High-Speed Compressible Flows

Abstract

This chapter is devoted to high-speed compressible inviscid flows with Mach numbers generally in excess of 0.6. Such flows, which usually involve the formation of shocks with characteristic discontinuities, are governed by the compressible Euler equations. For more than two decades, much attention in computational fluid dynamics has been focused on the efficient solution of the compressible Euler equations. This is mainly due to the fact that highspeed gas flows are of obvious practical importance and the cost of physical experiments is high. In this area, considerable success has been achieved by using finite difference and finite volume methods. There exists a large body of literature, see surveys in Hirsch (1990) and Feistauer (1993). The potential offered by finite element methods has been realized much later. The main advantage in the use of finite element approximation here is its capability for fitting complex geometry and permitting adaptive mesh refinement (Zienkiewicz and Taylor 1991).