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Page 1: Guido Morgenthal · Guido Morgenthal guido@morgenthal.org Vogelsangstr. 22, 70176 Stuttgart, Germany ¬‚ow User Guide v0.99 (last updated 13th April 2005)

Guido [email protected]

Vogelsangstr. 22, 70176 Stuttgart, Germany

http://www.morgenthal.org/vxflow

User Guide

v0.99(last updated 13th April 2005)

Page 2: Guido Morgenthal · Guido Morgenthal guido@morgenthal.org Vogelsangstr. 22, 70176 Stuttgart, Germany ¬‚ow User Guide v0.99 (last updated 13th April 2005)
Page 3: Guido Morgenthal · Guido Morgenthal guido@morgenthal.org Vogelsangstr. 22, 70176 Stuttgart, Germany ¬‚ow User Guide v0.99 (last updated 13th April 2005)

Contents

List of Symbols and Abbreviations iii

List of Figures iii

1 Introduction 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Running VXFlow 3

2.1 Installing the code . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Windows system . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Starting the code . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Running the code . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.4 Restarting the code . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 The VXFlow input file 7

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Sample input files . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3.1 M4 Neath Viaduct with full wind shielding . . . . . . . . . 19

4 Getting started 25

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Modelling issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.1 Solid body modelling . . . . . . . . . . . . . . . . . . . . . 25

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4.2.2 Grid selection . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2.3 Use of the grid . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.4 Flow parameters . . . . . . . . . . . . . . . . . . . . . . . 28

4.2.5 Further modelling parameters . . . . . . . . . . . . . . . . 28

4.2.6 Controlling resolution . . . . . . . . . . . . . . . . . . . . . 29

5 Postprocessing the VXFlow output 31

5.1 VXPost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2 Your own postprocessing . . . . . . . . . . . . . . . . . . . . . . . 31

Bibliography 33

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List of Figures

5.1 Flow field visualisation for the M4 Neath Viaduct with an addedsolid wind screen: instantaneous velocity field. . . . . . . . . . . . 32

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Page 6: Guido Morgenthal · Guido Morgenthal guido@morgenthal.org Vogelsangstr. 22, 70176 Stuttgart, Germany ¬‚ow User Guide v0.99 (last updated 13th April 2005)
Page 7: Guido Morgenthal · Guido Morgenthal guido@morgenthal.org Vogelsangstr. 22, 70176 Stuttgart, Germany ¬‚ow User Guide v0.99 (last updated 13th April 2005)

Chapter 1

Introduction

1.1 Introduction

VXflow is a flow solver based on the Vortex Particle Method. The main featuresof the code are as follows:

• Utilisation of the Boundary Element Method for the enforcement of theno-penetration boundary condition on solid surfaces.

• Surface circulation discretisation by means of elements of linearly varyingvorticity.

• Smooth Gaussian kernel for mutual vortex interactions.

• A fast P3M algorithm for the computation of the velocity field by Morgen-thal & Walther [9] based on the utilisation of Fast Fourier Transforms forthe solution of the underlying Poisson equation and a local Particle-Particlecorrection algorithm.

• A partial particle remeshing strategy developed by Morgenthal & Walther[9].

• The random walk method for diffusion modelling.

It is crucial for the user to be familiar with the method. This document does notattempt to cover the theory and implementation of the method and reference istherefore made to literature by Leonard [3], Spalart [10], Lewis [4] and Cottet &Koumoutsakos [2]. Furthermore, the reader is referred to the following publica-tions by the author: [5], [6], [8], [9] and [7], some of which are also available onlineat http://www.morgenthal.org/publications.html. The author’s PhD thesis [7]best describes the current implementation of the numerical code and features anumber of applications.

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Page 8: Guido Morgenthal · Guido Morgenthal guido@morgenthal.org Vogelsangstr. 22, 70176 Stuttgart, Germany ¬‚ow User Guide v0.99 (last updated 13th April 2005)
Page 9: Guido Morgenthal · Guido Morgenthal guido@morgenthal.org Vogelsangstr. 22, 70176 Stuttgart, Germany ¬‚ow User Guide v0.99 (last updated 13th April 2005)

Chapter 2

Running VXFlow

2.1 Installing the code

2.1.1 Windows system

Besides the installation of

• VXFlow

we recommend the installation of the following programs to do the postprocessingof VXFlow results:

• VXPost,

• Matlab,

• ImageMagick,

• Ghostview,

• pjBMP2AVI.

The executable vxflow.exe can simply be copied to a separate directory, sayc:\vxflow. In order to be able to run the code from any directory, the systempath variable needs to be set. To do this start the registry editor regedit (in theWindows system directory) and add the directory of the vxflow.exe to the PATHvariables in

HKEY_CURRENT_USER\Environment

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CHAPTER 2. RUNNING VXFLOW

and

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\

Session Manager\Environment.

The default parameter file vxfdefault9 must be placed in the directory c:\vxflow.Make sure this directory is write-enabled since the code also writes the FFT wis-dom files there.

The Matlab software must be installed in order to use the VXPost set of postpro-cessing tools. VXPost can be started in Matlab by running vxp.m. By standardVXPost created Encapsulated Postscript picture files which are a lossless vectorgraphics format. However, these are difficult to handle by Word and by Video soft-ware. Therefore, the program allows conversion into BMP format which makesuse of the ImageMagick software. When this is installed, it automatically suppliesa convert tool that is called from VXPost. For EPS to BMP conversion this againrequires Ghostview to be installed which can also be used to display and printthe EPS files directly. The BMP files can be bundled together and converted intoan AVI movie using the very simple software pjBMP2AVI.

2.2 Starting the code

The code can be started once an input file according to the format described inchapter 3 has been generated. This input file is given a master filename and mustcarry the extension ‘.in13’. If the program executable is placed in the projectdirectory, start the code by invoking

vxflow masterfilename

from the command prompt (the ‘.in13’ is omitted). For example, create a ‘test.in13’and do vxflow test. Under Linux a ./vxflow may be necessary.

Under Windows the use of a program like ‘Programmer’s File editor’ is recom-mended which can start and handle programs running in a DOS window.

2.3 Running the code

During the run a series of auxiliary output files will be created, according tothe options set in the input file. All files will carry the master filename and anextension determining the content of the file. Here is an overview:

• .hdr — header file containing some problem specific properties,

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2.4. RESTARTING THE CODE

• .o3 — main output carrying the most essential information like body forces,particle numbers and calculation times,

• .rst4 — restart files (these are numbered with the respective time stepnumber),

• .sp1 — sample vortex output,

• .gr2 — ’old’ vortex output (containing the vortex path including the randomwalk),

• .vx2 — ’new’ vortex output (containing vortex position and velocity),

• .pr1 — pressure output,

• .fv2 — ’isogrid’ velocity dump (the ’isogrid’ is a special grid defined in theinput file, on the nodes of which flow properties are evaluated and saved forlater contour- and iso-surface plotting),

• .fs2 — ’isogrid’ streamfunction dump,

• .sk2 — ’isogrid’ streakline dump,

Under Linux the code will open a graphics output window which enables theuser to check the behaviour of the solution. This is not currently available underWindows.

2.4 Restarting the code

If restart information files have been written (cf. the respective option in theinput file), the code can subsequently be restarted from any of the time stepsthat a ‘.rst4’ restart file exists for. In this case start the code doingvxflow masterfilename $N$, where N is the time step number for the restartrun. E.g. the command vxflow test 500 will cause the code to read in files‘test.in13’ and ‘test 500.rst4’.

During a restart run the auxiliary files created before are opened in ‘append mode’and new information are added at the end, thus conserving the previous output.However, if the restart option is not used, old auxiliary files are overwritten!

Under Linux the code can be expected to yield exactly the same solution as theoriginal run would have given. Under Windows this is not the case because therandom number generator used for the random walk algorithm is re-initialised ata restart. Under Linux the seed of the random number algorithm can be savedand used in the restart run.

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Chapter 3

The VXFlow input file

3.1 Introduction

The following table is a description of the format to be used for the input fileto VXFlow. Note, that due to the modular structure of slices and sections,separating ‘!!’ commands are needed as described below.

Comments can be added by starting with a single ‘!’.

No spaces are allowed within the command line (e.g. don’t do NSTEPS = 1000).

The setting of the relevant parameters is organised as follows. There is a filevxfdefault*, which carries a set of default parameters. This file is read in first(and is looked for in the working directory) and subsequently all parametersprovided in the actual ‘.in13’ input file are replaced by the given values. Thismeans, that only values different from the default ones need to be supplied,thus potentially reducing the size of the input file considerably. Furthermore,subsequent changes in the program structure leading to new input parametersonly require an adjustment of the input file if these values are actually needed,thus leading to a higher compatibility with old input files.

General remarks:

• Throughout the input file, a ‘flag’ means either 1=yes or 0=no.

• Parameter name suffices used throughout:

– (FL) flag

– (SLICE) slice to do the operation for

– (FROM) from time step

– (TO) to/until timestep (if TO is set to 0, the operation is performedthroughout the simulation (makes FROM obsolete, however STEP is

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CHAPTER 3. THE VXFLOW INPUT FILE

still considered))

– (STEP) stepping: do operation every STEPth step.

3.2 Input parameters

Tables 3.1 to 3.10 provide an overview of the parameters to be used in the VXFlowinput file. It is recommended to also consult the sample input files given in section3.3 and/or the ones provided with the code.

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3.2. INPUT PARAMETERS

Input parame-ter (default)

Description

NSLICES (none, haveto supply)

This is expected at the beginning of every input file: thenumber of DVM-slices along the bridge.

• For structural model 1: in principle this is only to beused with 1 slice, i.e. NSLICES=1 and performs theclassical 2-D section analysis.

• For structural model 2 (a pseudo-3D model, cf. [5]):N=NSLICES. If the data in the slice part of the in-put file are provided for each slice, NSLICES is giventhe respective positive value. If -NSLICES is input, theprogram expects only data for 1 slice and copies theseonto all the other slices. This is the common way asusually all slices along the beam are the same.

U0X (1.0) Onset flow velocity in x-directionU0Y (0.0) Onset flow velocity in y-directionDENSTY (1.2) Density of the fluidVISCTY (0.000015) Kinematic viscosity of the fluidDIFFU (1) Flag, diffusion simulation by means of random walks is only

performed if DIFFU=1 (i.e. otherwise viscosity value is ne-glected)

NONDIM (1) Flag determining whether non-dimensionalised input param-eters are used

DELTAT (1) Length of timestepNSTEPS (10000) number of timesteps to be performed; if NSTEPS=0 then

calculation is performed until user interruptionFASTMODE (2) The fast algorithm to be used for the velocity computation:

• 1 — Cell-to-Cell (CTC) scheme (Leonard); (Within re-gion of NR the mutual interactions between vortices ofthe two cells are performed rather than the faster cell-to-cell interaction. The distance between two cells iscalculated as the distance between their centres. For adiscussion on this, cf. [10], p. 61 and [4], p. 470.),

• 2 — P3M scheme (Morgenthal & Walther [9]),

• 3 — compare mode (runs both P3M and CTC and com-putes the L2-error-norm of the particle velocity differ-ence, the P3M velocity is then used for the actual con-vection),

Table 3.1: Input parameters for the VXFlow code (I)

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CHAPTER 3. THE VXFLOW INPUT FILE

Input parame-ter (default)

Description

NPANELFACT (1.0) Factor applied to the number of panels given in the sectiongeometry part. Use this to scale the panel numbers to achievehigher resolution without adjusting the individual polygonpanel numbers.

TINTEGR (1) The scheme for time integration: (1) simple Euler; (2) Runge-Kutta-2

SURF (2) The model for the discretisation of the surface vorticity: (1)point vortices; (2) vortex sheets of linearly varying strength(recommended)

INSIDE (2) Determines handling of vortices that travel inside the hull:(0) check switched off; (1) replace back to the surface of thehull; (2) delete; (3) absorb by surface

CROSS (0) Determines handling of vortices that cross the whole section:(0) check switched off; (1) replace back to the surface of thehull; (2) delete; (3) absorb by surface

COREMODEL (2) Determines model for vorticity distribution around the vortexpoint; (1) Rankine ( [4], p. 383); (2) Gauss ( [10], p.10)(recommended); (3) Spalart ( [10], p. 51)

DOMAIN (2) Determines the far-field boundary conditions: (1) periodic(use only for the P3M scheme); (2) free-field

NR (3) The neighbourhood size Nr of the fast algorithm. Either ap-plied directly for the P3M (within this cell distance — e.g. 3corresponding to the 3 next cells — direct particle-particle in-teraction is performed, outside the particle-mesh contributionis used) or the cut-off radius of the CTC scheme is computedfrom this value.

P3MNRRELAX (0) Relaxation value of the NR. Provide 0 to switch off this optionor get in touch with the author.

P3MINTP (2) The order of the interpolation particle −→ mesh and mesh−→ particle (only relevant in P3M mode): (1) M2 (linear);(2) M′

4 (3rd order)P3MFD (2) Order of Finite Differencing when determining the velocity

field from the streamfunction solution (only relevant in P3Mmode): (1) 2nd order; (2) 4th order

Table 3.2: Input parameters for the VXFlow code (II)

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3.2. INPUT PARAMETERS

Input parame-ter (default)

Description

PVARY (1) This decides whether a variable number of vortices per panel isintroduced on the surface. There will be at maximum NSUBPvortices at a panel. If PVARY =1 the number of vortices iscomputed from the surface vorticity whereas with PVARY=0then NSUBP vortices are introduced from each panel.

NSUBP (4) Cf. PVARYP3MSH (2) This determines how the bound surface vorticity sheets (i.e.

only relevant for SURF=2) is treated in the P3M scheme (oth-erwise irrelevant): (1) inside the P3M neighbourhood (cut-off(15 panel lengths) must be within P3M neighbourhood); (2)outside the P3M (added afterwards - no influence on cut-off);(3) sheet equations replaced by SHSUBST point vortices

SHSUBST (1) Cf. P3MSH (only relevant for P3MSH=3)RMSHST (-1) Remeshing of the particles every RMSHSTth time step (no

remeshing for RMSHST=0). Remeshing is done using the M′4

kernel.RMSHREF (1) Factor of refinement of the particle mesh wrt. the Poisson

mesh (e.g. RMSHREF=2 means 2x2 particles per Poissoncell)

RMSHRESP (1) Respect the body surface when remeshing, i.e. partial remesh-ing?: (0) No, remesh everywhere and whatever is generatedinside the body is deleted; (1) Yes, only remesh particles whichdon’t assign inside the bodyGraphics output window:

WINMINX (-1.0)WINMAXX (1.0)WINMINY (-1.0)WINMAXY (1.0)

Coordinate space to be covered by the particle output window— usually of ratio 2:1

WINSIZEX (800)WINSIZEY (600)

Size of the output window in pixels — recommended to be ofratio 4:3, in which case the particle output window will be ofratio 2:1

Table 3.3: Input parameters for the VXFlow code (III)

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CHAPTER 3. THE VXFLOW INPUT FILE

Input parame-ter (default)

Description

Graphics output flags:OUTFLSL (1) number of slice for which main graphics output is doneOUTFLGRID1 (0) main grid (fast algorithm grid)OUTFLGRID2 (0) subgrid (currently only used for streakline plotting)OUTFLSEC (1) sectionOUTFLHULL (0) hullOUTFLVORT (1) vortices: (0) no vortex plotting; (1) plot path of vortices; (2)

plot as point at current vortex locationOUTFLPRESS (0) pressure distributionOUTFLGRAPH1 (1) graph 1 (displacement time history)OUTFLGRAPH2 (1) graph 2 (force coefficient time history), c.f. STRCMODELOUTFLGRAPH3 (1) graph 3 (displaced shape of beam (mainly for structural model

2))OUTSTEP (10) Stepping for updating main window (plotting is only per-

formed every OUTSTEPth time step)OUTGRAPHST(500)

Number of timesteps shown by the graphs at the bottom(the graphs scroll through the window showing the last OUT-GRAPHST steps)

NORMPR (1.0) Value the plotted pressure coefficients are to be normalised to(if the pressure coefficient is equal to NORMPR then the lineplotted has the length of the y-dimension of a grid1 cell)

NORMDSPL (1.0) Normalisation value [m] of displacement plot (graph 1) (Forall graphs, a normalised value of unity corresponds to half thedistance between two horizontal axes)

NORMROT (1.0) Normalisation value [rad] of rotation plot (graph 1)FACTDSPL (1.0) Normalisation value [m] of displaced shape plot (graph 3)NORMDRAG (1.0) Normalisation value [-] of drag coefficient plot (graph 2)NORMLIFT (1.0) Normalisation value [-] of lift coefficient plot (graph 2)NORMMOMENT(1.0)

Normalisation value [-] of moment coefficient plot (graph 2)

NORMTRACK (1.0) Normalisation value [-] of vortex tracker plot (graph 2) — notcurrently used

Table 3.4: Input parameters for the VXFlow code (IV)

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3.2. INPUT PARAMETERS

Input parame-ter (default)

Description

STRKFL (0)STRKFROM (1)STRKTO (0)STRKSTEP (10)

Plotting of streaklines on screen

STRKFACT (0.5) Factor to scale the streakline length (STRKFACT=1 givesstreaklines of the length of a grid spacing, if the velocity isequal to the free flow velocity)

REFGRID (1) determines the spacing of the subgrid (grid2); the subgrid isderived from grid1 by inserting REFGRID*REFGRID cellsinto the grid1 cells

STRMFL (0)STRMFROM (1)STRMTOSTRMSTEP

Plotting of streamlines on screen

Streamline region: Region which is to be covered with stream-lines

STRMMINX (-1.0)STRMMAXX (1.0)STRMMINY (-1.0)STRMMAXY (1.0)

STRMNUM (100) Number of streamlines to be drawn, covering the area givenby STRMMINX,STRMMAXX...

Output file options: the following output files can be generated in order to creategraphics output using VXPost. The parameter names correspond to the output file’sfile extension which is completed by the file format version number. E.g. parameterSK (including SKFL, SKSLICE, SKFROM, SKTO, SKSTEP) corresponds to filemasterfilename.sk2, indicating VXFlow’s sk file format version 2.GR (0,1,0,100) Vortex path output (instantaneous path of the vortex includ-

ing the random walk)VX (0,1,0,100) Vortex velocity output (instantaneous vortex position and ve-

locity)SP (0,1,1,0,1) Sample vortex output (the path of the sample vortices)PR (0,1,1,0,1) Pressure outputRST (1,1,1,0,100) Restart fileFV (0,1,1,0,100) Absolute velocities on the isoline grid (for this, see ISOMINX

etc. below)FS (0,1,1,0,100) Streamfunction on the isoline gridFR (0,1,1,0,100) Vorticity on the isoline gridSK (0,1,1,0,100) Velocity vectors on the isoline grid (for streakline plotting)

Table 3.5: Input parameters for the VXFlow code (V)

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CHAPTER 3. THE VXFLOW INPUT FILE

Input parame-ter (default)

Description

ISOMINX (-1.0)ISOMAXX (1.0)ISODIMX (100)ISOMINY (-1.0)ISOMAXY (1.)ISODIMY (100)

The dimensions of the isogrid - on the nodes of this the FV,FS, FR and SK properties are computed and dumped to therespective file if desired.

SMPLCOLOR (5) Color code of the plotted sample vorticesSMPLMODE (3) Mode for sample vortices: (1) sample vortices deleted and re-

introduced at the dedicated positions after every time step;(2) smoke samples which get introduced at the left hand sideof the domain and then convected with the flow.

SMOKESTEP (1) Every SMOKESTEPth step smoke samples are createdSMOKENUM (100) Number of smoke particles created along the left hand side of

the domainDYNAMIC (0) Structural dynamics model: (0) static or forced vibration; (1)

fluid-structure interaction.STRCMODEL (1) Model for structural dynamics: (1): the classical 2-D section

model; (2): the multi-slice formulation based on Hermitianbeam elements, c.f. NSLICES

NMDELTA (0.5) The d parameter for the Newmark-Beta time integrationscheme for the structure (cf. Clough & Penzien [1], p. 121,where d is referred to as g)

NMBETA (0.5) The b value for Newmark-Beta time integration scheme forthe structure

DAMPRATIO (0.01) Rayleigh damping ratio ξ (of critical).RAYLA0 (1.0)RAYLA1 (1.0)

parameters a0 and a1 such that:

C = (a0M + a1K) ξ. (3.1)

These can be determined such that two modes are associatedwith the given damping:

(a0

a1

)=

2

ωm + ωn

(ωmωn

1

), (3.2)

cf. [1].TWOEILCUB(100000.0)

Stiffness 2EI/l3 of the beam (Only relevant for structuralmodel 2)

LENGTH (100.0) Length of beam elements for structural model 2

Table 3.6: Input parameters for the VXFlow code (VI)

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3.2. INPUT PARAMETERS

Input parame-ter (default)

Description

!! This ends the basic part of the input file. Followingare the individual slice parts. The data provided inthe slice part is slice-specific and unless NSLICES isgiven a negative value, NSLICES slice sections haveto be provided in the input file. In the most commoncase of a simple section analysis NSLICES=-1 andonly one slice part exists.

NUMSEC (1) Number of individual cross sections (separate bodies)GEOMROT (0.0) This rotates the section geometry provided in the input file

by the given angle [deg] around the origin of the coordinatesystem. Positive angles are clockwise.

ROTCENTREX (0.0) x-position of shear centre of section, the point about whichthe moment is computed and about which the rotation takesplace (this point will move with a vertical oscillation of thesection)

ROTCENTREY (0.0) y-position of shear centre of sectionMASS11 (1.)MASS12 (0.)MASS21 (0.)MASS22 (1.)

Mass matrix: m11, m12, m21, m22 — used as is for struc-tural model 1; for structural model 2 the individual slices areassigned masses and for the vertical and torsional D.O.F.,respectively. Note that this is the mass of the whole slice.Structural dynamics solutions for the individual sections of aslice have not yet been implemented.

STIFF11 (1.)STIFF12 (0.)STIFF21 (0.)STIFF22 (1.)

Stiffness matrix: k11, k12, k21, k22 — used as is for structuralmodel 1; not used for structural model 2. Note that this isthe stiffness for the assembly of all the sections of this slice.Structural dynamics solutions for the individual sections of aslice have not yet been implemented.

DAMP11 (0.)DAMP12 (0.)DAMP21 (0.)DAMP22 (0.)

Currently not used (evaluated from Rayleigh damping)

INITD (0.) Initial displacement [m] for FSI applicationsINITR (0.) Initial rotation [rad] for FSI applications dimensions of the

main grid (grid 1)GRIDMINX (-1.0) Minimum x-coordinateGRIDMAXX (1.0) Maximum x-coordinateGRIDNX (255) Number of cells in x-direction (note, that for the use of the

P3M algorithm FFTs are used to solve the Poisson equationon this grid and these are fastest for dimensions of powersof 2. Therefore, the number of cells (being one less than thenumber of nodes) are recommended to be “powers of 2 minus1”, e.g. 31, 63, 127 etc.

GRIDMINY (-1.0) Minimum y-coordinateGRIDMAXY (1.0) Maximum y-coordinateGRIDNY (255) Number of cells in y-direction; the same as for GRIDNX ap-

plies

Table 3.7: Input parameters for the VXFlow code (VII)

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CHAPTER 3. THE VXFLOW INPUT FILE

Input parame-ter (default)

Description

MERGOLD (-0.1) Old merging model: distance below which two vortices aremerged to one vortex (note: this needs to be switched to anegative value if, as recommended, the new merging algorithmshall be used)

CORER (1.2) Core radius for vorticity discretisation, cf. COREMODELSLCOLORDRAG (2) Color code for the slice drag coefficient plotting. Color codes

are: (0) black; (1) red; (2) green; (3) yellow; (4) blue; (5)purple; (6) turquoise (”Cambridge Blue”); (7) white; Notethat for all color codes the convention holds that specifying anegative color omits the plotting of this graph

SLCOLORLIFT (4) Color code for slice lift coefficientSLCOLORMOMENT(1)

Color code for slice moment coefficient

SLCOLORDSPL (3) Color code for slice vertical displacementSLCOLORROT (5) Color code for slice torsional rotationAVGPRESS (1) Number of time steps over which a moving average is per-

formed to smoothen pressures (and thus forces)Forced heave: this performs a forced heave motion on the section, if T > 0, i.e. toswitch this off, T has to be assigned a negative value. Function:

y = a sin

(2π(t − dt)

T

)+ dy (3.3)

HFORCEDT (-1.0) Period of forcing motionHFORCEDA (1.0) Amplitude [m]HFORCEDDT (0.0) Shift of sine on time axisHFORCEDDY (0.0) Shift on the displacement axisForced pitch: this performs a forced pitch motion on the section, if T > 0, i.e. toswitch this off, T has to be assigned a negative value.PFORCEDT (-1.0) Period of forcing motionPFORCEDA (1.0) Amplitude [rad]PFORCEDDT (0.0) Shift of sine on time axisPFORCEDDY (0.0) Shift on the displacement axis!! This ends the general parameters for this slice and

the data on the NUMSEC individual sections of theslice follow.

Table 3.8: Input parameters for the VXFlow code (VIII)

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3.2. INPUT PARAMETERS

Input parame-ter (default)

Description

num.cornerpoints Number of polygon points provided for this section, i.e. equalto the number of edges

release.distance Distance of the release points from the body surface (cf. [5]).Also, from these points the random walk is performed if ap-plicable — for a random walk release from the surface setrelease.distance to 0.

spacing.hull Spacing of the hull (clear distance between the body surfaceand the hull). If SURF=2 is set, this can be set to 0 (recom-mended).

away.shed Distance between the release points and the surface of thebody, measured perpendicular to the surface

spacing.hull Clear distance between the hull and the surface, measuredperpendicular to the surface

merg1 For the new merging algorithm: the distance of each vortexconsidered for merging from all sections is calculated (shortestdistance from any surface is considered) and then the mini-mum is selected as mergdist to calculate the merging limit atfollows: merg1 + merg2 ∗ mergdist + merg3 ∗ mergdist2

merg2 ”merg3 ”merg4 This is a cut-off value for the merging limitsec.color.drag Color code for drag coefficient plotting for the whole of this

section.sec.color.lift Color code for section lift coefficientsec.color.moment Color code for section moment coefficientsec.color.dspl Color code for section vertical displacementsec.color.rot Color code for section torsional rotation

Table 3.9: Input parameters for the VXFlow code (IX)

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CHAPTER 3. THE VXFLOW INPUT FILE

Input parame-ter (default)

Description

Here follow num.cornerpoints lines with the following format, providing informationon how to discretise the surface of the section, running in an anti-clockwise manneraround the section. The first point given is the leading ’edge’ (corner) and thenumber of panels given is inserted on the edge running from this point to the onein the next line. The last line contains the point on the circumference and panelinformation for the edge which closes the section. Rows look like:ID CX CY N MX MYID Edge shape identifier: (1)=linear edge; (2)=arc edgeCX X-coodinate of corner pointCY Y-coodinate of corner pointN Number of panels to be created on this edgeMX X-coordinate of the centre of the circle part of which this edge

is. MX and MY are only provided for arc edges, i.e. ID=2.The edge is constructed through the first point and aroundthe center given. The user has to ensure that this arc actuallygoes through the second point (geometrically the problem isoverdetermined).

MY Y-coordinate of centre, cf. also MXexample:

p1x, p1y

N1

p4x, p4y

p3x, p3y

p2x, p2y

N4

N3

N2

Mx3,My3

would be achieved by the following sequence:1 p1x p1y N1

1 p2x p2y N2

2 p3x p3y N3 Mx3 My3

1 p4x p4y N4

Table 3.10: Input parameters for the VXFlow code (X)

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3.3. SAMPLE INPUT FILES

3.3 Sample input files

3.3.1 M4 Neath Viaduct with full wind shielding

NSLICES=-1

U0X=40.0

VISCTY=0.000015

DIFFU=1

DELTAT=1.5

NSTEPS=4000

NPANELFACT=1.0

FASTMODE=2

TINTEGR=1

SURF=2

INSIDE=2

CROSS=0

COREMODEL=2

NR=3

P3MINTP=2

P3MFD=2

P3MNRRELAX=20

PVARY=1

NSUBP=3

P3MSH=3

SHSUBST=5

RMSHST=2

RMSHREF=1

RMSHRESP=1

RMSHRELAX=70

!WINMINX=-16.0

!WINMAXX=16.0

!WINMINY=-8.0

!WINMAXY=8.0

WINMINX=-20.0

WINMAXX=220.0

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CHAPTER 3. THE VXFLOW INPUT FILE

WINMINY=-60.0

WINMAXY=60.0

OUTSTEP=20

OUTFLGRID1=0

NORMDSPL=0.2

NORMLIFT=1.0

PRFL=1

PRSTEP=1

SKFL=1

SKSTEP=10

FVFL=1

FVSTEP=10

ISOMINX=-14.0

ISOMAXX=26.0

ISOMINY=-9.0

ISOMAXY=11.0

ISODIMX=200

ISODIMY=100

GRFL=1

GRSTEP=100

RSTFL=1

RSTSTEP=250

!!

NUMSEC=10

GEOMROT=0.0

GRIDMINX=-20.0

GRIDMAXX=220.0

GRIDNX=511

GRIDMINY=-59.883

GRIDMAXY=59.883

GRIDNY=255

CORER=1.2

SLCOLORDRAG=-2

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3.3. SAMPLE INPUT FILES

SLCOLORLIFT=4

SLCOLORMOMENT=-1

SLCOLORDSPL=2

SLCOLORROT=-5

!!

68 //num_cornerpoints****MAIN2

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 -13.2 -0.27 2

1 -13.2 -0.66 1

1 -13.08 -0.66 1

1 -13.08 -0.86 3

1 -12.39 -0.83 8

1 -12.18 -2.33 5

1 -11.21 -2.293 8

1 -11.0 -0.785 3

1 -10.44 -0.764 8

1 -10.23 -2.256 5

1 -9.26 -2.219 8

1 -9.05 -0.711 3

1 -8.49 -0.690 8

1 -8.28 -2.182 5

1 -7.31 -2.145 8

1 -7.1 -0.637 3

1 -6.54 -0.616 8

1 -6.33 -2.108 5

1 -5.36 -2.071 8

1 -5.15 -0.563 3

1 -4.59 -0.541 8

1 -4.38 -2.034 5

1 -3.41 -1.997 8

1 -3.2 -0.489 3

1 -2.64 -0.467 8

1 -2.43 -1.960 5

1 -1.46 -1.923 8

1 -1.25 -0.415 3

1 -0.69 -0.393 8

1 -0.48 -1.885 5

1 0.49 -1.848 8

1 0.7 -0.340 3

1 1.26 -0.319 8

1 1.47 -1.811 5

1 2.44 -1.774 8

1 2.65 -0.266 3

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CHAPTER 3. THE VXFLOW INPUT FILE

1 3.21 -0.245 8

1 3.42 -1.737 5

1 4.39 -1.700 8

1 4.6 -0.192 3

1 5.16 -0.171 8

1 5.37 -1.663 5

1 6.34 -1.626 8

1 6.55 -0.118 3

1 7.11 -0.097 8

1 7.32 -1.589 5

1 8.29 -1.552 8

1 8.5 -0.044 3

1 9.06 -0.023 8

1 9.27 -1.515 5

1 10.24 -1.478 8

1 10.45 0.030 3

1 11.01 0.051 8

1 11.22 -1.44 5

1 12.18 -1.40 8

1 12.39 0.11 3

1 13.08 0.14 1

1 13.08 0.34 1

1 13.2 0.34 2

1 13.2 0.73 3

1 12.7 0.71 3

1 12.1 0.46 53

1 1.5 0.0 1

1 1.5 0.1 15

1 -1.5 -0.01 1

1 -1.5 -0.11 53

1 -12.1 -0.46 3

1 -12.7 -0.25 3

4 //num_cornerpoints**PARA1UPSTREAM

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 -12.8 0.02 2

1 -12.7 0.02 1

1 -12.7 0.07 2

1 -12.8 0.07 1

4 //num_cornerpoints**PARA2UP

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 -12.8 0.34 2

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3.3. SAMPLE INPUT FILES

1 -12.7 0.34 1

1 -12.7 0.39 2

1 -12.8 0.39 1

4 //num_cornerpoints**PARA3UP

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 -12.8 0.66 2

1 -12.7 0.66 1

1 -12.7 0.71 2

1 -12.8 0.71 1

4 //num_cornerpoints**PARA1DOWN

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 12.7 0.98 2

1 12.8 0.98 1

1 12.8 1.03 2

1 12.7 1.03 1

4 //num_cornerpoints**PARA2DOWN

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 12.7 1.30 2

1 12.8 1.30 1

1 12.8 1.35 2

1 12.7 1.35 1

4 //num_cornerpoints**PARA3DOWN

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 12.7 1.62 2

1 12.8 1.62 1

1 12.8 1.67 2

1 12.7 1.67 1

4 //num_cornerpoints**PARA_MID_DESIGN2_LEFT

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 -0.23 0.63 3

1 -0.08 0.6 3

1 -0.08 0.8 3

1 -0.23 0.77 3

4 //num_cornerpoints**PARA_MID_DESIGN2_RIGHT

0.3 0.0 //release_distance*spacing_hull

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CHAPTER 3. THE VXFLOW INPUT FILE

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 0.08 0.6 3

1 0.23 0.63 3

1 0.23 0.77 3

1 0.08 0.8 3

4 //num_cornerpoints**SCREEN3(SCHEME3)

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 -13.15 0.14 2

1 -13.00 0.14 15

1 -13.00 3.14 2

1 -13.15 3.14 15

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Chapter 4

Getting started

4.1 Introduction

This chapter provides a few hint and comments on how flow modelling can bedone with VXFlow. It is based in experience from a number of cases for whichVXFlow was used and provided accurate and efficient solutions. It cannot replaceknowledge of fluid dynamics and aerodynamics.

4.2 Modelling issues

4.2.1 Solid body modelling

In the Vortex Particle Method used here only the surfaces of the solid bodies needto be discretised. This is done by providing a polygon decribing each individualbody. In VXFlow terminology these bodies are called ‘sections’.

The parameter NUMSEC defines the number of sections and in the subsequentpart of the input file the relevant paramter (including the shape polygon) needto be provided for each section separately.

Let’s assume the cross section of an H-shaped pylon consisting of two legs withrectangular shape shall be modelled. We set NUMSEC=2 and in the sectionparts look as follows

!!

4 //num_cornerpoints

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

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CHAPTER 4. GETTING STARTED

1 -3.0 -0.5 10

1 -2.0 -0.5 10

1 -2.0 0.5 10

1 -3.0 0.5 10

4 //num_cornerpoints

0.3 0.0 //release_distance*spacing_hull

0.02 0.001 0.0 -0.1 //merg1*merg2*merg3*merg4

-4 -3 -1 -3 -1 //section_color_coding:drag*lift*moment*displ*rotation

1 2.0 -0.5 10

1 3.0 -0.5 10

1 3.0 0.5 10

1 2.0 0.5 10

Here, each side of the quadratic legs is modelled by a straight line and discretisedby 10 boundary panels. On these panels the discrete vortices are introducedand thus the number of panels directly influences the resolution of the flow field,particularly close to the boundary. Usually, simple bridge sections should bemodelled using around 200...400 panels. All panels should ideally have the samelength, which needs to be considered when computing the number of panels perpolygon side. If several sections are present, also the sections should all havesimilar panel lengths. This cannot always be satisfied if very small sections arepresent, for example those modelling hand rails.

The number of panels can be globally scaled using the parameter ‘NPANELFACT’(default: ‘NPANELFACT=1.0’). The code then accordingly scales the numberof panels on each polygon side and rounds it to the next integer.

In the example above the release distance is set to 0.3∆s (panel length). Fromthis point the vortex is released into the flow through a random walk (if diffusionis switched on, DIFFU=1). The hull is an abondened modelling concept and canbe switched to 0.0. Also the merging algorithm need not be used anymore andis switched off by setting ‘merg4’ to a negative value (the other values are thenneglected). The colour coding paramters are only relevant for the graphics outputduring the computation and are therefore irrelevant to the Windows version ofthe code.

4.2.2 Grid selection

Whilst the original Vortex Particle Method is a grid-free method, VXFlow is basedon the Vortex-In-Cell (VIC) algorithm which uses a grid to speed-up the velocitycomputation. Therefore, a computational grid covering the modelled fluid domainneeds to be set up. This is easy, however, as we use regular rectangular gridsand hence only the boundaries and grid spacing needs to be provided. Theminimum and maximum coordinates in the two directions are given through

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4.2. MODELLING ISSUES

GRIDMINX, GRIDMAXX, GRIDMINY and GRIDMAXY. The number of cellsin the respective directions is given with GRIDNX and GRIDNY.

In X-direction one will usually select a grid running from 1...2 chord lengths up-stream from the leading edge to 6...10 chord lengths downstream from the leadingedge depending on the cross sectional shape and the wake features expected. Thenumber of cells should be “powers of 2 minus 1”, perhaps start with 255. Note,that contrary to other methods, the number of cells is a speed issue rather thanan accuracy one. For the majority of cases the user should aim for a simulationwith an average of 1...2 particles per cell. With large areas of the domain beingunused this yields approximately 10 particles per cell in the active cells. Hence,more cells will increase the speed only if there are too many particles (several percell).

In Y-direction it is important to provide enough space for the across-flow widthof the wake. It is recommended to choose quadratic cells and thus one will oftenchoose half the X-dimension for the Y-direction. For GRIDNY the same as aboveapplies. Example:

GRIDMINX=-10

GRIDMAXX=50

GRIDNX=511

GRIDMINY=-14.97

GRIDMAXY=14.97

GRIDNY=255

The grid must cover the sections entered and should cover all fluid domain ofinterest. Vortices moving outside of the grid are deleted from the simulation andthis should only happen sufficiently far downstream from the sections.

4.2.3 Use of the grid

The computational grid is used by the code in two very different numericalschemes, either in the traditional Cell-to-cell algorithm by Leonard or the P3Mscheme by the author [7]. The latter is recommended as it enables highly accu-rate flow modelling at low computational cost. Hence, setting ‘FASTMODE=2’is recommended. For the accuracy parameter Nr of the P3M method ‘NR=3’usually suffices, Nr = 4 provides almost exact results for the velocity but is notneeded in engineering applications. Note, that the solution time almost scaleswith N2

r !

Both the Finite Differencing and the kernel projection necessary are performedrather fast und hence the higher accuracy settings ‘P3MFD=2’ and ‘P3MINTP=2’.

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CHAPTER 4. GETTING STARTED

UPDATE: the exact velocity computation in Fourier space (described in Ap-pendix A of [7]) is switched on using ‘P3MFD=-1’ (this switches of the use ofFinite Differences altogether) and enables the reduction of Nr by 1!

The necessary accuracy of the velocity computation can usually be reduced fur-ther away from the solid surfaces as the degree of subgrid scales (which are re-solved by the P3M algorithm) is lower. Hence Nr can be reduced in these regionsto save computation time. To achieve this, the parameter P3MNRRELAX canbe used. It specifies the number of grid cells at which Nr is reduced by one. Ina region of P3MNRRELAX around the surface the value of NR is used. At adistance between P3MNRRELAX and 2xP3MNRRELAX the code uses Nr − 1etc. Hence, far downstream there is a region where Nr = −1, defined as not doinga P3M correction at all. If you don’t understand this, switch this option off bydoing ‘P3MNRRELAX=0’.

A special problem arises in modelling the immersed boundary (the solid surface)through the grid, when the P3M option is chosen. The panel strengths can beincluded in the P3M scheme (set P3MSH=1) in which case their influence mustbe confined to the Nr region. This requires

15∆s < Nr∆x, (4.1)

where ∆x is the grid spacing. Otherwise inaccuracies occur. If you are unsureor want to play save (the simulation speed will reduce only moderately), chooseP3MSH=2. The option P3MSH=3 has been shown not to converge and is thusnot recommended.

4.2.4 Flow parameters

The modelling of the solid regions has been described in section 4.2.1. The flowis further defined by its physical parameters as follows.

The onset flow speed U0X. This is the undisturbed flow speed in X-direction(given in length scales per second).

The fluid density. Use ‘DENSTY=1.2’ for air.

The fluid viscosity. Use ‘VISCTY=0.000015’ for air.

4.2.5 Further modelling parameters

The most important modelling parameters are as follows. By default (NONDIM=1)most of them are nondimensionalised which is herein denoted by an asterisk∗.

DELTAT. This is the time step. ∆t∗ = ∆tU∞/∆s.

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4.2. MODELLING ISSUES

NSTEPS. The number of time steps for the simulation. It should be noted, that apremature cancellation of the run does not damage any of the result files alreadywritten. Therefore, the simulation does not neet to be completed.

TINTEGR. For engineering applications the Euler time integration (TINTEGR=1)is sufficient and double as fast as the Runge-Kutta-2 scheme.

SURF. A linear discretisation of the surface vorticity is strictly recommended(SURF=2).

INSIDE. The most favourable algorithm for treating vortices that accidentilystray into a solid region has been shown to delete them (INSIDE=2).

CROSS. A checking for vortices crossing a solid region is only necessary if theseare very thin. Normally this check can be switched off (CROSS=0).

COREMODEL. The smooth Gausian kernel is most favourable (COREMODEL=2).

DOMAIN. This concerns the grid solution of the velocity computation. For freespace boundary conditions, i.e. the general wind engineering case, this needs tobe set to DOMAIN=2.

The algorithm for releasing the vortex particles from the surface is of particularimportance both to the accuracy and the efficiency of the simulation. A sufficientresolution of the surface boundary layer is needed to accurately model flow sepa-ration and reattachment. Only a high number of vortices leads to a convergence ofthe numerical scheme. The parameter NSUBP describes how many particles arereleased from one panel at each time step. To obtain vortices of similar strengthsit is necessary to shed more particles from panels with higher vorticity. This isenabled through setting PVARY=1 (switch off with PVARY=0), in which casestrongest panel will shed NSUBP vortices and the others a number of particlesproportional to their strengths (but at least 1 particle). As for setting NSUBP,this can usually be set to 4 if a suffient number of particles and a sufficientlysmall time step is chosen — also see section 4.2.6.

4.2.6 Controlling resolution

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Chapter 5

Postprocessing the VXFlowoutput

5.1 VXPost

With version v0.8 of VXFlow the unified postprocessing tool VXPost has beenintroduced. This includes all previous postprocessing scripts which are now ob-solete. VXPost can be downloaded from the VXFlow website(http://www.morgenthal.org/vxflow/) as both Matlab scripts and as a Windowsexecutable.

VXPost is self-explanatory, offering a number of post-processing options in amenu style. Visualisation of the flow field is offered either based on the particlemap (.vx2 file) or the streaklines (.sk2) and/or the velocity contours (.fv2). Therecommended option is a combined plot of streaklines and velocity contours,offering the best insight into the flow physics, cf. Fig. 5.1. For this, make sure.sk2 and .fv2 files are dumped at the same timesteps. A sequence of images isthen created which can be combined into an animation of the evolving flow field.

5.2 Your own postprocessing

Users who want to adapt VXPost to their needs are encouraged to do so, mak-ing use of the open nature of the Matlab scripts provided. The author can becontacted to obtain further information on the output file formats. These are allsimple text files and can also be processed by a variety of programs like GNU-PLOT, EXCEL etc.

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Figure 5.1: Flow field visualisation for the M4 Neath Viaduct with an added solid windscreen: instantaneous velocity field.

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Bibliography

[1] Clough, R., and Penzien, J. Dynamics of Structures, 2nd ed. McGrawHill, Inc., 1993.

[2] Cottet, G.-H., and Koumoutsakos, P. Vortex Methods: Theory andPractice. Cambridge University Press, New York, 2000.

[3] Leonard, A. Vortex methods for flow simulations. J. Comp. Phys. 37(1980), 289–335.

[4] Lewis, R. I. Vortex Element Methods for Fluid Dynamics Analysis ofEngineering Systems, 1 ed. Cambridge University Press, 1991.

[5] Morgenthal, G. Comparison of Numerical Methods for Bridge-DeckAerodynamics. M.Phil. Thesis, University of Cambridge, 2000.

[6] Morgenthal, G. Fluid-Structure Interaction in Bluff-Body Aerodynam-ics and Long-Span Bridge Design: Phenomena and Methods. Tech. Rep.CUED/D-STRUCT/TR.187, University of Cambridge, 2000.

[7] Morgenthal, G. Aerodynamic Analysis of Structures Using High-resolution Vortex Particle Methods. PhD thesis, University of Cambridge,2002.

[8] Morgenthal, G., and McRobie, F. A. A Comparative Study of Numer-ical Methods for Fluid Structure Interaction Analysis in Long-Span BridgeDesign. Journal of Wind and Structures 5 (2002), 101–114.

[9] Morgenthal, G., and Walther, J. H. An Immersed Boundary Methodfor the Vortex-in-Cell Algorithm. J. Comp. Phys., in preparation.

[10] Spalart, P. R. Vortex methods for separated flows. NASA TM, NASA,June 1988.

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