A Stable Penalty Method for the Compressible Navier--Stokes Equations: II. One-Dimensional Domain Decomposition Schemes

Abstract
This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier--Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier--Stokes equations in general curvilinear coordinates.The versatility of the proposed scheme for the compressible Navier--Stokes equations is illustrated for quasi-one-dimensional transonic nozzle flows and for flows around an infinitely long circular cylinder.