ABSTRACT
The Euler equations governing the flow of an inviscid, non-heat-conducting gas are introduced. Methods for solving these equations begin with application of the method of characteristics for linear systems followed by extension to nonlinear systems and the Euler equations. Classical shock capturing techniques including the MacCormack method are reviewed, and enhancements such as shock fitting are studied. Flux splitting using various approaches such as the van Leer and Steger–Warming schemes are included and the Roe Flux- difference splitting scheme is developed. Different approaches to boundary condition specification are considered including inviscid wall slip and shock boundaries. Reduced versions of the Euler equations are included for completeness and begin with the full potential equation and associated solution procedures. The small perturbation versions of the Euler equations, the Prandtl–Glauert equation, and the transonic small disturbance equation are also presented with solution procedures for each. Applications of solution methods for the governing equations are made throughout the chapter for both steady and unsteady flows. Finally, a very brief introduction to the idea of panel methods concludes the chapter.
