Cartesian
- Cartesian
cartesian
grid
Logically rectangular Cartesian mesh with optional non-uniform spacing per axis (1D / 2D / 3D).
- centered_2nd_uniform
finite_difference
cartesian
scheme
O(dx²)
Two-point centered second-order finite difference for ∂u/∂x on a uniform Cartesian axis.
- flux_limiter_minmod
limiter
cartesian
limiter
O(dx²) in smooth monotone regions; O(dx) at extrema
Minmod TVD flux limiter (Roe 1986) — the most diffusive of the symmetric second-order TVD limiters.
- flux_limiter_superbee
limiter
cartesian
limiter
O(dx²) in smooth monotone regions; compressive near discontinuities
Superbee TVD flux limiter (Roe 1986) — sits on the upper edge of the second-order TVD region.
- ppm_reconstruction
finite_volume
cartesian
scheme
O(dx³)
Piecewise-parabolic method (Colella & Woodward 1984) — 4th-order edge values + a parabola per cell, no limiter.
- upwind_1st
finite_difference
cartesian
scheme
O(dx)
First-order upwind (backward) finite difference for ∂u/∂x on a uniform Cartesian axis.
- weno5_advection
finite_volume
cartesian
scheme
O(dx⁵)
Jiang–Shu 5th-order WENO reconstruction — three sub-stencils, smoothness indicators, nonlinear weights.
- weno5_advection_2d
finite_volume
cartesian
scheme
O(h⁵) per axis
Dimension-by-dimension Jiang–Shu WENO5 reconstruction on a 2D structured uniform Cartesian grid.