Accurate and Efficient Flow Solvers for 3D Applications on Structured Meshes

Abstract

The present lecture describes well established techniques used for numerical simulations of complex aerodynamic flows. The paper is restricted to problems with steady mean flow, that is, steady-state solutions of the Euler equations governing and of the Reynolds/averaged Navier-Stokes equations. Attention is focused on the two major parts of the numerical algorithms. These are the spatial discretization and time stepping algorithms. Spatial discretization of the governing equations are outlined which perform accurate solutions with as few as possible discrete points in the flow domain. Care must be taken to resolve all relevant flow phenomena, i.e. smoothly varying regions of inviscid flows. Flow discontinuities as shocks and slip lines, and viscous layers which are governd by diffusion. Moreover, numerical analysis and well-known experience show that the choice of the spatial discretization also influences the convergence of the overall method to the desired steady-state.