Monotone

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)).
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.