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Cyp November 17, 2010 08:58

Two Phase Darcy flow with gravity -> problem
 
Hi everybody!

I am currently working on a Darcy two phase flow solver with IMPES method (IMplicit Pressure Explicit Saturation). I want to simulate a two phase flow in porous media in 3D. It is why I use permeability tensor fields. These permeabilities depend on the liquid saturation

Here is the snippet I programmed in OpenFOAM:
Code:


        M_beta  = K*pow(S,2)/mu_beta;
        M_gamma = K*pow((scalar(1.0)-S),2)/mu_gamma;

        phi_beta  = linearInterpolate( (rho_beta*M_beta & g))  & mesh.Sf();
        phi_gamma = linearInterpolate( (rho_gamma*M_gamma & g)) & mesh.Sf();


        fvScalarMatrix pEqn
        (
            fvm::laplacian((M_beta + M_gamma),p)
        == fvc::div(phi_beta) + fvc::div(phi_gamma)
        );   
        pEqn.relax();
        pEqn.solve();

        fvScalarMatrix SEqn
        (
          fvm::ddt(eps,S) - fvm::laplacian(diffS,S)
        == (fvc::laplacian(M_beta,p)) -  fvc::div(phi_beta)
        );
        SEqn.relax();
        SEqn.solve();

        U_beta = -(M_beta&fvc::grad(p))+((rho_beta*M_beta)&g);
        U_gamma = -(M_gamma&fvc::grad(p))+((rho_gamma*M_gamma)&g);

where
- S and p are volScalarFields
- M_beta and M_gamma are volTensorFields.
- K is a dimensionedTensor

The compilation is ok.

As a validation case, I simulate a the flow through a 1D vertical column: I inject a liquid at the top of column initially filled up with gas. the simulation is correct on a case without gravity (g= (0 0 0)). However, the code diverges when I tried to simulate a flow with gravity (g = (0 -9.81 0)).

Is there something wrong with the gravity in my code ?

Best Regards,
Cyp


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