# anisotropic diffusion fvm::laplacian

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 December 30, 2012, 11:18 anisotropic diffusion fvm::laplacian #1 New Member   Michael Buchmayr Join Date: Mar 2010 Posts: 16 Rep Power: 9 Sponsored Links Hi, I have had a look at the implicit discretization of anisotropic diffusion (fvm::laplacian). It seems to me that the implementation is wrong. At least I haven't yet managed to figure out why the coefficients are as they are. It is fairly easy to follow in Ferzinger & Peric how the non-orthogonal correction approach is done for scalar "gamma" fields. For tensor fields it's a bit more tricky. What is being passed to the uncorrected (implicit) laplacian function is the scalar field sfGammaSn. For me it would make sense to pass a vector field sfGamma and then split the derivative nabla(vf) into a derivative along d and a derivative along sfGamma_{unity}. I think the way fvm::laplacian is implemented now shouldn't even work for scalar "gammas" right? Otherwise there wouldn't exist a template version for fvm::laplacians for scalars. I would appriciate if anybody can exchange thoughts on this topic / approves my thoughts / teaches me wrong / explains to me the implementation. Cheers, Michi template tmp > gaussLaplacianScheme::fvmLaplacianUncorrected ( const surfaceScalarField& gammaMagSf, actually passes sfGammaSn const GeometricField& vf ) { tmp tdeltaCoeffs = this->tsnGradScheme_().deltaCoeffs(vf); const surfaceScalarField& deltaCoeffs = tdeltaCoeffs(); tmp > tfvm ( new fvMatrix ( vf, deltaCoeffs.dimensions()*gammaMagSf.dimensions()*v f.dimensions() ) ); fvMatrix& fvm = tfvm(); fvm.upper() = deltaCoeffs.internalField()*gammaMagSf.internalFie ld(); fvm.negSumDiag(); Last edited by MichiB; January 10, 2013 at 05:43.

 January 10, 2013, 05:47 #2 New Member   Michael Buchmayr Join Date: Mar 2010 Posts: 16 Rep Power: 9 I figured out that the coeffs indeed correspond to what I've derived which is (Sf dot Gamma dot Sf)/(Sf dot d) ... for the uncorrected laplacian. I hope I didn't confuse anyone that read this message! If so, sorry!

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