Finite_volume · EarthSciDiscretizations

advection_duo finite_volume unstructured scheme O(h) on a quasi-uniform icosahedral triangular mesh

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

advection_mpas finite_volume unstructured scheme O(h) L-inf median on a quasi-uniform Voronoi mesh (centered edge interpolation; NOT L-inf-convergent at maximally-distorted cells — see convergence fixture skip_reason)

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

advection_mpas_velocity_first finite_volume unstructured scheme O(h) L-inf median on a quasi-uniform Voronoi mesh (see advection_mpas)

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

covariant_fv_gradient_latlon_t1 finite_volume latlon scheme O(h^2)

Auto-generated catalog entry for the covariant_fv_gradient_latlon_t1 rule (finite_volume, grid family latlon). The discrete operator is pretty-printed directly from the rule's replacement AST.

covariant_fv_gradient_latlon_t2 finite_volume latlon scheme O(h^2)

Auto-generated catalog entry for the covariant_fv_gradient_latlon_t2 rule (finite_volume, grid family latlon). The discrete operator is pretty-printed directly from the rule's replacement AST.

covariant_fv_laplacian_latlon finite_volume latlon scheme O(h^2)

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

divergence_arakawa_c finite_volume arakawa scheme O(h²)

Two-point centered finite-volume divergence on a C-grid — F_x at face_x, F_y at face_y, divergence emitted at cell_center.

divergence_duo finite_volume unstructured scheme O(h) on a quasi-uniform icosahedral triangular mesh

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

divergence_mpas finite_volume unstructured scheme O(h^2) on a quasi-uniform Voronoi mesh

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

flux_1d_ppm finite_volume cartesian scheme O(h^3) interior; O(h) at active limiter constraints

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.

flux_duo finite_volume unstructured scheme O(h) on a quasi-uniform icosahedral triangular mesh

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

gradient_duo finite_volume unstructured scheme O(h) on a quasi-uniform icosahedral triangular mesh

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

gradient_mpas finite_volume unstructured scheme O(h^2) on a quasi-uniform Voronoi mesh

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

lax_friedrichs_flux finite_volume cartesian scheme O(h)

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)).

ppm_reconstruction finite_volume cartesian scheme O(dx³)

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

ppm_reconstruction_left_edge finite_volume cartesian scheme O(dx^4)

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.

ppm_reconstruction_right_edge finite_volume cartesian scheme O(dx^4)

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.

vertical_remap finite_volume vertical scheme O(dp^3) interior; O(dp) within two cells of the column top/bottom and at active CW84 limiter constraints

Conservative PPM vertical remap (Lin 2004) of a cell-averaged scalar from one set of vertical layer thicknesses to another: 4th-order CW84 edge interpolation + Colella–Woodward (1984) §4 monotonicity limiter + exact integration of the sub-grid parabola over the cumulative-pressure overlap. Documentation-only — deferred to a future ESS phase-hook RFC.

weno5_advection finite_volume cartesian scheme O(dx⁵)

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

weno5_advection_2d finite_volume cartesian scheme O(h⁵)

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