NONREFLECTING BOUNDARY-CONDITIONS FOR NON-LINEAR HYPERBOLIC SYSTEMS

Consider a nonlinear hyperbolic system νt + A(ν)νx = 0 for x > 0 and t > 0. Suppose that the boundary x = 0 has been introduced only in order to limit the size of a computational problem. Suppose also that on physical grounds we know that no waves cross the boundary from the region x < 0. We need a boundary condition at x = 0 which expresses this fact. If our problem has no strong outgoing shocks, we may use the condition that at x = 0 the solution v lies in the manifold generated by the Riemann invariants of the outgoing characteristics. For the equations of gas dynamics with an outflow boundary at x = 0 this condition may be written cνγaρ{variant}t + cνγaρ{variant}ut + aρ{variant}St = 0, where a is the sound speed. © 1979.