Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

Abstract

Exact non-reflecting boundary conditions for a linear incompletely parabolic system in one dimension have been studied. The system is a model for the linearized compressible Navier---Stokes equations, but is less complicated which allows for a detailed analysis without approximations. It is shown that well-posedness is a fundamental property of the exact non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, it is also shown that energy stability follows automatically.