# Reply To: Advection Diffusion D3Q19 Boundary Condition

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Dear Stephan,

Thank you for your reply. My argumentation is the following.

– At high Re, using BGK + D3Q7 (+ smagorinsky) for the advection-diffusion appears to violate the positivity of the solver (the scalar field is expected to remain positive but negative values are observed in the domain due to oscillations). Therefore, I need to stabilize the advection-diffusion lattice in some way.

– From the paper of Junk (2001) “A finite difference interpretation of the Lattice Boltzmann method”, I assume that the D3Q7 lattice is equivalent to centered finite difference scheme, which is known to be unstable at high values of Re (as stated for instance in the book of Versteeg and Malalasekera “An introduction to computational Fluid Dynamics: the finite volume method”, section 5.3).

– Therefore, a first idea would be to try the D3Q19 on the advection-diffusion lattice. Also, the D3Q19 would allow me to use an entropic collision operator for the advection diffusion in order to guarantee positivity, which would be (I think) a promising stabilization possibility.

So I tried to add the line “boundaryDynamics.collide(cell, statistics);” between the lines 113 and 114 of advectionDiffusionBoundaries.hh, but it turns out that the results are not better; the oscillations are more pronounced and the scalar field is less physical than before.

So I guess I will keep the previous version (without the collide), for which there might be a theoretical/practical justification.. by the way, maybe the problems I am facing here are related to something else than the inlet BC.

Anyway, if you have any general advice as to how to stabilize the advection-diffusion solver for high Re, I would be interested to know.

Thank you for your time!

Best regards

Mathis