This is the second of two volumes which together form a treatise on the theory and practice of the numerical computation of internal and external flows. It contains a presentation of computational methods for inviscid and viscous flow models as they have evolved over the last decade.
The book is divided into three parts. The first, Part V, deals with the simplest inviscid approximation which is, in certain flow regimes, equivalent to the full system of Euler equations, namely the full potential model. It contains three chapters, 13 to 15. Chapter 13 describes the various mathematical formulations of the potential model, through differential as well as integral, weak, formulations; Chapter 14 deals with the rather simple and by now classical computation of subsonic potential flows, and covers finite difference, finite volume and finite element techniques; Chapter 15 discusses the much more complex problem of transonic potential flow in which the potential equation changes from elliptic to hyperbolic type, indicating that the flow changes from a diffusive character to a propagation-dominated behaviour. It also introduces the concepts of artificial viscosity and upwinding which form the basis of several numerical schemes to be discussed in following chapters.
Part VI is devoted to a detailed presentation of the Euler equations and of the basic numerical techniques developed in order to discretize the complex system of inviscid, compressible conservation laws. It covers five chapters: the initial, Chapter 16, presents the mathematical formulation of the system of Euler equations in conservative, quasi-linear, and characteristic forms; this is followed by two chapters on numerical schemes, namely the Lax-Wendroff family of space-centered schemes and central schemes with independent time integration. The treatment of boundary conditions is the subject of Chapter 19, which presents a detailed discussion of the one-dimensional boundary treatment followed by the multi-dimensional aspects, far-field conditions, and the Kutta condition. This part closes with two chapters on Engineering Analysis with Boundary Elements (9) (1992)--