TABLE OF CONTENTS In Chapter 3, our attention was on the numerical solution of inviscid flow described by the Euler equations. We discussed the finite difference method applied to the problem with one space variable and the finite volume schemes for the numerical solution of multidimensional problems. The inviscid model gives physically acceptable results in some cases of internal and external aerodynamics. However, if the bodies immersed in the gas have a complicated structure or the angles of attack of flow past airfoils are large, then the inviscid model can no longer be applied. In order to obtain a correct physical solution of the flow of a real fluid, in many cases of practical interest one must use models taking the viscosity effects into account.
In this chapter we shall be mainly concerned with the numerical simulation of viscous compressible flow. This belongs to the most difficult areas of computational fluid dynamics (CFD) since all the difficulties appearing in CFD occur here: strong nonlinearities and mixed hyperbolic parabolic (or hyperbolic elliptic) types of governing equations, the treatment of convection dominating diffusion, shock waves, boundary layers, wakes and their interaction.
The starting point for the numerical solution of viscous gas flow is usually a numerical scheme for the solution of inviscid flow, which is completed by the discretization of viscous terms. In recent years, rapid progress has been made in this area. The finite volume method (FVM) appears to be the most popular in the engineering community. However, from the point of view of higher...
