simultaneously solve number of diffusion equations

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August 26, 2014, 08:21
simultaneously solve number of diffusion equations
#1
New Member

Shakil Masum
Join Date: Aug 2014
Posts: 10
Rep Power: 5
Hi,

I want to solve these equations using OpenFOAM. The diffusion equations are:

dC0/dt = D1 d2/dx2 C0
dC1/dt = D1 d2/dx2 C1 + D2 d2/dx2 C0 (please check the attachment, I have typed them properly in the attachment).

I can solve the equations using Laplacian Foam individually. But, I want to solve both equations simultaneously, I mean in every time steps. The problem is the second equation needs the value of C0 (from first equation) in every time step. What changes are required in laplacianFoam.C and also in the '0', 'constant' and 'system' folders? It will be much appreciated.

thanks
shakil
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 August 27, 2014, 06:04 #2 New Member   Alex Join Date: Apr 2011 Location: München Posts: 13 Rep Power: 8 You could try to define your concentrations C1 and C0 as a vector and solve one PDE system instead of two separate PDEs. That means a volVectorfield instead of a volScalarField in your createFields.H. Best regards, Al

 August 27, 2014, 08:59 simultaneously solve number of diffusion equations #3 New Member   Shakil Masum Join Date: Aug 2014 Posts: 10 Rep Power: 5 Thanks for your reply al_pr. But I am worried that you cannot consider C0 and C1 as vectors. These are concentrations which are scalars and direction independent.

 August 27, 2014, 09:45 #4 Member   Join Date: Nov 2012 Posts: 72 Rep Power: 7 you could formulate it is explicit. Equations. dC0/dt = D1 d2/dx2 C0 dC1/dt = D1 d2/dx2 C1 + D2 d2/dx2 C0 (please check the attachment, I have typed them properly in the attachment). in OpenFOAM: C0Eqn { fvm::ddt(C0) == fvm::laplacian(D1,C0) } C1Eqn { fvm::ddt(C1) == fvm::laplacian(D1,C1) +fvc::laplacian(D2,C0) }

 August 27, 2014, 13:07 #5 New Member   Shakil Masum Join Date: Aug 2014 Posts: 10 Rep Power: 5 Dear Henning86, Thanks a lot. I think this is a brilliant idea. I believe it will also solve the the problem of solving two equations simultaneously in every time step with the updated value of C0 to calculate C1. Am I right to interpret in this way? Thanks again

 August 29, 2014, 05:02 #6 Member   Join Date: Nov 2012 Posts: 72 Rep Power: 7 yes you are right. As C1Eqn has an explicit term you are limited by the time step.

 Tags diffusion, laplacian

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