Tensor op to calculate viscous terms

[jagmohas]

I IAMR (Diffusion.cpp, line 1647) Diffusion::getTensorViscTerms uses mlmg.apply to calculate the viscous terms. I can't figure out how it does so. Could you please suggest where to look for to understand this maths?

[WeiqunZhang]

Is this a programming question about what mlmg.apply does or a math question about what the viscous terms are?

[jagmohas]

Thanks Weiqun for looking into this. My question is how mmlg calculates the viscous terms. It could be mixed of both programming and math.

I understand that with tensorop.setScalars(a, b) where a=0,b=-1, we are solving (\nabla \cdot \beta \nabla ) \phi = f. I can't figure out where do we set f ?

And when we call mlmg.apply({&visc_tmp}, {&s_tmp});, s_tmp is velocity? I understand that s_tmp contains the data from S assigned at line 1678 of Diffusion.cpp

MultiFab::Copy(s_tmp,S,Xvel,0,AMREX_SPACEDIM,0);

[WeiqunZhang]

The apply function applies the linear operator L without involving the RHS of the linear system L(phi) = f. More specifically the linear system in the code you mentioned is alpha a v - beta div dot tau = rhs, where tau = eta [grad v + (grad v)^T] + (kappa-(2/3)eta) (div v) I, eta and kappa are shear and bulk viscosity, and I is identity tensor. See amrex/Src/LinearSolvers/MLMG/AMReX_MLTensorOp.H for more details.

[drummerdoc]

The getViscTerms function is a little different though. It is (1/Vol) Integral( Div(tau) ), i.e., does not have the time discretization terms that are usually the and is volume weighted, thus there's no a*alpha contribution, and b=-1 to get the sign right.