User guide

A simulation is built in three symbolic layers and run by a solver template on a backend:

Model ──────────▶ SystemModel ─────────▶ NumericalSystemModel ──▶ solver template ──▶ backend
PDE, closures,     operator slots          + reconstruction,        one sympy graph      JAX · foam · AMReX
BCs                (flux, source, ...)     Riemann solver, kernels  per time step        (printed, compiled)

page	what you choose there
Quick start	one case, run on JAX, foam and AMReX
Model	model family, closures, boundary conditions
SystemModel	nothing, usually: it is derived; inspect it, set initial conditions
NumericalSystemModel	reconstruction order and limiter, Riemann solver
Solvers and options	hyperbolic or Chorin, CFL / dt, time order, MOOD, IMEX, pressure solver
Backends	where it runs: CPU, MPI, GPU

The NSM is backend-neutral: the same object is handed to every backend, and the test matrix checks that the backends agree.