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Is div(grad(U))=laplacian(U) ???

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Old   October 4, 2012, 08:00
Default Is div(grad(U))=laplacian(U) ???
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M Mallikarjuna Reddy
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Hi Everyone,
I have a doubt about div() and laplacian(). For the general case in all solvers we written gamma*div(grad(U))=laplacian(gamma, U).
But when i checked by replacing fvc::laplacian(gamma, U) =gamma*fvc::div(fvc::grad(U)) for the icoFoam solver, the solution is diverging (Courant Number going to high value).
Anyone please clarify my doubt.

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Mallikarjuna
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Old   October 6, 2012, 06:51
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Hi
I think you see instability because you use a non-conservative form.
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Old   October 7, 2012, 01:39
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M Mallikarjuna Reddy
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Hi Ata,
Thanks very much quick reply. You are correct, i am getting instability. could you please suggest me to rectify this problem. I need to use div(gradU+gradU.T()) in my problem.

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Mallikarjuna
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Old   October 7, 2012, 05:02
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Hi
May using lower relaxations be helpful.
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Old   October 7, 2012, 06:41
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Hi Ata,
Thanks for your reply. I tried with low relaxation factor but it is not working. Is there any other method to solve this problem? If it is there please guide me

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Mallikarjuna.
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Old   October 7, 2012, 07:14
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Hi
Would you please tell me what relaxation factors you used?
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Old   October 7, 2012, 08:02
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hi Ata,
I have taken relaxation factor as 0.2. But still it is coming the same

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Mallikarjuna
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Old   October 7, 2012, 08:29
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Hi
Is the problem unsteady state? If yes how much is your time step and max courant number?
You used 0.2 for all equations?
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Old   October 8, 2012, 01:07
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Hi Ata,
My solver is steady state. I have taken relaxation factors as for p=0.2,U=0.07.

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Old   October 8, 2012, 05:08
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Hi
What is your solver?
Could you try both of relaxation factors 0.01?
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Old   October 8, 2012, 06:08
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Hi Ata,
I developed my own solver for predicting velocity profile(U) and particle concentration profile(T) for suspension flow (fluid+particles). And in my momentum equation, the viscosity is not constant, it is function of particle volume fraction(T).

I am attaching my solver.

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Mallikarjuna
Attached Files
File Type: gz sbmFoam.tar.gz (2.9 KB, 5 views)
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Old   October 9, 2012, 06:45
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Hi
Is it possible to write your solver in a conservative form?
Did you try both of relaxation factors 0.01?
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Old   October 9, 2012, 06:57
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Hi Ata,
I tried for both of relaxation factors 0.01. I think my solver is in non conservative form.
At First i tried for icoFoam solver by replacing laplacian (nu, U) by nu*fvc::div(fvc::grad(U)).
And i tried another method where laplacian(U)=div(faceFluxes).
Code:-

surfaceVectorField surfNormalGradDU = fvc::snGrad(U);
surfaceVectorField n = mesh.Sf()/mesh.magSf();
surfaceTensorField surfGradDU=(n*surfNormalGradDU) + ((I-n*n)&(fvc::interpolate(fvc::grad(U))));

fvVectorMatrix UEqn
(
fvm::ddt(U)
+ fvm::div(phi, U)
- nu*fvc::div(mesh.magSf()*(surfGradDU&n))
);


But i am getting the divergence problem.


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Mallikarjuna
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Old   October 9, 2012, 07:14
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Hi
Could you first calculate the viscosity and then use fvm::laplacian(nu, U) in your code?
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Old   October 10, 2012, 02:32
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Hi Ata,
I tried for the icoFoam solver and for cavity case. I taken relaxation factors as you suggested 0.01 for both p and U. Here nu is constant. And i used gauss linear for div() and Gauss linear corrected for laplacian().

Should i change these schemes to other schemes?

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Old   October 10, 2012, 05:23
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Ho
For start they are good. What did you got using these?
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Old   October 10, 2012, 05:32
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Hi Ata,
when i run my case by using modified icoFoam solver, it is running some iterations giving some error as follows.

Error:-

Time = 0.145

Courant Number mean: 7.93942e+94 max: 1.42329e+96
DILUPBiCG: Solving for Ux, Initial residual = 0.999994, Final residual = 0.980212, No Iterations 1001
DILUPBiCG: Solving for Uy, Initial residual = 1, Final residual = 1.46608, No Iterations 1001
DICPCG: Solving for p, Initial residual = 1, Final residual = 0.0270296, No Iterations 1001
time step continuity errors : sum local = 6.53592e+99, global = -4.90912e+83, cumulative = -4.90911e+83
#0 Foam::error:rintStack(Foam::Ostream&) in "/opt/openfoam211/platforms/linuxGccDPOpt/lib/libOpenFOAM.so"
#1 Foam::sigFpe::sigHandler(int) in "/opt/openfoam211/platforms/linuxGccDPOpt/lib/libOpenFOAM.so"
#2 Uninterpreted:
#3 Foam::PCG::solve(Foam::Field<double>&, Foam::Field<double> const&, unsigned char) const in "/opt/openfoam211/platforms/linuxGccDPOpt/lib/libOpenFOAM.so"
#4 Foam::fvMatrix<double>::solve(Foam::dictionary const&) in "/opt/openfoam211/platforms/linuxGccDPOpt/lib/libfiniteVolume.so"
#5
in "/home/malli_reddy/OpenFOAM/malli_reddy-2.1.1/platforms/linuxGccDPOpt/bin/testIcoFoam"
#6
in "/home/malli_reddy/OpenFOAM/malli_reddy-2.1.1/platforms/linuxGccDPOpt/bin/testIcoFoam"
#7 __libc_start_main in "/lib/i386-linux-gnu/libc.so.6"
#8
in "/home/malli_reddy/OpenFOAM/malli_reddy-2.1.1/platforms/linuxGccDPOpt/bin/testIcoFoam"
Floating point exception

i have checked the solution in paraView, the results are out of expectations.

Thanks
Regards
Mallikarjuna
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Old   October 10, 2012, 05:45
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Hi
How much is your max. Courant number?
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Old   October 10, 2012, 05:52
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Hi Ata,
At the last iteration it is max: 1.42329e+96. And my delta t is 0.005. At first iteration courant no < 1. But it is gradually increasing.

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Old   October 10, 2012, 08:15
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Hi
Decrease your delta T.
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