Module validation 

Validation by geometry

The evidence is grouped by the geometry of the problem. Each case gives the problem, its reference, the numbers, the figure and the test that enforces it.

Page	Geometry	Equations	Cases
one_dimension	1D Cartesian	advection, Burgers, Euler	convergence orders, shocks, fans, Toro’s five shock tubes, contacts
two_dimensions	2D Cartesian	advection, Euler	isentropic vortex, planar shock, Lax-Liu Riemann problems, shock-bubble
three_dimensions	3D Cartesian	Euler	blast in a closed box, axis permutations
cylindrical	cylindrical (1D radial and axisymmetric $(r,z)$)	Euler	sound wave, Noh, blast, the axisymmetric can
spherical	spherical (1D radial)	Euler	sound wave, Noh, blast
high_order	any dimension	advection, Euler, level set	stencil rules, stability limits, WENO5 against MUSCL, Zalesak’s disk, the vortex, reinitialisation

The numbers quoted were produced by the commands on the reproduction page. Results recorded here are from a run on 2026-10-25 on one thread of an Apple M1. The tests assert thresholds, not these digits, so the numbers can be reproduced but a test does not fail when the third significant figure moves. The thresholds are quoted where they matter.

Modules

cylindrical

Cylindrical coordinates

high_order

High-order reconstruction and the level set

one_dimension

One dimension

spherical

Spherical coordinates

three_dimensions

Three dimensions

two_dimensions

Two dimensions