On steady, inviscid shock waves at continuously curved, convex surfaces (Q1261650)

An accurate and efficient numerical method for steady, two-dimensional Euler equations is applied to study steady shock waves perpendicular to smooth, convex surfaces. The main subject of study is the flow near both ends of the shock wave: the shock-foot and shock-tip flow. For the inviscid shock-tip flow, two existing analytical solutions are reviewed. Numerical results are presented which agree with one of these two solutions. Good numerical accuracy is achieved through a monotone, second-order accurate, finite-volume discretization, iterative defect correction iteration and a multigrid acceleration technique which employs local grid refinement.