On Wed, 4 Dec 2013, Manav Bhatia wrote:
For some of my earlier work I had used Kelly's error estimator for
transonic flow problems, and it did exactly what you have described.
It kept on refining the elements at the shock, and around the
leading edge and trailing edge locations of an airfoil, which are
locations of singularity.
My experience was even worse than that - if the shock wasn't
completely refined on one pass, then those unrefined parts would *not*
be flagged for further refinement on the next pass. It wasn't just
overrefining into the shock, it was overrefining into somewhat
arbitrary subsets of the shock.
I am guessing that goal-oriented errors are better metrics to use,
since for many applications it does not make sense to refine the
shock locations beyond a certain point.
I think so. What I'd *really* like to see is a subnorm-based error,
though. Adjoint-based refinement optimizes for the error in a few
scalar-valued quantities of interest, standard refinement optimizes
for the error in a global norm like H1(Omega) or L2(Omega); why can't
I do something in between, like just optimizing for the error in a
seminorm? L2(Gamma_D) on some boundary, say.
So, it likely makes more sense to use an L2 norm in these regions of
shocks and singularities. Your comment about using patch recovery is
due to not having a reference solution (on a very refined mesh), so
post-processing the existing results is likely the only way to get a
better reference solution.
That's right.
Do you think patch recovery is a good approach for shock locations?
Yeah. Shocks are *easy* to detect. Whether patch recovery gives a
good balance between controlling error in the shock and error in a
boundary layer is more questionable.
Would error norms based on H1-norm be better choices than those
based on L2 norm for smoother solutions (no shocks, for example)?
I believe so.
---
Roy
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