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

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.