Non‐reflecting boundary conditions for the compressible Euler and Navier‐Stokes equations in the finite volume method

Abstract

AbstractThe paper is concerned with the numerical implementation of the inlet and outlet boundary conditions in the finite volume method for the solution of the 3D Euler and Navier‐Stokes equations. The explicit time marching procedure is described. The classical Riemann problem is modified for physically relevant boundary conditions with the aim to keep conservation laws. This technique was used in [2]. The initial condition in the Riemann problem is replaced by the suitable one‐sided boundary condition. This results in the acceleration of the numerical method itself. On the inlet the pressure and the density and the angle of attack or velocity vector and the entropy are prescribed. On the outlet the pressure or normal component of the velocity or temperature or mass flow are investigated in such a way to obtain the unique solution of the modified Riemann problem. Various combinations of inlet and outlet boundary conditions are investigated. This results in the sufficiently precise approximation of real flow boundary conditions. Numerical examples illustrating the usefulness of the proposed approach for cascade flow are presented. Another numerical example is shown in [3]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)