Approximate nonreflecting inflow-outflow boundary conditions for the calculation of navier-stokes equations in internal flows

Abstract

In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are proposed as a substitute of the nonreflecting boundary conditions inside boundary layers near rigid walls. These derived boundary conditions are then applied to calculations both for the Euler equations and the Navier-Stokes equations to determine if they can produce acceptable results for the subsonic flows in channels. The numerical results obtained by an implicit second-order upwind difference scheme show the effectiveness and generality of the boundary conditions. Furthermore, the formulae and the analysis performed here may be extended to three dimensional problems.