Which application should I use to solve this equation
 

Hello Foamers,
I am a beginner, which application should I use to solve these equation

In region 1
∇∙[(1-s)^1.5 ∇c]=0
∇∙[s^3 (-4.24s+〖3s〗^2)∇s]=0

In region 2
∇∙[(1-s)^1.5 ∇c]=1-s
∇∙[s^3 (-4.24s+〖3s〗^2)∇s]=1-s

anyhelp will be thankful.

I suggest to write your own application, that is what you can do with OpenFOAM relatively easily. No guarantees for convergent solutions however. Especially since you equations are not very linear in s :) Good luck!

Thanks.
Are there similar standard applications I can modify to solve it?

You can have a look in the basic solvers to start with.

Hi!

I think you can start from laplacianFoam and define a source term that depends on the region you consider. You can develop something like that :

where alpha is a volScalarField defined by
- 0 within Region 1
- 1 within Region 2

I advise you to use the setFields utility to set up alpha.
Be careful to the units.

Best regards,
Cyp

Thanks a lot
Another question, how can I deal with the interface boundary condition between region1 and region2. Suppose c(region1)=c(region2).

I guess that if you defined your 2 regions by an indicator function such as "alpha", the continuity is automatically garanteed.

Regards,
Cyp

You can use conjugateHeatFoam (in the dev versions) or chtMultiRegionFoam for this. These solvers will ensure a continuous flux between the regions as well as c(region1)=c(region2).