Numerical solution techniques for unsteady transonic aerodynamics problems

Abstract

Basic concepts of finite difference solution techniques for unsteady transonic flows are presented. The hierarchy of mathematical forumulations that approximate the Navier-Stokes equations are reviewed. The basic concepts involved in constructing numerical algorthms to solve these formulations are given. Semi-implicit and implicit schemes are constructed and analyzed. The discussion focuses primarily on techniques for solving the low frequency transonic small disturbance equation. This is the simplest formulation that contains the essence of inviscid unsteady transonic flow physics. The low frequency formulation is emphasized here because codes based on this theory can be run in minutes of processor time on currently available computers. Furthermore, numerical techniques involved in solving this simple formulation also apply to the more complicated formulations. Extensions to these formulations are briefly described. An indication of the present capability for solving unsteady transonic flows is provided. Important areas of future research for the advancement of computational unsteady transonic aerodynamics are described.