Finite-Volume
- 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.
- 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.
- 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.
- 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.