A down-stream boundary procedure for the euler equations

The steady slate problem for flow in a channel is considered. Down-stream boundary conditions are derived for the Euler equations by using Fourier-expansions of the solution. Not data are required at the down-stream boundary or at infinity, the condition used is simply the requirement of a bounded solution. A difference approximation is applied to the steady state equations, and Newton's method is used for solving the resulting non-linear system of equations.