First-Order
- 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)).
- upwind_1st
finite_difference
cartesian
scheme
O(dx)
First-order upwind (backward) finite difference for ∂u/∂x on a uniform Cartesian axis.