Topics in Numerical Computation of Compressible Flow

Abstract

This thesis aims to assist the development of a multiblock implicit Navier-Stokes code for hypersonic flow applications. There are mainly three topics, which concern the understanding of basic Riemann solvers, the implementing of implicit zonal method, and grid adaption for viscous flow. Three problems of Riemann solvers are investigated. The post-shock oscillation problem of slowly moving shocks is examined, especially for Roe's Riemann solver, and possible cures are suggested for both first and second order schemes. The carbuncle phenomenon associated with blunt body calculation is cured by a formula based on pressure gradient, which will not degrade the solutions for viscous calculations too much. The grid-dependent characteristic of current upwind schemes is also demonstrated. Several issues associated with implicit zonal methods are discussed. The effects of having different mesh sizes in different zones when shock present are examined with first order explicit scheme and such effects are shown to be unwanted therefore big mesh size change should be avoided. Several implicit schemes are tested for hypersonic flow. The conservative DDADI scheme is found to be the most robust one. A simple and robust implicit zonal method is demonstrated. A proper treatment of the diagonal Jacobian and choosing the updating method are found to be crucial. The final topic concerns the calculation and grid adaption of viscous flow. We study the linear advection-diffusion equation thoroughly. The results are unfortunately not applicable to Navier-Stokes equations directly. Nevertheless a suggestion on the mesh size control for viscous flow is made and demonstrated. An attempt to construct a cell-vertex TVD scheme is described in the appendix