Euler

The compressible Euler cases of FLUME: Riemann problems with exact solutions, a smooth exact solution for the order of accuracy, the immersed boundary, conservation across AMR seams, and the multi-realm forest. They verify the two space schemes, weno (WENO5 flux splitting on characteristic variables) and weno-riemann (WENO5 interpolation of the face states, an LLF, HLL or HLLC Riemann flux and a 6th-order flux correction), described in numerics.

Every case runs from its directory under src/tests/flume/verification/ through check.sh (CPU by default, FLUME_EXE=exe/adam_flume_fnl for the FNL backend), with 2 MPI ranks and WENO5 unless the page states otherwise. The oracles assert the physics (an exact solution, a reference, a symmetry or a conservation property), not a stored golden; the goldens of the regression suite are listed in each page's header.

Case	ID	What it verifies
Sod shock tube	V1, RV-3	$L_1(\rho )$ against the exact solution; $x$, $y$, $z$ bitwise equal; reflecting walls
Lax problem	RV-3	the Riemann solvers on a strong contact, bound $1.05\times$ the splitting scheme
Shu–Osher shock / entropy-wave interaction	RV-3	the entropy waves behind a Mach 3 shock against a 16× finer reference
Isentropic vortex: order of accuracy	V2, RV-2	the design order on a smooth exact solution, periodic blocks across ranks
Shock over a cylinder	V6	the immersed boundary with solid AMR: refinement, mirror symmetry, positivity
Conservation across AMR seams	V3, RV-4	the reflux at 2:1 faces: the volume integrals constant to round-off
Multi-realm runs	multirealm legs 1–6	mirror, misaligned and 2:1 inter-realm seams, across ranks: bitwise equal to one realm
Forward-facing step	EV-step	a three-realm forest on quadtrees against octrees; the Woodward–Colella step at $t=4$

The figures are drawn by src/tests/flume/verification/make_doc_figures.py from the work directories that the check.sh scripts leave behind (the step's with --keep):

cd src/tests/flume/verification
(cd sod && ./check.sh) ; (cd vortex && ./check.sh) ; (cd conservation && ./check.sh)
(cd riemann-flux && ./check.sh                                    # HLLC, every leg
   ./check.sh --solver split --legs lax ; ./check.sh --solver split --legs shu-osher
   ./check.sh --solver llf --legs lax --lax-l1-max 1 ; ./check.sh --solver llf --legs vortex
   ./check.sh --solver hll --legs vortex)                           # LLF exceeds the default Lax bound
(cd step && ./check.sh --legs trees,full --keep)
python3 make_doc_figures.py --out ../../../../docs/public/flume \
   --only sod lax shu-osher vortex shock-cylinder conservation step step-trees