Artificial Boundary Conditions for the Linearized Compressible Navier–Stokes Equations: II. The Discrete Approach

Abstract

In the first part of this paper (J. Comput. Phys.137, 1, 1997), continuous artificial boundary conditions for the linearized compressible Navier–Stokes equations were proposed which were valid for small viscosities, high time frequencies, and long space wavelengths. In the present work, a new hierarchy of artificial boundary conditions is derived from the so-called “discrete” approach, which consists in working directly on the discretized equations, under the assumption of low time frequencies instead of small viscosities. The discrete artificial boundary conditions are implemented in 1D and 2D model problems and they compare quite well with the continuous artificial boundary conditions. Being self-sufficient by construction, they can be used as numerical boundary conditions and be coupled to schemes having arbitrary stencils.