[shainath]

Central schemes like JST uses artificial dissipation for the stabilization. This modification is an artificial one. Does this additional term makes system inconsistent? Can we expect this term to be zero at the end of the simulation? This is in reference with incompressible flow schemes. In the following references they have used the pressure differences as a dissipation to continuity equations. Is it must to reach these terms to zero at the end of the simulation (steady)?

Reference 1(Link: http://heja.szif.hu/ANM/ANM-030110-A/anm030110a.pdf)


Reference 2(Link: http://www.sciencedirect.com/science...21999199963155)

[FMDenaro]

the scheme should be consistent in the sense that the numerical dissipation mathematical vanishes as the grid size goes to zero.
Of course, in any numerical simulation that does not happen and you have a "modified equation"

[shainath]

Thanks a lot FMDenaro Sir for the answer,
I still have a doubt. In principle for Artificial compressibility method lower values of norms of time derivative terms indicates the satisfaction of divergence of velocity. But in the above cases where artificial dissipation is added to continuity equation which will not go zero at the end of pseudo-transience. Will there also norms of time derivative terms indicates the satisfaction of divergence of velocity?

[FMDenaro]

Originally Posted by shainath

Thanks a lot FMDenaro Sir for the answer,
I still have a doubt. In principle for Artificial compressibility method lower values of norms of time derivative terms indicates the satisfaction of divergence of velocity. But in the above cases where artificial dissipation is added to continuity equation which will not go zero at the end of pseudo-transience. Will there also norms of time derivative terms indicates the satisfaction of divergence of velocity?

I never worked using such formulation thus I cannot give my experience but I suppose you should always define a norm on the residual of the equation.
You should provide some more details about your formulation

[shainath]

I am trying the formulation given in reference 2.