Engquist-Osher flux
= Engquist-Osher flux
{c}
{title2=$F_{\rm EO}(a,b)$}
The Engquist-Osher <numerical flux> is $F(a,b)=f(0)+\int_0^a\max(f\prime(s),0)ds+\int_0^b\min(f\prime(s),0)ds$. It sends positive-speed contributions from the left state and negative-speed contributions from the right state. Its consistency $F(u,u)=f(u)$ and opposite monotonicities in the two arguments yield a <monotone conservative scheme> under the appropriate <Courant–Friedrichs–Lewy condition>. For the <Inviscid Burgers equation>, it is $\tfrac12\max(a,0)^2+\tfrac12\min(b,0)^2$.