Numerical flux
= Numerical flux
{title2=$F(a,b)$}
A numerical flux approximates the transported quantity through a cell interface using nearby states. For a two-state flux $F(a,b)$ approximating a <scalar conservation law> with flux $f$, consistency requires $F(u,u)=f(u)$. A <monotone conservative scheme> uses a flux nondecreasing in its left state and nonincreasing in its right state, with a time step making the complete update monotone.