himag...ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0, output: 10000th...

HIMAG HyPerComp Incompressible MHD solver for Arbitrary Geometry

Appendix II: Benchmark Cases

HIMAG 2019 HyPerComp, Inc.

2629 Townsgate Rd, Suite

105

Westlake Village, CA 91361

http://www.hypercomp.net

(T) 805-371-7500

Release 1.0

July 2019

http://www.hypercomp.net/

HIMAG 2019

CONTENTS

1

Pre-Defined

Cases in HIMAG

1.1 Rectangular Duct, Insulating Walls

1.1.1 No MHD (Pure Hydrodynamics)

1.1.2 MHD with Uniform B Field

1.1.3 MHD with Exponential B Field

1.2 Rectangular Duct, Conducting Walls


1.2.2 MHD with Uniform B Field

1.2.3 MHD with Exponential B Field

1.3 Half Rectangular Duct, Insulating Walls


1.3.2 MHD

1.4 Half Rectangular Duct, Conducting Walls


1.4.2 With MHD

1.5 Circular Duct, Conducting Walls

1.5.1 Pure Hydrodynamics without Non-Orthogonal

Correction

1.5.2 Pure Hydrodynamics with Orthogonal Correction

1.5.3 MHD without Non-Orthogonal Correction

1.5.4 MHD with Non-Orthogonal Correction

1.5.5 MHD with Constant B Field

2

Benchmark Cases

2.1 Alex

2.2 Broken dam

2.3 Cavity

2.4 Cir3d_Re100

2.5 Cirful_Ha100 (Fully Developed)

2.6 Cirful_Re1k (Fully Developed)

2.7 Cond3d_Ha100

2.8 Demo1_Hunt3d

HIMAG 2019

2.9 Demo2_sher3d

2.10 Dissp_Full (Fully Developed)

2.11 Duct2d_Re10

2.12 Duct3d_Re15k

2.13 Ductful (Fully Developed)

2.14 Entrance

2.15 Ha500_2d

2.16 Huntful_Ha100_io2 (Fully Developed)

2.17 Huntful_Ha300 (Fully Developed)

2.18 Ppe_MHD

2.19 Sherful_Ha300 (Fully Developed)

2.20 Sherful_Ha500_io2 (Fully Developed)

2.21 Therm

2.22 Wall

HIMAG 2019

1 | M A I N I N D E X

1 CASES WITH PRE-DEFINED GRIDS IN

HIMAG GRID

HIMAG 2019


Case 1.1 : Rectangular Duct, Insulating Walls

Location : Home> work> himag> predef> case1

Grid Generation :

The grid for this case was made using the HIMAG Grid Generation code “xyz” using the following parameters:

L = 25 (For Pure Hydrodynamic Case, L = 85) a = 1 b = 1 Ha = 500 Re = 10 CPU = 1 nxcel = 32 nycel = 42 nzcel = 40

Mass Flow Rate (rho*ubar*area) = 4.00

Fig 1.1 Rectangular Duct Grid

HIMAG 2019


Case 1.1.1 : No MHD (Pure Hydrodynamics)

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 1.00E-01, rho1 = 1.0, sleng = 1.0, ubar = 1.0, dpdx = -0.0, iuvw = 1, ichan = 0, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, nvel = 0, iortho = 1, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,

Output: 50000th Iteration

ppe-CG step = 50000 0 -1.66045E+01 Tstep = 50000 1.00000E-03 -1.97761E-03 3.99802E+00 2.07680E+00 1.65479E-01

Mass Flow Rate : 3.99802E+00

Time : 120 min

HIMAG 2019


++ pres_res

Fig. 1.2a Pressure Residual

𝜕𝑝

𝜕𝑥= −0.711 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 14)

Fig. 1.2b Dpdx plot

𝜕𝑝

𝜕𝑥= −0.6912

0.711 – 0.6912 = 2.79% 0.711

file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf

HIMAG 2019


Case 1.1.2 : MHD with Constant B Field

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 5000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, dpdx = -0.0, nbf = -1, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0, Output: 5000th Iteration mhd-CG step = 5000 2 -1.01381E+01 -2.21411E+00 ppe-CG step = 5000 100 -5.44430E+00 Tstep = 5000 8.00000E-05 -9.11307E-03 3.99089E+00 4.93355E+00 -2.57849E-01


Time : 379 min

HIMAG 2019


## pres_res

++ mhd_res

Fig. 1.3a Pressure and MHD Residual

𝜕𝑝


Fig. 1.3b dpdx plot

𝜕𝑝

𝜕𝑥= −52.50

52.50 – 52.08 = 0.81% 52.08


HIMAG 2019


Case 1.1.3 : MHD with exponent B Field

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, iuvw = 1, dpdx = -0.0, ibf = 2, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,


mhd-CG step = 10000 99 -1.00513E+01 -1.96048E+00 ppe-CG step = 10000 100 -7.14327E+00 Tstep = 10000 8.00000E-05 -9.07993E-03 3.99092E+00 9.97569E+00 -5.21621E-01


HIMAG 2019


Time : 441 min

## pres_res

++ mhd_res

Fig. 1.4a Pressure and MHD Residual

𝜕𝑝


Fig. 1.4b dpdx plot

𝜕𝑝

𝜕𝑥= −52.23

52.23 – 52.08 = 0.3% 52.08


HIMAG 2019


Case 1.2 : Rectangular Duct with Conducting Walls


Grid Generation :


L = 25 (For pure Hydrodynamic Case, L = 85) a = 1 b = 1 Ha = 500 Re = 10 Cw = 0.1 CPU = 1 nxcel = 32 nycel = 50 nzcel = 48


Fig 1.5 Rectangular duct grid

HIMAG 2019



Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iuvw = 1, ibf = 2, ichan = 2, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, nvel = 0, iortho = 1, ngrad = 5, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,




HIMAG 2019


Time : 180 min

++ Pres_res

Fig 1.6a Pressure Residual

𝜕𝑝

𝜕𝑥= −0.711 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈)

Fig. 1.6b dpdx plot

𝜕𝑝

𝜕𝑥= −0.68

0.711 – 0.68 = 4.36%

0.711


HIMAG 2019


Case 1.2.2 : MHD with Uniform B Field

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 5000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, nbf = -1, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 1, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,


mhd-CG step = 5000 35 -1.02013E+01 -1.94567E+00 ppe-CG step = 5000 100 -8.96444E+00 Tstep = 5000 8.00000E-05 -2.24607E-01 3.77539E+00 9.38867E+00 1.45105E-02


Time : 369 min

HIMAG 2019


Residual Plot:

## pres_res

++ mhd_res

Fig 1.7a Pressure and MHD Residual

𝜕𝑝


Fig. 1.7b dpdx plot

𝜕𝑝

𝜕𝑥= −1439.033

1458.88 – 1439.033 = 1.36% 1458.88


HIMAG 2019


Case 1.2.3 : MHD with Exponent B Field

Input file :



mhd-CG step = 50000 4 -1.62384E+01 -5.06762E+00 ppe-CG step = 50000 100 -1.35522E+01 Tstep = 50000 8.00000E-05 -2.24605E-01 3.77539E+00 9.90765E+00 -1.09580E+00


HIMAG 2019


Time : 1810 min for 50000 iter.

Residual Plot:

## pres_res

++ mhd_res


𝜕𝑝


Fig. 1.8b dpdx plot

𝜕𝑝

𝜕𝑥= −1425.35

-1458.88 + 1425.35 = 2.29% -1458.88


HIMAG 2019


Case 1.3 : Half Rectangular Duct with Insulating Walls


Grid Generation :


L = 25 a = 1 b = 1 Ha = 500 Re = 10 CPU = 1 nxcel = 32 nycel = 21 nzcel = 40


Fig 1.9 Half Rectangular Duct Grid

HIMAG 2019



Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, dpdx = -0.0, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 0, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,


ppe-CG step = 10000 100 -7.28344E+00 Tstep = 10000 8.00000E-05 8.63320E-05 2.00009E+00 1.83297E+00 1.39289E-05


Time : 10000 iterations in 150 min

HIMAG 2019


Residual Plot:

## pres_res


𝜕𝑝


Fig. 1.10b dpdx plot

𝜕𝑝

𝜕𝑥= −0.7027

0.711 – 0.7027 = 1.17% 0.711


HIMAG 2019


Case 1.3.2 : With MHD

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, dpdx = -0.0, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,

Output: 10000th Iteration mhd-CG step = 10000 10 -1.00398E+01 -2.04951E+00 ppe-CG step = 10000 100 -7.69985E+00 Tstep = 10000 8.00000E-05 -4.53992E-03 1.99546E+00 9.97569E+00 -5.21560E-01


Time : 10000 iterations in 500 min

HIMAG 2019


Residual Plot :

## pres_res

++ mhd_res


𝜕𝑝

𝜕𝑥= −52.08 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 )


𝜕𝑝

𝜕𝑥= −52.52

52.52 – 52.08 = 0.85% 52.08


HIMAG 2019


Case 1.4 : Half Rectangular Duct with Conducting Walls


Grid Generation :


L = 25 (For Pure Hydrodynamic case, L = 85) a = 1 b = 1 Ha = 500 Re = 10 Cw = 0.1 CPU = 1 nxcel = 32 nycel = 25 nzcel = 48

Mass Flow Rate (rho*ubar*Area) = 3.14

Fig 1.12 Half Rectangular Duct Grid

HIMAG 2019



Input file :


Output: 50000th Iteration ppe-CG step = 50000 100 -7.34940E+00 Tstep = 50000 8.00000E-05 4.12956E-05 2.00004E+00 2.05773E+00 1.42469E-05


HIMAG 2019


Time : 50000 iterations in 285 min.

## pres_res


Dpdx plot : 𝜕𝑝



𝜕𝑝

𝜕𝑥= −0.7039

0.711 – 0.7039 = 1.01% 0.711


HIMAG 2019


Case 1.4.2 : With MHD

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 2, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,


mhd-CG step = 10000 0 -1.00606E+01 -2.02677E+00 ppe-CG step = 10000 100 -7.67125E+00 Tstep = 10000 8.00000E-05 -1.12304E-01 1.88770E+00 9.90583E+00 -1.10797E+00


Time : 10000 iterations in 510 min.

HIMAG 2019


Residual plot :

## mhd_res

++ pres_res


𝜕𝑝



𝜕𝑝

𝜕𝑥= −1426.88

-1458.88 + 1426.88 = 2.19% -1458.88


HIMAG 2019


Case 1.5 : Circular Duct with Conducting Walls (No MHD)


Grid Generation :


L = 85 t = 0.1 Ha = 0 Re = 400 CPU = 1 nxcel = 32 nycel = 19 nzcel = 50


Fig 1.15 Circular duct grid where length of the duct is 85m

HIMAG 2019


Case 1.5.1 : Pure Hydrodynamics without Correction

Input File : nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.50E-03, rho1 = 1.0, sleng = 1.0, ubar = 1.0, dpdx = -0.0, iortho = 1, nvel = 1, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, iuvw = 1 ichan = 11, nskp = 10, ipmax = 40, immax = 40, lambdu = 1.0, epsmin = -16.0,




Time : 155 min. on a single cpu for 50000 iter.

𝜕𝑝

𝜕𝑥= −

𝑄

(𝜋𝜌𝑎4

8𝜇 )= −0.02

HIMAG 2019


Fig. 1.16a dpdx plot

𝜕𝑝

𝜕𝑥= −0.0205

0.0205 – 0.02 = 2.5% 0.02

Convergence:

++ Mass Flow Rate

Fig 1.16b Mass Flow Rate

HIMAG 2019


## pressure_res

Fig 1.16c Pressure Residual

HIMAG 2019


Case 1.5.2 : Pure Hydrodynamics with Non-Orthogonal Correction

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.50E-03, rho1 = 1.0, sleng = 1.0, ubar = 1.0, dpdx = -0.0, iuvw = 1, ichan = 11, iortho = 2, nvel = 1, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, nskp = 10, ipmax = 40, immax = 40, lambda = 1.0, epsmin = -16.0,




Time : 510 min on single cpu for 50000 iter.

𝜕𝑝

𝜕𝑥= −

𝑄

(𝜋𝜌𝑎4

8𝜇 )= −0.02

HIMAG 2019



𝜕𝑝

𝜕𝑥= −0.0204

0.0204 – 0.02 = 2.0%

0.02

Convergence History

++ Mass Flow Rate

Fig 1.17b Mass Flow Rate vs Number of Iterations

HIMAG 2019


xx Press_res

Fig 1.17c Pressure Residual

HIMAG 2019


Case 1.5.3 : Circular Duct with Conducting Walls (for MHD)

Location : Home > work > himag_08_27_2015 > predef > case5

Grid Generation :


L = 25 t = 0.1 Ha = 100 Re = 500 nxcel = 32 nycel = 19 nzcel = 50

Mass Flow Rate (rho*ubar*Area) = 3.14

Fig 1.18 Circular duct grid where length is 25m

HIMAG 2019


Case 1.5.3 : MHD without Non-Orthogonal Correction

Input file :





Time : 150 min. on a single cpu for 10000 iter.

HIMAG 2019


𝜕𝑝



𝜕𝑝

𝜕𝑥= −1.172

1.1876 – 1.172 = 1.31%

1.1876

Convergence:

++ Mass Flow Rate

Fig 1.19b Mass Flow Rate vs Number of Iterations


HIMAG 2019


** mhd_res ## ppe_res

Fig 1.19c Pressure and MHD Residual

HIMAG 2019


Case 1.5.4 : MHD with Non-Orthogonal Correction

Input file :



mhd-CG step = 10000 0 -1.00089E+01 -3.66591E+00 ppe-CG step = 10000 0 -1.01164E+01 Tstep = 10000 1.00000E-03 -3.42491E-03 3.12289E+00 1.70492E+00 – 2.73358E-03


Time : 190 min on single cpu for 10000 iter.

HIMAG 2019


𝜕𝑝



𝜕𝑝

𝜕𝑥= −1.2004

1.2004 - 1.1876 = 1.08%

1.1876

Convergence:

** Mass Flow Rate Fig 1.20b Mass Flow Rate vs Number of Iterations


HIMAG 2019


** mhd_res

## ppe_res

Fig 1.20c Pressure and MHD Residual

HIMAG 2019


Case 1.5.5 : MHD with Constant B Field

Input file :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.00E-03, rho1 = 1.0, sgmf1 = 2.00E+01, sgmw1 = 1.00E+01, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iuvw = 1, ibf = 2, nbf = -1, ichan = 11, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, nvel = 1, iortho = 2, ngrad = 5, nskp = 10, ipmax = 40, immax = 40, lambdu = 1.0, epsmin = -16.0,



HIMAG 2019



Time : 10000 Iteration in 155 min.

𝜕𝑝

𝜕𝑥= −1.1876 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 ℎ𝑖ℎ𝑎. 𝑝𝑑𝑓 𝑝𝑔. 58)


𝜕𝑝

𝜕𝑥= −1.2011

1.2011 - 1.1876 = 1.14%

1.1876

Convergence:

** mhd_res ## ppe_res

Fig 1.21b Pressure and MHD Residual

file:///C:/Users/Rupanshi/Desktop/HIMAG/Documentation/hiha.pdf

HIMAG 2019


2 BENCHMARK CASES

HIMAG 2019


Case 2.1 : ALEX

Half circular duct with conducting walls, polar grid

Case 5 Location : Home > mhd > bench > alex

Grid Generation :

L = 25 Ha = 10 Re = 10 CPU = 04 Total number of cells : 16313


Fig 2.1a Rectangular duct grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 10000, iskip = 5000, nwrite = 5000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 10.0, sgmw1 = 10.0, sgmw2 = 1.0e-4, alpha = 1.0, omega = 1.00, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.1, dpdx = -2.00451775, iortho = 2, nvel = 1, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, icha = 12, nskp = 10, lpois = 1, ipmax = 20, immax = 20, igmax = 2,

Output :



Time : 60 min on 4 CPUs

HIMAG 2019


Fig 2.1b U_contour1

Fig 2.1c U_contour2

HIMAG 2019


Fig 2.1d U-in-out

HIMAG 2019


Case 2.2 : BROKEN DAM

Level Set Case

Case 5 Location : Home > mhd > bench > brokendam

Grid Generation :


Mass Flow Rate (rho*ubar*area) = 0


HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 1500, iskip = 100, nwrite = 2000, dtime = 2.0e-3, dratio = 1000., vratio = 1000., visc1 = 1.e-3, rho1 = 1.0, omega = 1.00, sleng = 2.2, ubar = 0.0, dpdx = 0.0, lambda = 1.0, ssig = 1.0e-2, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 11, ichan = 0, nskp = 1, ipmax = 20, irmax = 10, irinit = 10, epsmin = -16.0, igravt = 1, gx = 0, gy = -1, gz = 0,

Output :

ppe-CG step = 1500 20 -7.04451E+00 level set residual= -9.84345E-01 reinitialization res at it = 11 -2.56133E+00 Tstep = 1500 2.00000E-03 0.00000E+00 0.00000E+00 2.85237E+00 -1.70767E+00


Time : 41 sec on 2 CPUs

HIMAG 2019


Fig.2.2b rho – x (1500)

Fig.2.2c rho – x (800)

HIMAG 2019


Case 2.3 : CAVITY

Heat Transfer for Cavity Problem

Case 5 Location : Home > mhd > bench > cavity

Grid Generation :

L = 1 Ra = 1.0E+06 Ha = 0 Re = 1.4085 CPU = 2 Total number of cells : 200



HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 5000, iskip = 5000, nwrite = 5000, dtime = 2.0e-4, sleng = 1.0, visc1 = 0.71, rho1 = 1.00, alpha = 1.0, omega = 1.00, dpdx = -0.0, hk1 = 1.0, cp1 = 1.0, hkw1 = 1.00, cpw1 = 1.00, tref = 0.00, deltT = 1.00, gras = 1.4084507e6, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 0, nheat = 6, ncase = 22, ilevels = 0, ichan = 0, nskp = 10, ipmax = 20, ihmax = 100, ibuoy = 1, igravt = 0, idissp = 0, gx = 0.0, gy = -9.81, gz = 0.0,

Output :

ppe-CG step = 5000 1 -1.63597E+01 Heat step = 5000 -2.57268E+01 9.74582E-01 2.75067E-02 6.83897E-13 1.06108E+01 Tstep = 5000 2.00000E-04 0.00000E+00 0.00000E+00 1.26413E+02 2.43162E+02

HIMAG 2019



Time : 10 sec for 2 CPUs

Fig. 2.3b T-xy

Fig.2.3c Streamlines

HIMAG 2019


Fig. 2.3d Iso_therm

HIMAG 2019


Case 2.4 : CIR3D_RE100

Half Circular Duct, 3-D Polar Grid

Case 5 Location : Home > mhd > bench > cir3d_re100

Grid Generation :

L = 10 Ha = 0.00 Re = 100.00 Cw = 0.00 CPU = 2 Total number of cells = 8800

Re = rho*ubar*r0/visc1 Therefore, r0 = 1


Fig 2.4a Half Circular Duct 3-D Polar Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 7000, iskip = 5000, nwrite = 7000, dtime = 1.0e-1, visc1 = 1.0e-1, rho1 = 10., alpha = 1.0, omega = 1.92, sleng = 1.0, ubar = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -0.8, iortho = 2, nvel = 1, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, iuvw = 1, ntrit = 0, iwall = 0, ngrad = 5, ichan = 12, nskp = 10, igmax = 2, ipmax = 20, epsmin = -16.0,

Output :



Time : 16 min. on 2 CPUs

HIMAG 2019


Fig 2.4b x_u_p

HIMAG 2019


Case 2.5 : CIRFUL_HA100

Half Circular Duct, Fully-Developed, Polar Grid

Case 5 Location : Home > mhd > bench > cirful_ha100

Grid Generation :

Ha = 100 Re = 10 Cw = 0.00 CPU = 2 Total number of cells = 1080



Fig 2.5a Half Circular Duct Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 1000., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.92, sleng = 1.0, ubar = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -12.363593, iortho = 2, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, iuvw = 1, ntrit = 0, iwall = 0, ngrad = 2, ichan = 12, nskp = 10, igmax = 2, immax = 200, epsmin = -16.0,

Output :

mhd-CG step = 2000 200 -1.58628E+01 -5.86315E+00 Tstep = 2000 1.00000E-04 1.15510E-15 1.57178E+00 1.21579E+00 8.13749E-03



HIMAG 2019


Fig 2.5b U_yz

HIMAG 2019


Case 2.6 : CIRFUL_RE1K

Half Circular Duct, Fully-Developed, Polar Grid

Case 5 Location : Home > mhd > bench > cirful_Re1k

Grid Generation :

Ha = 0.00 Re = 1000 Cw = 0.00 CPU = 2 Total number of cells = 960



Fig 2.6a Half Circular Duct Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 10000, iskip = 10000, nwrite = 10000, dtime = 1.00e-1, visc1 = 1.0e-1, rho1 = 100., alpha = 1.0, omega = 1.92, sleng = 1.0, ubar = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -0.8, iortho = 2, nvel = 1, nmomt = 1, nppe = 0, nmhd = 0, nheat = 0, ilevels = 0, ichan = 12, nskp = 10, igmax = 2, ipmax = 20, epsmin = -16.0,

Output :

Tstep = 10000 1.00000E-01 1.75005E-08 1.57303E+02 1.97379E+00 2.89501E-02


Time : 31 sec. on 2 CPUs

HIMAG 2019


Fig 2.6b U_yz

HIMAG 2019


Case 2.7 : COND3D_HA100

Hunt’s 3D Conducting Walls

Case 5 Location : Home > mhd > bench > condo3d_ha100

Grid Generation :

L = 20 a = 1 b = 1 Ha = 100 Re = 10 CPU = 2 Total number of cells = 11520


Fig 2.7a Rectangular Duct Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 1000., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.1, dpdx = -82.2700358, lambda = 1.0, iuvw = 1, ibf = 2, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 2, ichan = 1, nskp = 10, ipmax = 50, immax = 50, epsmin = -16.0,

Output :



HIMAG 2019


Time : 5.3 min on 2 CPUs

Fig 2.7b V_Comp

HIMAG 2019


Case 2.8 : DEMO1_HUNT3D

Hunt’s Half, 3-D Conducting Walls

Case 5 Location : Home > mhd > bench > demo1_hunt3d

Grid Generation :


Mass Flow Rate : (rho*ubar*area) = 2.00

Fig2.8a Half Rectangular Duct Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1000, iskip = 1000, nwrite = 1000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 1000., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 4.0, twal = 0.1, dpdx = -82.2700358, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 2, ichan = 2, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,

Output :




HIMAG 2019


Fig 2.8b V_Comp

HIMAG 2019


Case 2.9 : DEMO2_SHER3D

Shercliff’s 3-D Flow

Case 5 Location : Home > mhd > bench > demo2_sher3d

Grid Generation :




HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 20000, iskip = 10000, nwrite = 5000, dtime = 2.5e-5, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 25000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.0, dpdx = -52.0854546, iortho = 1, nvel = 1, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 50, immax = 50, epsmin = -16.0,

Output :




HIMAG 2019


Fig.2.9b V_Comp.

HIMAG 2019


Case 2.10 : DISSP_FULL

Fully- Developed Heat Transfer with Dissipation

Case 5 Location : Home > mhd > bench > dissp_full

Grid Generation :




HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 400, iskip = 400, nwrite = 4000, dtime = 1.0e-1, visc1 = 1.0, rho1 = 1.0, omega = 1.00, dpdx = -7.11353706, hk1 = 1.00, cp1 = 1.00, hkw1 = 1.00, cpw1 = 1.00, tref = 1.00, deltT = 0.00, gras = 9.81, iortho = 1, nvel = 0, nmomt = 1, nppe = 0, nmhd = 0, nheat = 6, ncase = 23, ilevels = 0, ichan = 0, nskp = 1, ihmax = 1000, nbcg = 1, ibuoy = 0, igravt = 0, idissp = 1, gx = 0.0, gy =-1.0, gz = 0.0,

Output :

Heat-BCG step = 400 539 -1.60108E+01 2.09351E+00 1.00107E+00 2.84225E+01 7.62144E+00 Tstep = 400 1.00000E-01 4.77919E-16 4.01701E+00 2.09078E+00 2.80072E-03


HIMAG 2019



Fig 2.10b UT_y

HIMAG 2019


Case 2.11 : DUCT2D_RE10

2-D (XY) Duct Flow, Irregular Grid

Case 5 Location : Home > mhd > bench > duct2d_re10

Grid Generation :

L = 20 Ha = 0 Re = 10 CPU = 2 Total number of cells = 400


Fig 2.11a 2D XY Duct Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 500, iskip = 500, nwrite = 5000, dtime = 2.0e-2, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, omega = 1.00, alpha = 1.0, iortho = 2, nvel = 20, invel = 20, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ichan = 0, nskp = 1, ipmax = 40, epsmin = -16.0,

Output :



Time : 6 sec. on 2 CPUs

HIMAG 2019


Fig 2.11b dpdx

Fig 2.11c Velocity Profile

HIMAG 2019


Case 2.12 : DUCT3D_RE15

3-D Duct Flow, Hex Grid

Case 5 Location : Home > mhd > bench > duct3d_re15

Grid Generation :

L = 35 Ha = 0 Re = 15250 CPU = 4 Total number of cells = 20000



HIMAG 2019


Input File :

nodes = 4, iread = 0, grid_scale = 4.39e-2, istart = 0, nmax = 10000, iskip = 5000, nwrite = 5000, dtime = 5.0e-3, visc1 = 8.2175e-4, rho1 = 865.0, alpha = 1.00, omega = 1.00, sleng = 1.0, ubar = 0.33, dpdx = -1.000945, lambda = 0.0, lambda = 0.0, iortho = 1, nvel = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, ichan = 0, nskp = 10, lpois = 1, ipmax = 50, igmax = 2, epsmin = -16.0,

Output :

ppe-CG step = 10000 50 -1.41983E+01 Tstep = 10000 5.00000E-03 -1.37814E-07 2.20037E+00 3.81456E-01 1.58111E-05


Time : 65 min on 4 CPUs

HIMAG 2019


Fig 2.12b U profile

Fig 2.12c U-yz

HIMAG 2019


Case 2.13 : DUCTFUL

Fully-Developed Duct Flow

Case 5 Location : Home > mhd > bench > ductful

Grid Generation :




HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 1.0e-2, visc1 = 1.0e-1, rho1 = 1.0, ubar = 1.0, dpdx = -0.711354, iuvw = 1, iortho = 1, nvel = 1, nmomt = 1, nppe = 0, nmhd = 0, nheat = 0, ilevels = 0, ichan = 0, epsmin = -16.0,

Output :

Tstep = 2000 1.00000E-02 -7.96012E-15 4.01195E+00 2.09102E+00 3.09946E-03


Time : 2 sec approx. on 2 CPUs

Fig 2.13b U Profile

HIMAG 2019


Fig 2.13c V_Comp

HIMAG 2019


Case 2.14 : ENTRANCE

Heat Transfer for Entrance Problem

Case 5 Location : Home > mhd > bench > entrance

Grid Generation :

L = 20 Ha = 0 Re = 1000 CPU = 2 Total number of Cells : 1750

Mass Flow Rate (rho*ubar*area) =


HIMAG 2019


Input File(s) : ent_hex.input/ent_prm.input/enter_prm_nppe1.input/ent_prm1.input

nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 500,/../2500/.. iskip = 500,/../2500/.. nwrite = 5000, dtime = 2.0e-2,/../../1.0e-2 cfl = 2.70, visc1 = 1.0e-4, rho1 = 1.0, alpha = 0.75,/../1.00 omega = 1.00, ubar = 1.0, dpdx = -0.0, lambda = 1.0, hk1 = 1.0e+2, cp1 = 1.0e+4, hkw1 = 1.00, cpw1 = 1.00, tref = 0.00, deltT = 1.00, gras = 1.0e+3, iortho = 2, nvel = 20, nmomt = 1, nppe = 3,/../1/3 (nppe = 5 does not work for this case) nmhd = 0, nheat = 6,/../1 ncase = 21, ilevels = 0, ichan = 0, nskp = 10,/../1/.. ipmax = 50, ihmax = 2000,/../../- epsmin = -16.0, ibuoy = 0, igravt = 0, idissp = 0, gx = 0.0, gy =-9.81, gz = 0.0,


HIMAG 2019


Fig 2.14b T- Contour

Fig 2.14c T-Profile

HIMAG 2019


Case 2.15 : HA500_2D

2-D Hartmann Flow, Hex Grid

Case 5 Location : Home > mhd > bench > ha500_2d

Grid Generation :




HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 5.0e-4, cfl = 2.70, visc1 = 1.0e-4, rho1 = 1.0, sgmf1 = 25., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.0, dpdx = -0.0, iortho = 1, nvel = 20, nmomt = 1, nppe = 5, nmhd = 3, nheat = 0, ichan = 0, nskp = 10, lpois = 3, ipmax = 50, epsmin = -10.0,

Output :




HIMAG 2019


Fig 2.15b U-Profile

Fig 2.15c U-Y

HIMAG 2019


Fig 2.15d P,u - x

HIMAG 2019


Case 2.16 : HUNTFUL_HA100_IO2

Hunt’s Fully-Developed with Conducting Walls, Triangle Grid

Case 5 Location : Home > mhd > bench > huntful_ha100_io2

Grid Generation :

L = 1 a = 1 b = 1 Ha = 100 Re = 10 CPU = 2 Total number of cells : 3168


Fig 2.16a Rectangular Duct Triangle Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1000, iskip = 1000, nwrite = 1000, dtime = 5.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 500., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.50, ubar = 1.0, bval = 1.0, twal = 0.1, dpdx = -52.7434288, c_rest = 0.0, lambda = 1.0, iortho = 2, nvel = 0, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 2, ichan = 1, nskp = 10, immax = 200, igmax = 3, epsmin = -16.0,

Output :




HIMAG 2019


Fig 2.16b Velocity Profile

Fig 2.16c V_Comp

HIMAG 2019


Case 2.17 : HUNTFUL_HA300

Hunt’s Fully-Developed Conducting Walls, Hex Grid

Case 5 Location : Home > mhd > bench > huntful_ha300

Grid Generation :

L = 1 Cw = 0.05 Ha = 300 Re = 10 CPU = 2 Total number of cells : 1058


‘

Fig 2.17a Rectangular Duct Hex Grid

HIMAG 2019


Input File :

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1000, iskip = 1000, nwrite = 1000, dtime = 2.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 9000., sgmw1 = 4500., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.92, ubar = 1.0, bval = 1.0, twal = 0.1, dpdx = -374.896134, c_rest = 0.0, lambda = 1.0, iuvw = 1, ibf = 2 iortho = 1, nvel = 0, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 1, nskp = 10, immax = 50, epsmin = -16.0,

Output :

mhd-CG step = 1000 28 -1.60258E+01 -5.18635E+00 Tstep = 1000 2.00000E-04 -3.42418E-15 4.10837E+00 3.63715E+00 1.06906E-02



HIMAG 2019


Fig. 2.17b Velocity Profile

Fig. 2.17c V_Comp

HIMAG 2019


Case 2.18 : PPE_MHD

Poisson’s Equation Only, for PPE and MHD

Case 5 Location : Home > mhd > bench > ppe_mhd

Grid Generation :

L = 1 Ha = 0, 1.58, 3.16 Re = 0 CPU = 2 Total number of cells : Between 600-4800

Input File : mhd50/mhd51/mhd52/mhd53/mhd54.input

nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1, iskip = 1, nwrite = 100, dtime = 1.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1.0, sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0/../0.7/1.0/1.0 omega = 1.00, sleng = -/-/-/1.0/.. ubar = 0.0, bx0 = -10., twal = 0.0, dpdx = -0.0, iortho = 2/../../1/2 nvel = 0, nmomt = 0, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0,

HIMAG 2019


ncase = 0/1/2/3/4 ngrad = 2 ichan = 0/../../../10 nskp = 1, ipmax = 5000, immax = 5000, epsmin = -16.0/../-10.0/-16.0/.. Input File : ppe50/ppe51/ppe52/ppe53/ppe54/ppe56.input nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1, iskip = 1, nwrite = 100, nout = -/-/-/0/-/- dtime = 1.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1.0, sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0/../0.7/1.0/../.. omega = 1.00, sleng = -/-/-/1.0/../- ubar = 0.0, bx0 = -10., dpdx = -0.0, ibcpat = -/-/-/-/-/1, iortho = 2, nvel = 0, nmomt = 0, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, ncase = 0/1/2/3/4/6, ichan = 0/../../../10/0, nskp = 1, ipmax = 5000, immax = 5000, epsmin = -16.0/../-10.0/-16.0/-8.0/-16.0,

Boundary Conditions:

ncase = 0

HIMAG 2019


x=0,1: (42222) dphi/dn=0 y=-1,1: (51221) phi=0 z=-1: (51221) phi=0 z=1: (51221) phi=1

ncase = 1

x=0,1: (42222) dphi/dn=0 y=-1,1: (52222) dphi/dn=0 z=-1: (51221) phi=-1 z=1: (51221) phi=1

ncase = 2

x=0,1: (42222) dphi/dn=0 y=-1,1: (52222) dphi/dn=0 z=-1,1: (52222) dphi/dn=0

ncase = 3

x=0,1: (42222) dphi/dn=0 y=0: (41221) phi=sin(pi*z) y=1: (41221) phi=exp(pi)*sin(pi*z)+0.5*z*z z=0: (41221) phi=0 z=1: (41221) phi=0.5*y*y

ncase = 4

x=0,1: (42222) dphi/dn=0 r=1: (51221) phi=z

ncase = 6

x=0,: (21221) phi=1 x=4: (41221) phi=0 y=-1,1: (52222) dphi/dn=0 z=-1,1: (52222) dphi/dn=0

Mass Flow Rate :

HIMAG 2019

100 | M A I N I N D E X

Fig. 2.18a

Fig. 2.18b

HIMAG 2019

101 | M A I N I N D E X

Fig. 2.18c

Fig. 2.18d

HIMAG 2019

102 | M A I N I N D E X

Fig.2.18e

Fig.2.18f

HIMAG 2019

103 | M A I N I N D E X

Fig. 2.18g

Fig. 2.18h

HIMAG 2019

104 | M A I N I N D E X

Fig. 2.18k

Fig. 2.18m

HIMAG 2019

105 | M A I N I N D E X

Fig. 2.18n

Fig. 2.18p

HIMAG 2019

106 | M A I N I N D E X

Case 2.19 : SHERFUL_HA300

Shercliff’s Fully-Developed Flow

Case 5 Location : Home > mhd > bench > sherful_ha300

Grid Generation :




HIMAG 2019

107 | M A I N I N D E X

Input File :

nodes = 2, iread = 0, grid_scale = 1.0, istart = 0, nmax = 7000, iskip = 7000, nwrite = 7000, dtime = 2.0e-4, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 9000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, ubar = 1.0, bval = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -31.6583368, iortho = 1, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, immax = 40, epsmin = -16.0,

Output :



Time : 1 min approx. on 2 CPUs

HIMAG 2019

108 | M A I N I N D E X

Fig. 2.19b U Profile

Fig. 2.19c U-yz

HIMAG 2019

109 | M A I N I N D E X

Fig. 2.19d V_Comp

HIMAG 2019

110 | M A I N I N D E X

Case 2.20 : SHERFUL_HA500_IO2

Shercliff’s Fully-Developed Flow, Irregular Grid

Case 5 Location : Home > mhd > bench > sherful_ha500_io2

Grid Generation :



Fig 2.20a Rectangular Duct Irregular Grid

HIMAG 2019

111 | M A I N I N D E X

Input File :

nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 20000, iskip = 10000, nwrite = 10000, dtime = 7.5e-5, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 25000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, ubar = 1.0, bval = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -52.0854546, c_rest = 0.0, iortho = 2, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, immax = 20, igmax = 3, epsmin = -16.0,

Output :



Time : 6 min approx. on 2 CPUs

HIMAG 2019

112 | M A I N I N D E X

Fig. 2.20b Velocity Profile

Fig. 2.20c U-yz

HIMAG 2019

113 | M A I N I N D E X

Fig. 2.20d V_Comp

HIMAG 2019

114 | M A I N I N D E X

Case 2.21 : THERM

Heat Transfer

Case 5 Location : Home > mhd > bench > therm

Grid Generation :

L = 1 Ha = 0 Re = 0 CPU = 1 or 2 Total number of cells : 300-600



HIMAG 2019

115 | M A I N I N D E X

Fig 2.21b Rectangular duct grid

Input File : heat10_prm / heat11_prm / heatk2_prm.input

nodes = 2 /1 /1 iread = 0, grid_scale = 1.0, nmax = 1, iskip = 1, nwrite = 5000, dtime = 1.0e-2 /.. /5.0e-2 cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, alpha = 1.0 /.. /0.4 omega = 1.92, ubar = 0.0, dpdx =-0.0, hk1 = 1.00, cp1 = 1.00, hkw1 = 1.00 /.. /4.00 cpw1 = 1.00, tref = 1.00, deltT = 1.00 /2.00 / 1.00 iortho = 2, nvel = 0, nmomt = 0, nppe = 0, nmhd = 0,

HIMAG 2019

116 | M A I N I N D E X

nheat = 2, ncase = 10 /11 /12 ilaw = 0, ilevels = 0, ichan = 0 /.. /4 nskp = 10, ipmax = 2000, ibuoy = 0, igravt = 0, idissp = 0, gx = 0.0, gy =-9.81, gz = 0.0,

HIMAG 2019

117 | M A I N I N D E X

Case 2.22 : WALL

Wall Function at Hartmann Layer, Shercliff’s Flow

Case 5 Location : Home > mhd > bench > wall

Grid Generation :




HIMAG 2019

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Input File :

nodes = 1, iread = 0, nmax = 3000, iskip = 3000, nwrite = 10000, dtime = 5.0e-5, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 25000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, omega = 1.0, dpdx = -52.0854546, iortho = 1, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, iuvw = 1, ngrad = 2, ichan = 0, nskp = 10, immax = 50,

Output :




HIMAG 2019

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Fig. 2.22b U profile

Fig. 2.22c Velocity

HIMAG 2019

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Fig. 2.22d Jy Jz

Fig. 2.22e Current

HIMAG 2019

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Fig. 2.22f U_Contour

himag...ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0, output: 10000th...

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