TVD schemes, questions about limitedLinear
Join Date: Apr 2014
Posts: 32Rep Power: 3
I've been reading about the numerical schemes in OpenFOAM, and I found (perhaps) some divergence concerning the TVD schemes and Sweby limiters.
In Dr. Jasak's thesis (pg 98), it says that:
So for ψ = 1 we get a Higher Order scheme (central difference), while ψ = 0 we get Upwind.
The thing is, at OpenFOAM's website (http://cfd.direct/openfoam/user-guid...20-1140004.4.5), it is said that "Some TVD/NVD schemes require a coefficient ψ,0 ≤ ψ ≤ 1 where ψ = 1 corresponds to TVD conformance, usually giving best convergence and ψ = 0 corresponds to best accuracy". But doesn't that mean that for ψ = 0 we get the higher order (more accurate) and ψ = 1 we get less accurate (Upwind)? And isn't it the opposite of what is written in Dr. Jasak's thesis?
I expected that limitedLinear 0.5 would be the same as linearUpwind grad(U), but when I run the same case for these two schemes, the results are different.
Also, as stated in this thread (A few simple questions about linearUpwind and limitedLinear), I thought that limitedLinear 0 would be equal to upwind and limitedLinear 1 would be equal to linear, but it is not the case.
Did I understand thing in a wrong way, or is there an inconsistency? Also, should these schemes be indeed the same or not?
Thanks in advance.
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