Upwind scheme

Summary

An upwind scheme is a finite difference or finite volume scheme for advection problems. Its spatial differences are taken on the side from which the information comes. For the transport equation $u_t + a u_x = 0$ with $a > 0$, waves move to the right. So the scheme uses the values at the point and at its left neighbour. Following the direction of propagation gives stable schemes under the Courant–Friedrichs–Lewy condition, while the centred or the opposite choice leads to instability. The first-order upwind scheme is the basic building block of Godunov-type methods for conservation laws.