[JasmineFeng]

Originally Posted by FMDenaro

One of the fundamental property of a convection-diffusion PDE is that it does not create new extrema in the solution. Therefore, it is clear that in a numerical solution the presence of new extrema is not physically meaningful. Monotone schemes have a property to guarantee that.

But, if a source term is added in the PDE, the action of such a term can actually produce new physical extrema.

I see. A positive (negative) source can create a local maximum (minimum), in which case the values of internal nodes will exceed those of the boundary nodes, namely unbounded results.

[JasmineFeng]

Originally Posted by FMDenaro

I don't understand what you are doing. Negative Peclet means an anti-diffusive problem.

Are you just trying to replicate the 1D stready convection-diffusion exercise shown in the textbook of Ferzigr, Peric and Street?

I don't think diffusion will change with the sign of the grid Peclect number.
Pe=ρ*u*Δx/Γ
So Pe > 0 denotes u>0 and Pe<0 denotes u<0, but the diffusive coefficient Γ keeps the same.

Yeah, this is a 1D steady convection-diffusion exercise without any source term. But from Versteeg and Malalasekera's textbook instead of Ferziger et al's.

[arjun]

Originally Posted by JasmineFeng

I got it. Because schemes like SOU and MUSCL are unconditionally stable, so they will always produce bounded results without wiggles.

Yes. If you got stable and good results with CD on those peclet numbers you would have broken known mathematics. When we use unbounded CD all the solvers produce wiggle in solution or just diverge. This is why we have bounded central differencing schemes in solvers. This scheme blends enough upwind scheme to the make it stable.

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