A numerical convergence study of some open boundary conditions for euler equations

Abstract

We discuss herein the suitability of some open boundary conditions. Considering the Euler system of gas dynamics, we compare approximate solutions of one-dimensional Riemann problems in a bounded sub-domain with the restriction in this sub-domain of the exact solution in the infinite domain. Assuming that no information is known from outside of the domain, some basic open boundary condition specifications are given, and a measure of the $$L^1$$-norm of the error inside the computational domain enables to show consistency errors in situations involving outgoing shock waves, depending on the chosen boundary condition formulation. This investigation has been performed with Finite Volume methods, using approximate Riemann solvers in order to compute numerical fluxes for inner interfaces and boundary interfaces.