anisotropic porous media in OpenFOAM
Does anyone have any experience in simulating flow in anisotropic porous media in OF? I mean simulations in which the permeability in x direction is different from the permeability in y direction.
My main problem is that when I am adding the darcy soource term as + ((1/Perm)*(fvm::Sp(Visc,U))) I do not know how to tell the OF that Perm will be different based on the direction! comments are appreciated! 
hi mahdi
is in this condition permeability ("Prem") a vectorField? if yes, you can define a volVectorField for Prem, then assign your directional variation with setFields in 0 folder 
Permeability Vector
Hi nimasam
Thanks for the comment. But, if I define the permeability as volVectorField then, when I want to multiply it by velocity what kind of vector multiplication do I have to use; definitely not inner or cross product. Right? 
Hi Mahdi
In the case of nonisotropic permeability, the permeability is a symmetric tensor. For anisotropy, you should assign zero offdiagonal values and be left with kxx, kyy and kzz. Hope this helps! Regards Hisham 
multiplying permeability tensor and velocity vector
Dear Hisham
Thanks for the comment. I know that true, but, as I mentioned in my previous post, I am not sure how to multiply permeability tensor and velocity vector in the momentum equation. What kind of multiplication operator do I have to use? 
dear mahdi,
if you want to divide Ux/Kx , Uy/Ky , Uz/Kz then i guess you may want to use some thing like this : forAll(U,celli) { S[celli].x() = U[celli].x()/Kx[celli].x(); ........ } 
I think you first would have to define the tensor as k (kxx 0 0 kyy 0 kzz), then get the inverse of the tensor as inv(k). The product should be an inner product: + (inv(k) & (fvm::Sp(Visc,U))
I would appreciate it if you report what happened! Best regards, Hisham 
Dear Hisham
I have define a tensor named PermTenInv which has diagonal terms of 1/kxx,1/kyy and 1/kzz. Now when i am doing explicit calculations in form of + ((PermTen) & (fvc::Sp(Visc,U))) there is no error. However, for implicit calculations in form of ((PermTen) & (fvm::Sp(Visc,U))) I get the following error  BR1IM003.C:84:40: error: no match for ‘operator&’ in ‘PermTen & Foam::fvm::Sp(const Foam::dimensionedScalar&, Foam::GeometricField<Type, Foam::fvPatchField, Foam::volMesh>&) [with Type = Foam::Vector<double>, Foam::dimensionedScalar = Foam::dimensioned<double>](((Foam::GeometricField<Foam::Vector<double>, Foam::fvPatchField, Foam::volMesh>&)(& U)))’ /opt/openfoam171/src/OpenFOAM/lnInclude/wordI.H:167:19: note: candidates are: Foam::word Foam::operator&(const Foam::word&, const Foam::word&) /opt/openfoam171/src/OpenFOAM/lnInclude/dimensionSet.H:273:29: note: Foam::dimensionSet Foam::operator&(const Foam::dimensionSet&, const Foam::dimensionSet&) /opt/openfoam171/src/finiteVolume/lnInclude/readPISOControls.H:8:10: warning: unused variable ‘momentumPredictor’ /opt/openfoam171/src/finiteVolume/lnInclude/readPISOControls.H:11:10: warning: unused variable ‘transonic’ /opt/openfoam171/src/finiteVolume/lnInclude/readPISOControls.H:14:9: warning: unused variable ‘nOuterCorr’ make: *** [Make/linux64GccDPOpt/BR1IM003.o] Error 1  Unfortunately, I have to discretise this source term implicitly. Any ideas how to fix this error? 
Dear Mahdi,
It is really sad that this did not work directly. You can report this as a bug (assuming a similar feature should be available). If you are highly motivated for your problem you can try to add a new fvm::Sp function to fvmSup.C/.H that can take a "dimensionedVector & sp" argument. You then have to dig deep into OpenFOAM's number crunching mechanisms and figure out which elements of fvm.diag() should you multiply by which component. Here ends my ideas. I hope you can find an easier solution! Code:
template<class Type> Hisham 
THnaks Hisham. I am going to discuss it in a new post to be sure that this is a bug in OF.

Hello Mhadi,
is there any progress in the subject? I am coding something similar for solidification and encounter the same problem. Regards, Anja 
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Any solution?
Hi y'all,
I also need to implement an implicit anisotropic source term. Did anyone find a way to do that? fvm::Sp seems to not accept a tensor as coefficient... thanks 
Try to create an homogeneous hydrodynamic resistance and then subtract a given fraction (fAniso) in the direction nT (unitary vector):
+ fvm::Sp(Rmush,U)  fAniso*Rmush*(U&nT)*nT if fAniso is 1, the resistance in the direction nT is zero, if fAniso is 0 then you have no anisotropy. 
Didn't get it
Thanks for the reply, Vitor, but I didn't get it.
In your suggestion, what is Rmush? Because if it is a tensor, it does not work... Maybe what you're suggesting is something I've already tried: to implement that in 2 terms, one implicit and isotropic, and one explicit and anisotric. But in my case it does not work, because the largest part of the resistance is specifically the anisotropic part, and any explicit treatment of that refuses to converge... 
Rmush is a volScalarField which may be computed for instance by the Kozeny Carman correlation.

How to code the anisotropic heterogeneous source term as implicit?
Ok, but this way the anisotropic part is still explicit, right? Any way to code the anisotropic heterogeneous source term as implicit?

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