(Puzzling) gradient assembly for art. comp. viscous fluxes

Sprotte · March 31, 2016, 07:10

Hi,

currently I am working through the code (primarily the NS-Solver in incompressible mode) and now I got stuck at the first lines that I don't understand.
I think I will need some help here, so maybe it's time for my first post..

I totally "agree" with the CNumerics::GetViscousArtCompProjFlux-routine (called by CNSSolver::Viscous_Residual via CAvgGradCorrectedArtComp_Flow::ComputeResidual), but the corresponding CNumerics::GetViscousArtCompProjJacs-routine puzzles me.
I wrote out the Mean_GradPrimVar-Variables in terms of conservative variables, but despite for the second term in the term for the gradient correction, which - after multiplying with the edge normal - contributes a factor that is itself named "factor" in GetViscousArtCompProjJacs, there were no promising matches.
On top of that, I can't figure out why - for viscous fluxes in this particular case - the i-th residual is dependent from other than the i-th conservative variable, as the code for the Jacobian assembly indicates.

If anyone could provide me with a hint on what's going on there, I would be really grateful. Thanks in advance!!

Regards, Ole

Sprotte · April 1, 2016, 08:47

I found a partial answer to my question (though I'm not sure whether to edit my first post or to reply, but since it is not really a correction..)

I found out that gradients for flow and Jacobian calculations are obviously approximated differently. In my first attempt, I wanted to take the derivative of the Green-Gauß method (with subsequent averaging) and I ended up just finding the right coefficient for the correction term that was not calculated by Green-Gauß (but by "TSL", if that's correct?).

My other question remains open. Why is the vanishing flow divergence assumption for incompressible fluids only used for flow calculation, but not for the calculation of its Jacobian?

Thank you for any effort

March 31, 2016, 07:10	(Puzzling) gradient assembly for art. comp. viscous fluxes	#1
Sprotte Member Ole Burghardt Join Date: Mar 2016 Location: Kiel, Germany Posts: 60 Rep Power: 10	Hi, currently I am working through the code (primarily the NS-Solver in incompressible mode) and now I got stuck at the first lines that I don't understand. I think I will need some help here, so maybe it's time for my first post.. I totally "agree" with the CNumerics::GetViscousArtCompProjFlux-routine (called by CNSSolver::Viscous_Residual via CAvgGradCorrectedArtComp_Flow::ComputeResidual), but the corresponding CNumerics::GetViscousArtCompProjJacs-routine puzzles me. I wrote out the Mean_GradPrimVar-Variables in terms of conservative variables, but despite for the second term in the term for the gradient correction, which - after multiplying with the edge normal - contributes a factor that is itself named "factor" in GetViscousArtCompProjJacs, there were no promising matches. On top of that, I can't figure out why - for viscous fluxes in this particular case - the i-th residual is dependent from other than the i-th conservative variable, as the code for the Jacobian assembly indicates. If anyone could provide me with a hint on what's going on there, I would be really grateful. Thanks in advance!! Regards, Ole

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April 1, 2016, 08:47		#2
Sprotte Member Ole Burghardt Join Date: Mar 2016 Location: Kiel, Germany Posts: 60 Rep Power: 10	I found a partial answer to my question (though I'm not sure whether to edit my first post or to reply, but since it is not really a correction..) I found out that gradients for flow and Jacobian calculations are obviously approximated differently. In my first attempt, I wanted to take the derivative of the Green-Gauß method (with subsequent averaging) and I ended up just finding the right coefficient for the correction term that was not calculated by Green-Gauß (but by "TSL", if that's correct?). My other question remains open. Why is the vanishing flow divergence assumption for incompressible fluids only used for flow calculation, but not for the calculation of its Jacobian? Thank you for any effort