Cartesian

Logically rectangular Cartesian mesh with optional non-uniform spacing per axis (1D / 2D / 3D).

Auto-generated catalog entry for the centered_2nd_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the centered_2nd_nonuniform_cartesian rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Two-point centered second-order finite difference for ∂u/∂x on a uniform Cartesian axis, expressed as a closed §4.2 arrayop lowering.

Auto-generated catalog entry for the centered_4th_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the centered_4th_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the centered_6th_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the centered_6th_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the centered_8th_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the centered_8th_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

PPM-based 1D flux-form transport face flux: 4th-order CW84 edge interpolation + Colella-Woodward (1984) §4 monotonicity limiter + Courant-fraction flux integral + ifelse upwind selection on the per-face Courant.

Minmod TVD flux limiter (Roe 1986) — the most diffusive of the symmetric second-order TVD limiters.

Superbee TVD flux limiter (Roe 1986) — sits on the upper edge of the second-order TVD region.

Auto-generated catalog entry for the godunov_norm_1st_uniform_cartesian_2d rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the laplacian_2nd_uniform_cartesian rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Lax–Friedrichs first-order numerical flux for 1D linear advection on a uniform Cartesian axis. For face-staggered Courant c the LF flux reduces to first-order upwinding F_{i+1/2} = max(c,0)·q_i + min(c,0)·q_{i+1}, with upwind cell selection encoded directly in an abs op (no caller-side branching on sign(c)).

Auto-generated catalog entry for the midpoint_1d rule (integral, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the mixed_deriv_2nd_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the mixed_deriv_2nd_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the nonlinear_laplacian_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the nonlinear_laplacian_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Periodic boundary handling as a downstream index-rewrite rule: wraps an out-of-range stencil access index(u, i − offset) to index(u, mod(i − offset + Nx, Nx)) on axes declared periodic by the domain.

Piecewise-parabolic method (Colella & Woodward 1984) — 4th-order edge values + a parabola per cell, no limiter.

Auto-generated catalog entry for the ppm_reconstruction_left_edge rule (finite_volume, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the ppm_reconstruction_right_edge rule (finite_volume, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the spherical_laplacian_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Auto-generated catalog entry for the spherical_laplacian_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

First-order upwind (backward) finite difference for ∂u/∂x on a uniform Cartesian axis.

Auto-generated catalog entry for the upwind_1st_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.

Jiang–Shu (1996) 5th-order WENO reconstruction expressed as a closed §4.2 arrayop+ifelse lowering — canonical nonlinear-scheme exemplar.

Dimension-by-dimension Jiang–Shu WENO5 reconstruction on a 2D structured uniform Cartesian grid.

Auto-generated catalog entry for the weno5_grad rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.