NumericalSystemModel

The NumericalSystemModel (NSM) is the SystemModel plus the scheme choices that are not a solver option: what is reconstructed and how, the Riemann solver, the wave speed. It also carries the kernels (nsm.call.<slot>: flux, fluctuations, source, boundary states, …) that every backend prints from the same expressions.

What you write:

from zoomy_core.numerics import Limiter, NumericalSystemModel, ReconstructionSpec
nsm = NumericalSystemModel.from_system_model(
    sm, reconstruction=ReconstructionSpec(order=2, limiter=Limiter.minmod))

option	default	meaning
reconstruction.order	1	1: piecewise constant; 2: LSQ gradients, limited
reconstruction.limiter	Limiter.venkatakrishnan	also minmod, barth_jespersen, none; per row: limiters={"b": Limiter.none}
reconstruction.variables	ReconstructedVariables.model	model: the model’s reconstruction variables (SWE/SME: $\eta = b + h$, $u = q/h$); conservative: $Q$
reconstruction.bed	BedReconstruction.derived	bed at the faces from $\eta - h$ (lake at rest, $h_f \ge 0$); reconstructed
reconstruction.ties	{}	{row: lead}: a row is limited at least as much as its lead
riemann	from the model’s tags, else NonconservativeRusanov (C1 bump: PositiveNonconservativeRusanov)	zoomy_core.fvm.riemann_solvers: Rusanov, NonconservativeRusanov, HLL, HLLC, …
diffusion	on if diffusion_matrix is nonzero	DiffusionSpec
spectral_radius_method	zoomy_core.symsolver.WAVE_SPEED = "power"	wave speed of a model without closed-form eigenvalues: power iteration on $A^2$, the same on every backend and device

MOOD (the a-posteriori order fallback) is a solver option (Solvers); what it tests is the model’s admissibility (e.g. $h \ge 0$; Euler: $\rho, p > 0$).

Connects to: every solver takes the NSM unchanged (solver.setup(mesh, nsm) on JAX, solver.run(mesh, nsm, Q0, workdir) on foam / AMReX). The mesh is an LSQMesh (zoomy_core.mesh: LSQMesh.create_1d/2d/3d, or from a gmsh file); its least-squares stencils serve gradients and boundary closures.

API: zoomy_core.numerics, zoomy_core.mesh.