemesh. You will then read the surface mesh into TGrid, and complete thegrid generation there. See Section 5.3.3 for information about TGrid gridles.

    5.3.5 ICEMCFD Grid Files

    You can use ICEMCFD to create structured grids in FLUENT 4 formatand unstructured grids in RAMPANT format. To import a FLUENT 4grid, follow the instructions in Section 5.3.8. To import a RAMPANTgrid, use the File/Read/Case... menu item, as described in Section 3.2.Note that the current FLUENT format is the same as the RAMPANTformat; it is not the same as the FLUENT 4 format. After reading atriangular or tetrahedral ICEMCFD volume mesh, you should performsmoothing and swapping (as described in Section 23.11) to improve itsquality.

    5.3.6 Grid Files from Third-Party CAD Packages

    FLUENT can import grid les from a number of third-party CAD pack-ages, including I-DEAS, NASTRAN, PATRAN, and ANSYS.

    I-DEAS Universal Files

    There are three dierent ways in which you can import an I-DEAS Uni-versal le into FLUENT:

    1. You can generate an I-DEAS surface or volume mesh containingtriangular, quadrilateral, tetrahedral, wedge and/or hexahedral el-ements, and import it into TGrid using the commands described inthe TGrid Users Guide and adhering to the restrictions describedin Appendix B of the TGrid Users Guide. In TGrid, complete thegrid generation (if necessary) and then follow the instructions inSection 5.3.3.

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  • 5.3 Grid Import

    2. You can generate an I-DEAS volume mesh with linear triangular,quadrilateral, tetrahedral, wedge, or hexahedral elements, and im-port it directly using the File/Import/IDEAS Universal... menu item,as described in Section 3.2.6.

    3. You can generate an I-DEAS volume mesh with linear triangular,quadrilateral, tetrahedral, wedge, or hexahedral elements, and thenuse the lter fe2ram to convert the Universal le to the format usedby FLUENT. To convert an input le in I-DEAS Universal format toan output le in FLUENT format, follow the instructions on page5-24. After the output le has been written, you can read it intoFLUENT using the File/Read/Case... menu item, as described inSection 3.2.

    Recognized I-DEAS Datasets

    The following Universal le datasets are recognized by the FLUENT gridimport utility:

    Node Coordinates dataset number 15, 781, 2411

    Elements dataset number 71, 780, 2412

    Permanent Groups dataset number 752, 2417, 2429, 2430, 2432, 2435

    For 2D volume grids, the elements must exist in a constant z plane.

    Note that mesh area/mesh volume datasets are not recognized. This im-plies that writing multiple mesh areas/mesh volumes to a single Universalle may confuse FLUENT.

    Grouping Nodes to Create Face Zones

    Nodes are grouped in I-DEAS using the Group command to create bound-ary face zones. In FLUENT, boundary conditions are applied to eachzone. Faces that contain the nodes in a group are gathered into a singlezone. It is important not to group nodes of internal faces with nodes ofboundary faces.

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  • Reading and Manipulating Grids

    One technique is to generate groups automatically based on curves ormesh areas|i.e., every curve or mesh area will be a dierent zone inFLUENT. You may also create the groups manually, generating groupsconsisting of all nodes related to a given curve (2D) or mesh area (3D).

    Grouping Elements to Create Cell Zones

    Elements in I-DEAS are grouped using the Group command to create themultiple cell zones. All elements grouped together are placed in a singlecell zone in FLUENT. If the elements are not grouped, FLUENT will placeall the cells into a single zone.

    Deleting Duplicate Nodes

    I-DEAS may generate duplicate or coincident nodes in the process of cre-ating elements. These nodes must be removed in I-DEAS before writingthe universal le for import into FLUENT.

    NASTRAN Files

    There are three dierent ways in which you can import a NASTRAN leinto FLUENT:

    1. You can generate a NASTRAN surface or volume mesh containingtriangular, quadrilateral, tetrahedral, wedge, and/or hexahedralelements, and import it into TGrid using the commands describedin the TGrid Users Guide and adhering to the restrictions describedin Appendix B of the TGrid Users Guide. In TGrid, complete thegrid generation (if necessary) and then follow the instructions inSection 5.3.3.

    2. You can generate a NASTRAN volume mesh with linear triangu-lar, quadrilateral, tetrahedral, wedge, or hexahedral elements, andimport it directly using the File/Import/NASTRAN... menu item,as described in Section 3.2.7.

    3. You can generate a NASTRAN volume mesh with linear triangular,quadrilateral, tetrahedral, wedge, or hexahedral elements, and then

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  • 5.3 Grid Import

    use the lter fe2ram to convert the NASTRAN le to the formatused by FLUENT. To convert an input le in NASTRAN format toan output le in FLUENT format, follow the instructions on page5-24. After the output le has been written, you can read it intoFLUENT using the File/Read/Case... menu item, as described inSection 3.2.

    After reading a triangular or tetrahedral NASTRAN volume mesh usingmethod 2 or 3 above, you should perform smoothing and swapping (asdescribed in Section 23.11) to improve its quality.

    Recognized NASTRAN Bulk Data Entries

    The following NASTRAN le datasets are recognized by the FLUENTgrid import utility:

    GRID single-precision node coordinates

    GRID* double-precision node coordinates

    CBAR line elements

    CTETRA, CTRIA3 tetrahedral and triangular elements

    CHEXA, CQUAD4, CPENTA hexahedral, quadrilateral, and wedgeelements

    For 2D volume grids, the elements must exist in a constant z plane.

    Deleting Duplicate Nodes

    NASTRAN may generate duplicate or coincident nodes in the process ofcreating elements. These nodes must be removed in NASTRAN beforewriting the le for import into FLUENT.

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  • Reading and Manipulating Grids

    PATRAN Neutral Files

    There are three dierent ways in which you can import a PATRAN Neutralle into FLUENT.

    1. You can generate a PATRAN surface or volume mesh containingtriangular, quadrilateral, tetrahedral, wedge, and/or hexahedralelements, and import it into TGrid using the commands describedin the TGrid Users Guide and adhering to the restrictions describedin Appendix B of the TGrid Users Guide. In TGrid, complete thegrid generation (if necessary) and then follow the instructions inSection 5.3.3.

    2. You can generate a PATRAN volume mesh with linear triangular,quadrilateral, tetrahedral, wedge, or hexahedral elements (group-ing nodes with the same component-group name) and import itdirectly to FLUENT by selecting the File/Import/ PATRAN... menuitem, as described in Section 3.2.8.

    3. You can generate a PATRAN volume mesh with linear triangular,quadrilateral, tetrahedral, wedge, or hexahedral elements and thenuse the lter fe2ram to convert the Neutral le into the format usedby FLUENT. To convert an input le in PATRAN Neutral format toan output le in FLUENT format, follow the instructions on page5-24. After the output le has been written, you can read it intoFLUENT using the File/Read/Case... menu item, as described inSection 3.2.

    After reading a triangular or tetrahedral PATRAN volume mesh usingmethod 2 or 3 above, you should perform smoothing and swapping (asdescribed in Section 23.11) to improve its quality.

    Recognized PATRAN Datasets

    The following PATRAN Neutral le packet types are recognized by theFLUENT grid import utility:

    Node Data Packet Type 01

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  • 5.3 Grid Import

    Element Data Packet Type 02

    Distributed Load Data Packet Type 06

    Node Temperature Data Packet Type 10

    Name Components Packet Type 21

    File Header Packet Type 25

    For 2D volume grids, the elements must exist in a constant z plane.

    Grouping Elements to Create Cell Zones

    Elements are grouped in PATRAN using the Named Component commandto create the multiple cell zones. All elements grouped together areplaced in a single cell zone in FLUENT. If the elements are not grouped,FLUENT will place all the cells into a single zone.

    ANSYS Files

    There are three dierent ways in which you can import an ANSYS leinto FLUENT.

    1. You can generate a surface or volume mesh containing triangu-lar, quadrilateral, tetrahedral, wedge, or hexahedral elements usingANSYS or ARIES, and import it into TGrid using the commandsdescribed in the TGrid Users Guide and adhering to the restric-tions described in Appendix B of the TGrid Users Guide. In TGrid,complete the grid generation (if necessary) and then follow the in-structions in Section 5.3.3.

    2. You can generate an ANSYS volume mesh with linear triangular,quadrilateral, tetrahedral, wedge, or hexahedral elements and im-port it directly to FLUENT using the File/Import/ANSYS... menuitem, as described in Section 3.2.5.

    3. You can generate an ANSYS volume mesh with linear triangular,quadrilateral, tetrahedral, wedge, or hexahedral elements and then

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  • Reading and Manipulating Grids

    use the lter fe2ram to convert the ANSYS le into the format usedby FLUENT. To convert an input le in ANSYS 5.4 or 5.5 format toan output le in FLUENT format, follow the instructions on page5-24. After the output le has been written, you can read it intoFLUENT using the File/Read/Case... menu item, as described inSection 3.2.

    After reading a triangular or tetrahedral volume mesh using method 2or 3 above, you should perform smoothing and swapping (as describedin Section 23.11) to improve its quality.

    Recognized ANSYS 5.4 and 5.5 Datasets

    FLUENT can import mesh les from ANSYS 5.4 and 5.5 (.cdb les),retaining original boundary names. The following ANSYS le datasetsare recognized by the FLUENT grid import utility:

    NBLOCK node block data

    EBLOCK element block data

    CMBLOCK element/node grouping

    The elements must be STIF63 linear shell elements. In addition, if el-ement data without an explicit element ID is used, the lter assumessequential numbering of the elements when creating the zones.

    Using the fe2ram Filter to Convert Files

    If you choose to convert the CAD le manually before reading it intoFLUENT, you can enter the following command:

    utility fe2ram [dimension] format [zoning] input-le output-le

    where items enclosed in square brackets are optional. (Do not type thesquare brackets.)

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  • 5.3 Grid Import

    dimension indicates the dimension of the dataset. Replace dimension by-d2 to indicate that the grid is 2-dimensional. For a 3D grid, do notenter anything for dimension, because 3D is the default.

    format indicates the format of the le you wish to convert. Replace for-mat by -tANSYS for an ANSYS le, -tIDEAS for an I-DEAS le, -tNASTRANfor a NASTRAN le, or -tPATRAN for a PATRAN le. To check if conver-sion from any other CAD packages has been added, typeutility fe2ram -cl -help.

    zoning indicates how zones were identied in the CAD package. Replacezoning by -zID for a grid that was zoned by property IDs, or -zNONEto ignore all zone groupings. For a grid zoned by group, do not enteranything for zoning, because zoning by groups is the default.

    input-le and output-le are the names of the original le and the le towhich you want to write the converted grid information, respectively.

    For example, if you wanted to convert the 2D I-DEAS volume mesh lesample.unv to an output le called sample.grd, you would enter thefollowing command:

    utility fe2ram -d2 -tIDEAS sample.unv sample.grd

    5.3.7 FLUENT/UNS and RAMPANT Case Files

    If you have a FLUENT/UNS 3 or 4 case le or a RAMPANT 2, 3, or 4case le and you want to run a FLUENT simulation using the same grid,you can read it into FLUENT using the File/Read/Case... menu item, asdescribed in Section 3.4.

    5.3.8 FLUENT 4 Case Files

    If you have a FLUENT 4 case le and you want to run a FLUENT sim-ulation using the same grid, you can import it into FLUENT using theFile/Import/FLUENT 4 Case... menu item, as described in Section 3.5.FLUENT will read grid information and zone types from the FLUENT 4case le.

    Note that FLUENT 4 may interpret some pressure boundaries dierently!

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  • Reading and Manipulating Grids

    from the current release of FLUENT. Check the conversion informationprinted out by FLUENT to see if you need to modify any boundary types.

    To manually convert an input le in FLUENT 4 format to an output lein the current FLUENT format, enter the following command:

    utility fl42seg input-lename output-lename

    After the output le has been written, you can read it into FLUENTusing the File/Read/Case... menu item, as described in Section 3.2.

    5.3.9 FIDAP Neutral Files

    If you have a FIDAP Neutral le and you want to run a FLUENT simula-tion using the same grid, you can import it using the File/Import/FIDAP...menu item, as described in Section 3.6. FLUENT will read grid informa-tion and zone types from the FIDAP le.

    To manually convert an input le in FIDAP format to an output le inFLUENT format, enter the following command:

    utility fe2ram [dimension] -tFIDAP7 input-le output-le

    where the item in square brackets is optional. (Do not type the squarebrackets.) For a 2D le, replace dimension with -d2. For a 3D le, donot enter anything for dimension, because 3D is the default.

    After the output le has been written, you can read it into FLUENTusing the File/Read/Case... menu item, as described in Section 3.2.

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  • 5.3 Grid Import

    5.3.10 Reading Multiple Mesh Files

    There may be some cases in which you will need to read multiple meshles (subdomains) to form your computational domain. Some examplesare listed below:

    If you plan to solve on a multiblock mesh, you can generate eachblock of the mesh in the grid generator and save it to a separategrid le.

    For very complicated geometries, it may be more ecient to savethe mesh for each part as a separate grid le.

    Note that you do not need to ensure that the grid node locations areidentical at the boundaries where two separate meshes meet; FLUENTcan handle non-conformal grid interfaces. See Section 5.4 for detailsabout non-conformal grid boundaries.

    The procedure for reading multiple grid les is as follows:

    1. Generate the grid for the whole domain in the grid generator, andsave each cell zone (or block or part) to a separate grid le forFLUENT.

    If one (or more) of the grids you wish to import is structured (e.g.,!a FLUENT 4 grid le), you will need to rst convert it to FLUENTformat using the fl42seg lter described in Section 5.3.8.

    2. Before you start the solver, use either TGrid or the tmerge lterto combine the grids into one grid le. The TGrid method is moreconvenient, but the tmerge method allows you to rotate, scale,and/or translate the grids before they are merged.

    To use TGrid, follow the procedure below:(a) Read all of the grid les into TGrid. When TGrid reads the

    grid les, it will automatically merge them into a singlegrid.

    (b) Save the merged grid le.

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  • Reading and Manipulating Grids

    See the TGrid Users Guide for information about reading andwriting les in TGrid.

    To use the tmerge lter, follow the procedure below (beforestarting FLUENT):

    (a) For 3D problems, type utility tmerge -3d. For 2Dproblems, type utility tmerge -2d.

    (b) When prompted, specify the names of the input les (theseparate grid les) and the name of the output le inwhich to save the complete grid. For each input le, youcan specify scaling factors, translation distances, or a ro-tation angle. In the example below, no scaling, transla-tion, or rotation is performed.

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  • 5.3 Grid Import

    user@mymachine:> utility tmerge -2d

    Starting /Fluent.Inc/utility/tmerge2.1/ultra/tmerge_2d.2.1.7

    Append 2D grid files.tmerge2D Fluent Inc, Version 2.0.16

    Enter name of grid file (ENTER to continue) : my1.msh

    x,y scaling factor, eg. 1 1 : 1 1

    x,y translation, eg. 0 1 : 0 0

    rotation angle (deg), eg. 45 : 0

    Enter name of grid file (ENTER to continue) : my2.msh

    x,y scaling factor, eg. 1 1 : 1 1

    x,y translation, eg. 0 1 : 0 0

    rotation angle (deg), eg. 45 : 0

    Enter name of grid file (ENTER to continue) :

    Enter name of output file : final.msh

    Reading...node zone: id 1, ib 1, ie 1677, typ 1node zone: id 2, ib 1678, ie 2169, typ 2

    .

    .

    .done.Writing...492 nodes, id 1, ib 1678, ie 2169, type 2.1677 nodes, id 2, ib 1, ie 1677, type 1.

    .

    .

    .done.Appending done.

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  • Reading and Manipulating Grids

    In the above example, where no scaling, translation, or rota-tion is requested, you could simplify the inputs to the follow-ing:

    utility tmerge -2d -cl -p my1.msh my2.msh final.msh

    3. Read the combined grid le into the solver in the usual manner(using the File/Read/Case... menu item).

    For a conformal mesh, if you do not want a boundary between the ad-jacent cell zones, you can use the Fuse Face Zones panel to fuse the\overlapping" boundaries (see Section 5.7.7). The matching faces willbe moved to a new zone with a boundary type of interior. If all faces oneither or both of the original zones have been moved to the new zone,the original zone(s) will be discarded.

    If you are planning to use sliding meshes, or if you have non-conformal!boundaries between adjacent cell zones, you should not fuse the overlap-ping zones. You must instead change the type of the two overlappingzones to interface (as described in Section 5.4).

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  • 5.4 Non-Conformal Grids

    5.4 Non-Conformal Grids

    In FLUENT it is possible to use a grid composed of cell zones with non-conformal boundaries. That is, the grid node locations do not need tobe identical at the boundaries where two subdomains meet. FLUENThandles such meshes using the same technique that is used in the slidingmesh model, although in this situation the meshes do not slide.

    5.4.1 Non-Conformal Grid Calculations

    To compute the flux across the non-conformal boundary, FLUENT mustrst compute the intersection between the \interface" zones that com-prise the boundary. The resulting intersection produces an interior zonewhere the two interface zones overlap (see Figure 5.4.1). If one of theinterface zones extends beyond the other (as shown in Figure 5.4.2),FLUENT will create one or two additional wall zones for the portion(s)of the boundary where the two interface zones do not overlap.

    interface zone 1

    interface zone 2

    interior zone

    Figure 5.4.1: Completely Overlapping Grid Interface Intersection

    interface zone 2

    interface zone 1interior zone

    wall zone 1 wall zone 2

    Figure 5.4.2: Partially Overlapping Grid Interface Intersection

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  • Reading and Manipulating Grids

    Principally, fluxes across the grid interface are computed using the facesresulting from the intersection of the two interface zones, rather thanfrom the interface zone faces themselves. In the example shown in Fig-ure 5.4.3, the interface zones are composed of faces A-B and B-C, andfaces D-E and E-F. The intersection of these zones produces the facesa-d, d-b, b-e, and e-c. Faces produced in the region where the two cellzones overlap (d-b, b-e, and e-c) are grouped to form an interior zone,while the remaining face (a-d) forms a wall zone. To compute the fluxacross the interface into cell IV, for example, face D-E is ignored andfaces d-b and b-e are used instead, bringing information into cell IVfrom cells I and III, respectively.

    A B C

    D E F

    a b e cd

    cell zone 1

    cell zone 2

    interfacezone 2

    interfacezone 1

    I II

    III

    IV VI

    V

    Figure 5.4.3: Two-Dimensional Non-Conformal Grid Interface

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  • 5.4 Non-Conformal Grids

    5.4.2 Requirements and Limitations of Non-Conformal Grids

    Please note the following requirements and limitations when using non-conformal grids:

    The grid interface can be any shape (including a non-planar sur-face, in 3D), provided that the two interface boundaries are basedon the same geometry. If there are sharp features (e.g., 90-degreeangles) or curvature in the mesh, it is especially important thatboth sides of the interface closely follow that feature.

    For example, consider the case of two concentric circles that denetwo fluid zones with a circular, non-conformal interface betweenthem, as shown in Figure 5.4.4. Because the node spacing on theinterface edge of the outer fluid zone is coarse compared to theradius of curvature, the interface does not closely follow the feature(in this case, the circular edge.)

    In general, the maximum tolerance between two interfaces should!not be larger than their adjacent cell size at that location; i.e., nocell should be completely enclosed between two interfaces.

    Large tolerances betweeninterfaces should be avoided

    Figure 5.4.4: A Circular Non-Conformal Interface

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    A face zone cannot share a non-conformal interface with more thanone other face zone. This is best illustrated by an example, asshown in Figure 5.4.5. Each volume in the gure is meshed sepa-rately and does not match node-to-node at the interface. To createthe non-conformal interface, you will need to work with three sur-faces: one side of the box (rectangle 1) and an end cap from eachpipe (circle 1 and circle 2). To create interfaces between rectangle 1and the two circles, there needs to be one-to-one mapping betweeneach end cap and the side of the box (see Figure 5.4.6).

    rectangle 1

    circle 2

    circle 1

    Figure 5.4.5: Box with Two Pipes Intersecting One Side

    If you create a single grid with multiple cell zones separated bya non-conformal boundary, you must be sure that each cell zonehas a distinct face zone on the non-conformal boundary. The facezones for two adjacent cell zones will have the same position andshape, but one will correspond to one cell zone and one to theother. (Note that it is also possible to create a separate grid lefor each of the cell zones, and then merge them as described inSection 5.3.10.)

    All periodic zones must be correctly oriented (either rotational ortranslational) before you create the non-conformal interface. Peri-odic non-conformal interfaces must overlap exactly; i.e., they need

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  • 5.4 Non-Conformal Grids

    Allowed: Divide rectangle 1 into two surfaces

    interface pairings are:

    rectangle 1a circle 2rectangle 1b circle 1

    Not allowed: Keeping things as they are

    rectangle 1 circle 2rectangle 1 circle 1

    Not Valid:

    rectangle 1a rectangle 1b

    circle 2 circle 1

    rectangle 1

    circle 2 circle 1

    Figure 5.4.6: One-to-One Mapping

    to have the same rotational or translational extent and, in addi-tion, have the same axial extent. This is not true for interfaces ingeneral, where a wall zone is created for non-overlapping regions.

    For 3D cases, if the interface is periodic, only one pair of periodicboundaries can neighbor the interface.

    See also Section 5.4.4 for information about using non-conformal FLU-ENT/UNS and RAMPANT cases.

    5.4.3 Using a Non-Conformal Grid in FLUENT

    If your multiple-zone grid includes non-conformal boundaries, you mustfollow the procedure below (after ensuring that your grid meets all therequirements listed in Section 5.4.2) to ensure that FLUENT can obtaina solution on your mesh:

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  • Reading and Manipulating Grids

    1. Read the grid into FLUENT. (If you have multiple grid les thathave not yet been merged, rst follow the instructions in Sec-tion 5.3.10 to merge them into a single grid.)

    2. After reading in the grid, change the type of each pair of zones thatcomprises the non-conformal boundary to interface (as described inSection 6.1.3).

    Dene !Boundary Conditions...3. Dene the non-conformal grid interfaces in the Grid Interfaces panel

    (Figure 5.4.7).

    Dene !Grid Interfaces...

    Figure 5.4.7: The Grid Interfaces Panel

    (a) Enter a name for the interface in the Grid Interface eld.

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  • 5.4 Non-Conformal Grids

    (b) Specify the two interface zones that comprise the grid inter-face by selecting one in the Interface Zone 1 list and one inthe Interface Zone 2 list.

    If one of your interface zones is much smaller than the other,!you should specify the smaller zone as Interface Zone 1 toimprove the accuracy of the intersection calculation.

    (c) Set the Interface Type, if appropriate. There are two options:

    Enable Periodic for periodic problems. Enable Coupled if the interface lies between a solid zone

    and a fluid zone.

    (d) Click on Create to create a new grid interface. For all types ofinterfaces, FLUENT will create boundary zones for the inter-face (e.g., wall-9, wall-10), which will appear under Bound-ary Zone 1 and Boundary Zone 2. If you have enabled theCoupled option, FLUENT will also create wall interface zones(e.g., wall-4, wall-4-shadow), which will appear under In-terface Wall Zone 1 and Interface Wall Zone 2.

    (e) If the two interface zones did not overlap entirely, check theboundary zone type of the zone(s) created for the non-overlap-ping portion(s) of the boundary. If the zone type is not cor-rect, you can use the Boundary Conditions panel to changeit.

    (f) If you have any Coupled-type interfaces, dene boundary con-ditions (if relevant) by updating the interface wall zones inthe Boundary Conditions panel.

    Dene !Boundary Conditions...If you create an incorrect grid interface, you can select it in theGrid Interface list and click on the Delete button to delete it. (Anyboundary zones or wall interface zones that were created when theinterface was created will also be deleted.)

    You may then proceed with the problem setup as usual.

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    5.4.4 Starting From a FLUENT/UNS or RAMPANT Case

    FLUENT/UNS and RAMPANT case les with non-conformal interfacescan be read and used by FLUENT without any changes. However, youmay want to recompute the grid interface to take advantage of FLU-ENTs improved intersection calculation. You cannot simply delete theoriginal grid interface and recompute it. Instead, you must use thedefine/grid-interfaces/recreate text command.

    define ! grid-interfaces !recreateWhen you select this command, FLUENT will recreate all grid interfacesin the domain. You can then continue the problem setup or calculationas usual.

    If you have a FLUENT/UNS or RAMPANT data le for the non-conformal!case, you must read it in before you use the recreate command.

    5.5 Checking the Grid

    The grid checking capability in FLUENT provides domain extents, vol-ume statistics, grid topology and periodic boundary information, veri-cation of simplex counters, and (for axisymmetric cases) node positionverication with respect to the x axis. You can obtain this informationby selecting the Check menu item in the Grid pull-down menu.

    Grid !CheckIt is generally a good idea to check your grid right after reading it into!the solver, in order to detect any grid trouble before you get started withthe problem setup.

    5.5.1 Grid Check Information

    The information that FLUENT generates when you use the Check itemwill appear in the console window. Sample output is shown below:

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  • 5.5 Checking the Grid

    Grid Check

    Domain Extents:x-coordinate: min (m) = 0.000000e+00, max (m) = 6.400001e+01y-coordinate: min (m) = -4.538534e+00, max (m) = 6.400000e+01

    Volume statistics:minimum volume (m3): 2.782193e-01maximum volume (m3): 3.926232e+00

    total volume (m3): 1.682930e+03Face area statistics:minimum face area (m2): 8.015718e-01maximum face area (m2): 4.118252e+00

    Checking number of nodes per cell.Checking number of faces per cell.Checking thread pointers.Checking number of cells per face.Checking face cells.Checking face handedness.Checking element type consistency.Checking boundary types:Checking face pairs.Checking periodic boundaries.Checking node count.Checking nosolve cell count.Checking nosolve face count.Checking face children.Checking cell children.Checking storage.Done.

    The domain extents list the minimum and maximum x, y, and z coor-dinates in meters. The volume statistics include minimum, maximum,and total cell volume in m3. A negative value for the minimum volumeindicates that one or more cells have improper connectivity. Cells witha negative volume can often be identied using the Iso-Value Adaptioncapability to mark them for adaption and view them in the graphics win-dow. For more information on creating and viewing isovalue adaptionregisters, see Section 23.5. You must eliminate these negative volumesbefore continuing the flow solution process.

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  • Reading and Manipulating Grids

    The topological information to be veried begins with the number offaces and nodes per cell. A triangular cell (2D) should have 3 facesand 3 nodes, a tetrahedral cell (3D) should have 4 faces and 4 nodes, aquadrilateral cell (2D) should have 4 faces and 4 nodes, and a hexahedralcell (3D) should have 6 faces and 8 nodes.

    Next, the face handedness for each zone is checked. The zones shouldcontain all right-handed faces. Usually a grid with negative volumes willalso have left-handed faces. Again, you cannot obtain a flow solutionuntil you eliminate these connectivity problems.

    The last topological verication is checking the element-type consistency.If a mesh does not contain mixed elements (quadrilaterals and trianglesor hexahedra and tetrahedra), FLUENT will determine that it does notneed to keep track of the element types. By doing so, it can eliminatesome unnecessary work.

    For axisymmetric cases, the number of nodes below the x axis is listed.Nodes below the x axis are forbidden for axisymmetric cases, since theaxisymmetric cell volumes are created by rotating the 2D cell volumeabout the x axis; thus nodes below the x axis would create negativevolumes.

    For solution domains with rotationally periodic boundaries, the mini-mum, maximum, average, and prescribed periodic angles are computed.A common mistake is to specify the angle incorrectly. For domains withtranslationally periodic boundaries, the boundary information is checkedto ensure that the boundaries are truly periodic.

    Finally, the simplex counters are veried. The actual numbers of nodes,faces, and cells the solver has constructed are compared to the valuesspecied in the corresponding header declarations in the grid le. Anydiscrepancies are reported.

    5.5.2 Repairing Duplicate Shadow Nodes

    If the Grid/Check report includes the following message:

    WARNING: node on face thread 2 has multiple shadows.

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  • 5.6 Reporting Grid Statistics

    you can repair the grid using the following text commands:

    For coupled-type walls:grid ! modify-zones !repair-duplicate-shadowsNo further inputs are required.

    For periodic-type walls:grid ! modify-zones !repair-periodicIf the interface is rotational periodic, you will be prompted for therotation angle.

    5.6 Reporting Grid Statistics

    There are several methods for reporting information about the grid afterit has been read into FLUENT. You can report the amount of memoryused by the current problem, the grid size, and statistics about the gridpartitions. Zone-by-zone counts of cells and faces can also be reported.

    Information about grid statistics is provided in the following sections:

    Section 5.6.1: Grid Size Section 5.6.2: Memory Usage Section 5.6.3: Grid Zone Information Section 5.6.4: Partition Statistics

    5.6.1 Grid Size

    You can print out the numbers of nodes, faces, cells, and partitions inthe grid by selecting the Grid/Info/Size menu item.

    Grid ! Info !SizeA partition is a piece of a grid that has been segregated for parallelprocessing (see Chapter 28).

    A sample of the resulting output follows:

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  • Reading and Manipulating Grids

    Grid Size

    Level Cells Faces Nodes Partitions0 7917 12247 4468 1

    2 cell zones, 11 face zones.

    If you are interested in how the cells and faces are divided among thedierent zones, you can use the Grid/Info/Zones menu item, as describedin Section 5.6.3.

    If you are using the coupled explicit solver, the grid information will beprinted for each grid level. The grid levels result from creating coarse gridlevels for the FAS multigrid convergence acceleration (see Section 22.5.4).A sample of the resulting output is shown below:

    Grid Size

    Level Cells Faces Nodes Partitions0 7917 12247 4468 11 1347 3658 0 12 392 1217 0 13 133 475 0 14 50 197 0 15 17 78 0 1

    2 cell zones, 11 face zones.

    5.6.2 Memory Usage

    During a FLUENT session you may want to check the amount of memoryused and allocated in the present analysis. FLUENT has a feature thatwill report the following information: the numbers of nodes, faces, cells,edges, and object pointers (generic pointers for various grid and graph-ics utilities) that are used and allocated; the amount of array memory(scratch memory used for surfaces) used and allocated; and the amountof memory used by the solver process.

    You can obtain this information by selecting the Grid/Info/Memory Usagemenu item.

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  • 5.6 Reporting Grid Statistics

    Grid ! Info !Memory UsageThe memory information will be dierent for UNIX and Windows sys-tems.

    UNIX Systems

    On UNIX systems, the process memory information includes the follow-ing:

    Process Static memory is essentially the size of the code itself. Process Dynamic memory is the allocated heap memory used to

    store the grid and solution variables

    Process Total memory is the sum of static and dynamic memory.

    Windows Systems

    On Windows systems, the process memory information includes the fol-lowing:

    Process Physical memory is the allocated heap memory currentlyresident in RAM.

    Process Virtual memory is the allocated heap memory currentlyswapped to the Windows system page le.

    Process Total memory is the sum of physical and virtual memory.

    Note the following:

    The memory information does not include the static (code) mem-ory.

    In the serial version of FLUENT, the heap memory value includesstorage for the solver (grid and solution variables), and Cortex (GUIand graphics memory), since Cortex and the solver are containedin the same process.

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  • Reading and Manipulating Grids

    In the parallel version, Cortex runs in its own process, so the heapmemory value includes storage for the grid and solution variablesonly.

    On Windows systems, you can also get more information on the FLUENTprocess (or processes) by using the Task Manager (see your Windows doc-umentation for details). For the serial version, the process image namewill be something like fl542s.exe. For the parallel version, examplesof process image names are as follows: cx332.exe (Cortex), fl542.exe(solver host), and fl smpi542.exe (one solver node).

    5.6.3 Grid Zone Information

    You can print information in the console window about the nodes, faces,and cells in each zone using the Grid/Info/Zones menu item.

    Grid ! Info !ZonesThe grid zone information includes the total number of nodes and, foreach face and cell zone, the number of faces or cells, the cell (and, in 3D,face) type (triangular, quadrilateral, etc.), the boundary condition type,and the zone ID. Sample output is shown below:

    Zone sizes on domain 1:21280 hexahedral cells, zone 4.

    532 quadrilateral velocity-inlet faces, zone 1.532 quadrilateral pressure-outlet faces, zone 2.

    1040 quadrilateral symmetry faces, zone 3.1040 quadrilateral symmetry faces, zone 7.

    61708 quadrilateral interior faces, zone 5.1120 quadrilateral wall faces, zone 6.

    23493 nodes.

    5.6.4 Partition Statistics

    You can print grid partition statistics in the console window by selectingthe Grid/Info/Partitions menu item.

    Grid ! Info !Partitions

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  • 5.7 Modifying the Grid

    The statistics include the numbers of cells, faces, interfaces, and neigh-bors of each partition. See Section 28.4.5 for further details, includingsample output.

    5.7 Modifying the Grid

    There are several ways in which you can modify or manipulate the gridafter it has been read into FLUENT. You can scale or translate the grid,merge or separate zones, create or slit periodic zones, and fuse bound-aries. In addition, you can reorder the cells in the domain to decreasebandwidth. Smoothing and diagonal swapping, which can be used to im-prove the mesh, are described in Section 23.11. Methods for partitioninggrids to be used in a parallel solver are discussed in Section 28.4.

    Whenever you modify the grid, you should be sure to save a new case!le (and a data le, if data exist). If you have old data les that youwould like to be able to read in again, be sure to retain the original casele as well, as the data in the old data les may not correspond to thenew case le.

    Information about grid manipulation is provided in the following sec-tions:

    Section 5.7.1: Scaling the Grid Section 5.7.2: Translating the Grid Section 5.7.3: Merging Zones Section 5.7.4: Separating Zones Section 5.7.5: Creating Periodic Zones Section 5.7.6: Slitting Periodic Zones Section 5.7.7: Fusing Face Zones Section 5.7.8: Slitting Face Zones Section 5.7.9: Extruding Face Zones Section 5.7.10: Reordering the Domain and Zones

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  • Reading and Manipulating Grids

    5.7.1 Scaling the Grid

    Internally, FLUENT stores the computational grid in meters, the SI unitof length. When grid information is read into the solver, it is assumedthat the grid was generated in units of meters. If your grid was createdusing a dierent unit of length (inches, feet, centimeters, etc.), you mustscale the grid to meters. To do this, you can select from a list of com-mon units to convert the grid or you can supply your own custom scalefactors. Each node coordinate will be multiplied by the correspondingscale factor.

    Scaling can also be used to change the physical size of the grid. Forinstance, you could stretch the grid in the x direction by assigning ascale factor of 2 in the x direction and 1 in the y and z directions.This would double the extent of the grid in the x direction. However,you should use anisotropic scaling with caution, since it will change theaspect ratios of the cells in your grid.

    If you plan to scale the grid in any way, you should do so before you!initialize the flow or begin calculations. Any data that exist when youscale the grid will be invalid.

    You will use the Scale Grid panel (Figure 5.7.1) to scale the grid from astandard unit of measurement or to apply custom scaling factors.

    Grid !Scale...

    Using the Scale Grid Panel

    The procedure for scaling the grid is as follows:

    1. Indicate the units in which you created the grid by choosing the ap-propriate abbreviation for centimeters, millimeters, inches, or feetin the Grid Was Created In drop-down list. The Scale Factors willautomatically be set to the correct values (e.g., 0.0254 meters/inchor 0.3048 meters/foot). If you created your grid using units otherthan those in the list, you can enter the Scale Factors (e.g., thenumber of meters per yard) manually.

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  • 5.7 Modifying the Grid

    Figure 5.7.1: The Scale Grid Panel

    2. Click on the Scale button. The Domain Extents will be updatedto show the correct range in meters. If you prefer to use youroriginal unit of length during the FLUENT session, you can followthe procedure described below to change the unit.

    Changing the Unit of Length

    As mentioned above in step 2, when you scale the grid you do not changethe units; you just convert the original dimensions of your grid pointsfrom your original units to meters by multiplying each node coordinateby the specied Scale Factors. If you want to work in your original units,instead of in meters, you can click on the Change Length Units button.This is a shortcut for changing the length unit in the Set Units panel(see Section 4.4). When you click on the Change Length Units button,the Domain Extents will be updated to show the range in your originalunits. This unit will be used for all future inputs of length quantities.

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  • Reading and Manipulating Grids

    Unscaling the Grid

    If you use the wrong scale factor, accidentally click the Scale buttontwice, or wish to undo the scaling for any other reason, you can clickon the UnScale button. \Unscaling" simply divides each of the nodecoordinates by the specied Scale Factors. (Selecting m in the Grid WasCreated In list and clicking on Scale will not unscale the grid.)

    Changing the Physical Size of the Grid

    You can also use the Scale Grid panel to change the physical size of thegrid. For example, if your grid is 5 feet by 8 feet, and you want to modelthe same geometry with dimensions twice as big (10 16), you can enter2 for the X and Y Scale Factors and click on Scale. The Domain Extentswill be updated to show the new range.

    5.7.2 Translating the Grid

    You can \move" the grid by applying prescribed osets to the Cartesiancoordinates of all the nodes in the grid. This would be necessary for arotating problem if the grid were set up with the axis of rotation notpassing through the origin, or for an axisymmetric problem if the gridwere set up with the axis of rotation not coinciding with the x axis. Itis also useful if, for example, you want to move the origin to a particularpoint on an object (such as the leading edge of a flat plate) to make anXY plot have the desired distances on the x axis.

    You can translate grid points in FLUENT using the Translate Grid panel(Figure 5.7.2).

    Grid !Translate...

    Using the Translate Grid Panel

    The procedure for translating the grid is as follows:

    1. Enter the desired translations in the x, y, and (for 3D) z directions(i.e., the desired delta in the axes origin) in the X, Y, and Z elds

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    under Translation Osets. You can specify positive or negative realnumbers in the current unit of length.

    2. Click on the Translate button. The Domain Extents will be updatedto display the new extents of the translated grid. (Note that theDomain Extents are purely informational; you cannot edit themmanually.)

    Figure 5.7.2: The Translate Grid Panel

    5.7.3 Merging Zones

    To simplify the solution process, you may want to merge zones. Mergingzones involves combining multiple zones of similar type into a single zone.Setting boundary conditions and postprocessing may be easier after youhave merged similar zones.

    Zone merging is performed in the Merge Zones panel (Figure 5.7.3).

    Grid !Merge...

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    Figure 5.7.3: The Merge Zones Panel

    When to Merge Zones

    FLUENT allows you to merge zones of similar type into a single zone.This is not necessary unless the number of zones becomes prohibitive toecient setup or postprocessing of the numerical analysis. For example,setting the same boundary condition parameters for a large number ofzones can be time-consuming and may introduce inconsistencies. In ad-dition, the postprocessing of the data often involves surfaces generatedusing the zones. A large number of zones often translates into a largenumber of surfaces that must be selected for the various display options,such as color contouring. Fortunately, surfaces can also be merged (seeSection 24.11), minimizing the negative impact of a large number ofzones on postprocessing eciency.

    Although merging zones can be helpful, there may be cases where youwill want to retain a larger number of zones. Since the merging processis not fully reversible, a larger number of zones provides more flexibilityin imposing boundary conditions. Although a large number of zones canmake selection of surfaces for display tedious, it can also provide morechoices for rendering the grid and the flow-eld solution. For instance, itcan be dicult to render an internal flow-eld solution. If the outer do-main is composed of several zones, the grids of subsets of these zones can

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    be plotted along with the solution to provide the relationship betweenthe geometry and solution eld.

    Using the Merge Zones Panel

    The procedure for merging multiple zones of the same type into a singlezone is as follows:

    1. Select the zone type in the Multiple Types list. This list containsall the zone types for which there are multiple zones. When youchoose a type from this list, the corresponding zones will appearin the Zones of Type list.

    2. Select two or more zones in the Zones of Type list.

    3. Click on the Merge button to merge the selected zones.

    Remember to save a new case le (and a data le, if data exist).!

    5.7.4 Separating Zones

    There are several methods available in FLUENT that allow you to sepa-rate a single face or cell zone into multiple zones of the same type. If yourgrid contains a zone that you want to break up into smaller portions,you can make use of these features. For example, if you created a singlewall zone when generating the grid for a duct, but you want to specifydierent temperatures on specic portions of the wall, you will need tobreak that wall zone into two or more wall zones. If you plan to solve aproblem using the sliding mesh model or multiple reference frames, butyou forgot to create dierent fluid zones for the regions moving at dif-ferent speeds, you will need to separate the fluid zone into two or morefluid zones.

    After performing any of these separations, you should save a new case!le. If data exist, they are automatically assigned to the proper zoneswhen separation occurs, so you should also write a new data le.

    There are four ways to separate face zones and two ways to separatecell zones. The face separation methods will be described rst, followed

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    by the cell separation tools. Slitting (decoupling) of periodic zones isdiscussed in Section 5.7.6.

    Note that all of the separation methods allow you to report the result ofthe separation before you commit to performing it.

    Separating Face Zones

    Methods for Separating Face Zones

    For geometries with sharp corners, it is often easy to separate face zonesbased on signicant angle. Faces with normal vectors that dier by anangle greater than or equal to the specied signicant angle will be placedin dierent zones. For example, if your grid consists of a cube, and all 6sides of the cube are in a single wall zone, you would specify a signicantangle of 89. Since the normal vector for each cube side diers by 90

    from the normals of its adjacent sides, each of the 6 sides will be placedin a dierent wall zone.

    If you have a small face zone and would like to put each face in the zoneinto its own zone, you can do so by separating the faces based on face.

    You can also separate face zones based on the marks stored in adap-tion registers. For example, you can mark cells for adaption based ontheir location in the domain (region adaption), their boundary close-ness (boundary adaption), isovalues of some variable, or any of the otheradaption methods discussed in Chapter 23. When you specify whichregister is to be used for the separation of the face zone, all faces of cellsthat are marked will be placed into a new face zone. (Use the ManageAdaption Registers panel to determine the ID of the register you wish touse.)

    Finally, you can separate face zones based on contiguous regions. Forexample, when you use coupled wall boundary conditions you need thefaces on the zone to have a consistent orientation. Consistent orienta-tion can only be guaranteed on contiguous regions, so you may need toseparate face zones to allow proper boundary condition specication.

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    Inputs for Separating Face Zones

    To break up a face zone based on angle, face, adaption mark, or region,use the Separate Face Zones panel (Figure 5.7.4).

    Grid ! Separate !Faces...

    Figure 5.7.4: The Separate Face Zones Panel

    If you are planning to separate face zones, you should do so before!performing any adaptions using the (default) hanging node adaptionmethod. Face zones that contain hanging nodes cannot be separated.

    The steps for separating faces are as follows:

    1. Select the separation method (Angle, Face, Mark, or Region) underOptions.

    2. Specify the face zone to be separated in the Zones list.

    3. If you are separating by face or region, skip to the next step. Oth-erwise, do one of the following:

    If you are separating faces by angle, specify the signicantangle in the Angle eld.

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    If you are separating faces by mark, select the adaption reg-ister to be used in the Registers list.

    4. (optional) To check what the result of the separation will be beforeyou actually separate the face zone, click on the Report button. Thereport will look like this:

    Zone not separated.45 faces in contiguous region 030 faces in contiguous region 111 faces in contiguous region 214 faces in contiguous region 3Separates zone 4 into 4 zone(s).

    5. To separate the face zone, click on the Separate button. FLUENTwill print the following information:

    45 faces in contiguous region 030 faces in contiguous region 111 faces in contiguous region 214 faces in contiguous region 3Separates zone 4 into 4 zone(s).Updating zone information ...created zone wall-4:001created zone wall-4:002created zone wall-4:010

    done.

    When you separate the face zone by adaption mark, you may sometimes!nd that a face of a corner cell will be placed in the wrong face zone. Youcan usually correct this problem by performing an additional separation,based on angle, to move the oending face to a new zone. You can thenmerge this new zone with the zone in which you want the face to beplaced, as described in Section 5.7.3.

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    Separating Cell Zones

    Methods for Separating Cell Zones

    If you have two or more enclosed cell regions sharing internal boundaries(as shown in Figure 5.7.5), but all of the cells are contained in a single cellzone, you can separate the cells into distinct zones using the separation-by-region method. Note that if the shared internal boundary is of typeinterior, you must change it to another double-sided face zone type (fan,radiator, etc.) prior to performing the separation.

    zone 1 zone 2

    Figure 5.7.5: Cell Zone Separation Based on Region

    You can also separate cell zones based on the marks stored in adaptionregisters. You can mark cells for adaption using any of the adaptionmethods discussed in Chapter 23 (e.g., you can mark cells with a certainisovalue range or cells inside or outside a specied region). When youspecify which register is to be used for the separation of the cell zone,cells that are marked will be placed into a new cell zone. (Use the ManageAdaption Registers panel to determine the ID of the register you wish touse.)

    Inputs for Separating Cell Zones

    To break up a cell zone based on region or adaption mark, use the Sep-arate Cell Zones panel (Figure 5.7.6).

    Grid ! Separate !Cells...If you are planning to separate cell zones, you should do so before!

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    Figure 5.7.6: The Separate Cell Zones Panel

    performing any adaptions using the (default) hanging node adaptionmethod. Cell zones that contain hanging nodes cannot be separated.

    The steps for separating cells are as follows:

    1. Select the separation method (Mark or Region) under Options.

    2. Specify the cell zone to be separated in the Zones list.

    3. If you are separating cells by mark, select the adaption register tobe used in the Registers list.

    4. (optional) To check what the result of the separation will be beforeyou actually separate the cell zone, click on the Report button. Thereport will look like this:

    Zone not separated.Separates zone 14 into two zones, with 1275 and 32 cells.

    5. To separate the cell zone, click on the Separate button. FLUENTwill print the following information:

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    Separates zone 14 into two zones, with 1275 and 32 cells.No faces marked on thread, 2No faces marked on thread, 3No faces marked on thread, 1No faces marked on thread, 5No faces marked on thread, 7No faces marked on thread, 8No faces marked on thread, 9No faces marked on thread, 61Separates zone 62 into two zones, with 1763 and 58 faces.All faces marked on thread, 4No faces marked on thread, 66Moved 20 faces from face zone 4 to zone 6Updating zone information ...Moved 32 cells from cell zone 14 to zone 10created zone interior-4created zone interior-6created zone fluid-14:010

    done.

    As shown in the example above, separation of a cell zone will often resultin the separation of face zones as well. When you separate by mark, facesof cells that are moved to a new zone will be placed in a new face zone.When you separate by region, faces of cells that are moved to a new zonewill not necessarily be placed in a new face zone.

    If you nd that any faces are placed incorrectly, see the comment above,at the end of the inputs for face zone separation.

    5.7.5 Creating Periodic Zones

    FLUENT allows you to set up periodic boundaries using either conformalor non-conformal periodic zones. You can assign periodicity to your gridby coupling a pair of face zones. If the two zones have identical node andface distributions, you can create a conformal periodic zone. If the twozones are not identical at the boundaries within a specied tolerance,

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    then you can create a non-conformal periodic zone. (See Section 5.4 formore information about non-conformal grids.)

    Remember to save a new case le (and a data le, if data exist) after!creating or slitting a periodic boundary.

    Creating Conformal Periodic Zones

    To create conformal periodic boundaries, you will use the make-periodictext command.

    grid ! modify-zones !make-periodicYou will need to specify the two face zones that will comprise the periodicpair (you can enter their full names or just their IDs), and indicatewhether they are rotationally or translationally periodic. The order inwhich you specify the periodic zone and its matching shadow zone is notsignicant.

    /grid/modify-zones> mp

    Periodic zone [()] 1

    Shadow zone [()] 4Rotational periodic? (if no, translational) [yes] nCreate periodic zones? [yes] yes

    computed translation deltas: -2.000000 -2.000000all 10 faces matched for zones 1 and 4.

    zone 4 deletedCreated periodic zones.

    When you create a conformal periodic boundary, the solver will check tosee if the faces on the selected zones \match" (i.e., whether or not thenodes on corresponding faces are coincident). The matching tolerancefor a face is a fraction of the minimum edge length of the face. If theperiodic boundary creation fails, you can change the matching toleranceusing the matching-tolerance command, but it should not exceed 0.5or you may match up the periodic zones incorrectly and corrupt the grid.

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    grid ! modify-zones !matching-tolerance

    Creating Non-Conformal Periodic Zones

    To create non-conformal periodic boundaries, you need to change thenon-conformal periodic zones to interface zones. You will then need to setup the origin as well as the axes of the adjacent cell zone. For example, ifinterface-15 and interface-2 are the two non-conformal periodic zones, thenon-conformal periodic boundaries are set up using the make-periodiccommand in the define/grid-interfaces text menu.

    define ! grid-interfaces !make-periodicFor example:

    /define/grid-interfaces> make-periodic

    Periodic zone [()] interface-15

    Shadow zone [()] interface-2Rotational periodic? (if no, translational) [yes] yes

    Rotation angle (deg) [0] 40.0Create periodic zone? [yes] yes

    grid-interface name [] fan-periodic

    5.7.6 Slitting Periodic Zones

    If you wish to decouple the zones in a periodic pair, you can use theslit-periodic command.

    grid ! modify-zones !slit-periodicYou will specify the periodic zones name or ID, and the solver willdecouple the two zones in the pair (the periodic zone and its shadow)and change them to two symmetry zones:

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    /grid/modify-zones> sp

    periodic zone [()] periodic-1

    Separated periodic zone.

    5.7.7 Fusing Face Zones

    The face fusing utility is a convenient feature that can be used to fuseboundaries (and merge duplicate nodes and faces) created by assemblingmultiple mesh regions. When the domain is divided into subdomains andthe grid is generated separately for each subdomain, you will combine thesubdomains into a single le before reading the grid into the solver. (SeeSection 5.3.10 for details.) This situation could arise if you generate eachblock of a multiblock grid separately and save it to a separate grid le.Another possible scenario is that you decided, during grid generation,to save the mesh for each part of a complicated geometry as a separatepart le. (Note that the grid node locations need not be identical at theboundaries where two subdomains meet; see Section 5.4 for details.)

    The Fuse Face Zones panel (Figure 5.7.7) allows you to merge the dupli-cate nodes and delete these articial internal boundaries.

    Grid !Fuse...The boundaries on which the duplicate nodes lie are assigned zone IDnumbers (just like any other boundary) when the grid les are combined,as described in Section 5.3.10. You need to keep track of the zone IDnumbers when tmerge or TGrid reports its progress or, after the completegrid is read in, display all boundary grid zones and use the mouse-probebutton to determine the zone names (see Section 25.3 for informationabout the mouse button functions).

    Inputs for Fusing Face Zones

    The steps for fusing face zones are as follows:

    1. Select the zones to be fused in the Zones list.

    2. Click on the Fuse button to fuse the selected zones.

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    Figure 5.7.7: The Fuse Face Zones Panel

    If all of the appropriate faces do not get fused using the default Tolerance,you should increase it and attempt to fuse the zones again. (This toler-ance is the same as the matching tolerance discussed in Section 5.7.5.)The Tolerance should not exceed 0.5, or you may fuse the wrong nodes.

    Remember to save a new case le (and a data le, if data exist) after!fusing faces.

    Fusing Zones on Branch Cuts

    Meshes imported from structured mesh generators or solvers (such asFLUENT 4) can often be O-type or C-type grids with a reentrant branchcut where coincident duplicate nodes lie on a periodic boundary. SinceFLUENT uses an unstructured grid representation, there is no reason toretain this articial internal boundary. (Of course, you can preserve theseperiodic boundaries and the solution algorithm will solve the problemwith periodic boundary conditions.)

    To fuse this periodic zone with itself, you must rst slit the periodiczone, as described in Section 5.7.6. This will create two symmetry zonesthat you can fuse using the procedure above.

    Note that if you need to fuse portions of a non-periodic zone with itself,

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    you must use the text command fuse-face-zones.

    grid ! modify-zones !fuse-face-zonesThis command will prompt you for the name or ID of each zone tobe fused. (You will enter the same zone twice.) To change the nodetolerance, use the matching-tolerance command.

    5.7.8 Slitting Face Zones

    The face-zone slitting feature has two uses:

    You can slit a single boundary zone of any double-sided type (i.e.,any boundary zone that has cells on both sides of it) into twodistinct zones.

    You can slit a coupled wall zone into two distinct, uncoupled wallzones.

    When you slit a face zone, the solver will duplicate all faces and nodes,except those nodes that are located at the ends (2D) or edges (3D) ofthe zone. One set of nodes and faces will belong to one of the resultingboundary zones and the other set will belong to the other zone. Theonly ill eect of the shared nodes at each end is that you may see someinaccuracies at those points when you graphically display solution datawith a slit boundary. (Note that if you adapt the boundary after slitting,you will not be able to fuse the boundaries back together again.)

    Normally, you will not need to manually slit a face zone. Two-sided wallsare automatically slit, but remain coupled. (This coupling refers only tothe grid; it is independent of thermal coupling.) The adaption processtreats these coupled walls just like periodic boundaries; adapting on onewall causes the same adaption on the shadow. If you want to adapt onewall independent of its shadow, you should slit the coupled wall to obtaintwo distinct walls.

    You should not confuse \slitting" a face zone with \separating" a face!zone. When you slit a face zone, additional faces and nodes are createdand placed in a new zone. When you separate a face zone, a new zone

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    will be created, but no new faces or nodes are created; the existing facesand nodes are simply redistributed among the zones.

    Inputs for Slitting Face Zones

    If you wish to slit a face zone, you can use the slit-face-zone com-mand.

    grid ! modify-zones !slit-face-zoneYou will specify the face zones name or ID, and the solver will replacethe zone with two zones:

    /grid/modify-zones> slfz

    face zone id/name [] wall-4

    zone 4 deletedface zone 4 createdface zone 10 created

    Remember to save a new case le (and a data le, if data exist) after!slitting faces.

    5.7.9 Extruding Face Zones

    The ability to extrude a boundary face zone allows you to extend thesolution domain without having to exit the solver. A typical applica-tion of the extrusion capability is to extend the solution domain whenrecirculating flow is impinging on a flow outlet. The current extrusioncapability creates prismatic or hexahedral layers based on the shape ofthe face and normal vectors computed by averaging the face normals tothe face zones nodes. You can dene the extrusion process by specifyinga list of displacements (in SI units) or by specifying a total distance (inSI units) and parametric coordinates.

    Specifying Extrusion by Displacement Distances

    You can specify the extrusion by entering a list of displacement distances(in SI units) using the extrude-face-zone-delta command.

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    grid ! modify-zones !extrude-face-zone-deltaYou will be prompted for the boundary face zone ID or name and a listof displacement distances.

    Specifying Extrusion by Parametric Coordinates

    You can specify the extrusion by specifying a distance (in SI units) andparametric coordinates using the extrude-face-zone-para command

    grid ! modify-zones !extrude-face-zone-paraYou will be prompted for the boundary face zone ID or name, a totaldistance, and a list of parametric coordinates. The list of parametriccoordinates should begin with 0.0 and end with 1.0. For example, thefollowing list of parametric coordinates would create two equally spacedextrusion layers: 0.0, 0.5, 1.0.

    5.7.10 Reordering the Domain and Zones

    Reordering the domain can improve the computational performance ofthe solver by rearranging the nodes, faces, and cells in memory. TheGrid/Reorder submenu contains commands for reordering the domain andzones, and also for printing the bandwidth of the present grid partitions.The domain can be reordered to increase memory access eciency, andthe zones can be reordered for user-interface convenience. The band-width provides insight into the distribution of the cells in the zones andin memory.

    To reorder the domain, select the Domain menu item.

    Grid ! Reorder !DomainTo reorder the zones, select the Zones menu item.

    Grid ! Reorder !ZonesFinally, you can print the bandwidth of the present grid partitions byselecting the Print Bandwidth menu item. This command prints the semi-bandwidth and maximum memory distance for each grid partition.

    Grid ! Reorder !Print Bandwidth

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    Remember to save a new case le (and a data le, if data exist) after!reordering.

    About Reordering

    The Reverse Cuthill-McKee algorithm [44] is used in the reordering pro-cess to construct a \level tree" initiated from a \seed cell" in the domain.First a cell (called the seed cell) is selected using the algorithm of Gibbs,Poole, and Stockmeyer [74]. Each cell is then assigned to a level basedon its distance from the seed cell. These level assignments form the leveltree. In general, the faces and cells are reordered so that neighboringcells are near each other in the zone and in memory. Since most of thecomputational loops are over faces, you would like the two cells in mem-ory cache at the same time to reduce cache and/or disk swapping|i.e.,you want the cells near each other in memory to reduce the cost of mem-ory access. The present scheme reorders the faces and cells in the zone,and the nodes, faces, and cells in memory.

    You may also choose to reorder the zones. The zones are reorderedby rst sorting on zone type and then on zone ID. Zone reordering isperformed simply for user-interface convenience.

    A typical output produced using the domain reordering is shown below:

    >> Reordering domain using Reverse Cuthill-McKee method:zones, cells, faces, done.

    Bandwidth reduction = 809/21 = 38.52Done.

    If you print the bandwidth, you will see a report similar to the following:

    Maximum cell distance = 21

    The bandwidth is the maximum dierence between neighboring cells inthe zone|i.e., if you numbered each cell in the zone list sequentially andcompared the dierences between these indices.

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