High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

Abstract

A class of high-resolution implicit total variation diminishing (TVD) type algorithms suitable for transonic multidimensional Euler and Navier-Stokes equations has been extended to hypersonic computations. The improved conservative shock-capturing schemes are spatially second- and third-order and are fully implicit. They can be first- or second-order accurate in time and are suitable for either steady or unsteady calculations. Enhancement of stability and convergence rate for hypersonic flows is discussed. With the proper choice of the temporal discretization and implicit linearization, these schemes are fairly efficient and accurate for very complex two-dimensional hypersonic inviscid and viscous shock interactions. This study is complemented by a variety of steady and unsteady viscous and inviscid hypersonic blunt-body flow computations. Due to the inherent stiffness of viscous flow problems, numerical experiments indicated that the convergence rate is in general slower for viscous flows than for inviscid steady flows.