A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations

摘要

We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in Kreiss et al. (SIAM J. Numer. Anal. 40(5): 1940-1967, 2002) and for the Euler equations of compressible fluid flow in Sjogreen and Peterson (Commun. Comput. Phys. 2:1199-1219, 2007), to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.