One-dimensional characteristic boundary conditions using nonlinear invariants

Abstract

A new treatment of boundary conditions using the flow decomposition in characteristics is derived for inviscid one-dimensional flows using nonlinear invariants. The new set of equations is equivalent to the relations of Thompson (1987) [5] but it has the advantage to provide a physical interpretation of the characteristics for nonlinear perturbations. This interpretation is a major advantage to deal with the nonlinear injection of waves in the domain. In particular, the limitation of the standard relations to the injection of waves without nonlinear interactions on the boundary is addressed. Associated errors are evaluated analytically and numerically and a clear improvement of the results is demonstrated with the new expressions. To avoid a drift of the mean values, relaxation terms are usually added in the relations and the boundary conditions become almost non-reflecting. The consequences of these relaxation terms on outgoing and ingoing waves are widely investigated in the present paper and a nonlinear correction is proposed to recover perfectly non-reflecting conditions without drift. To end, simulations are performed on the generation of indirect combustion noise through a nozzle to illustrate the advantages of the new formulation.