use adaptive stepping for exact Riemann integration

zingale commented 4 weeks ago

PR summary

There are 2 main changes here:

the riemann_support.H header is now split into 2, one for shocks and one for rarefactions
the rarefaction integration no longer uses a fixed stepsize, but instead now does an adaptive RK4 integration

This changes results to roundoff / tol error, as expected.

PR motivation

PR checklist

[ ] test suite needs to be run on this PR
[ ] this PR will change answers in the test suite to more than roundoff level
[ ] all newly-added functions have docstrings as per the coding conventions
[ ] the CHANGES file has been updated, if appropriate
[ ] if appropriate, this change is described in the docs

zingale commented 3 weeks ago

Here are comparisons of density for the 4 test problems from our 2015 paper:

riemann_compare_test1 riemann_compare_test2 riemann_compare_test3 riemann_compare_test4

zingale commented 2 weeks ago

Here are some of my notes for this: exact_riemann.pdf

zingale commented 2 weeks ago

I don't think that the expression I am using is wrong. If the iteration were successful, then u_star,l = u_star,r, so this average is just dealing with the tolerance of the solver.

zingale commented 2 weeks ago

it is actually just a different average, the Z's there are the slope at the intersection, which should be the same if we've converged the root finding.

AMReX-Astro / Castro