On Mon, 31 May 2010, Jonathan wrote:
> As mentioned in the subject, I have two main questions. The first is
> in regard to patch definition. I know how to define them and so on..
> but what I would like to know is if there are general guidelines to
> efficient patch definition when it comes to problems with (non-
> rectangle) internal boundaries.
> For example, in the problem of a 2D inert shock passing over an
> obtuse triangle, with the lower edge lying along the south boundary of
> the domain. Is it best to have two patches, meeting at the peak of the
> triangle? Or one patch per ramp and one for each flat area, before and
> after the triangle? Does it matter?
The short answer is that it should not really matter.
Therefore do whatever is convenient for the problem in hand.
>
> My second question is also tied to the example above. The gap between
> the peak of the triangle and the north boundary is very small (a
> requirement of the problem). As the shock wave passes through the gap,
> the ensuing rapid expansion causes a negative pressure, generating a
> NaN, with the solvers I have tried, with the exception of the
> Godunov_km solver. However, Matei has informed me that the Godunov
> solver is over diffusive and my simulation loses wanted detail in the
> post-shock sections. Is there a list of non reactive Euler equation
> solvers (including a few positivity conserving ones) other than the
> ones mentioned in the VKI notes, ie. godunov, roe, hlle and ausm.
The Godunov solver is not that much more diffusive than say the Roe
solver, but in some circumstances a small loss in resolution may be
enough to undermine the refinement criteria used. Therefore I'd
be inclined to stick with the most robust solver you have then
check that the refinement criteria are working as intended.
If they are then you can always add in more refinement to recover the
flow details. And if they aren't, they need fixing before you worry
about the patch integrator.
James