Fluid Flow Computation: Incompressible Flows

Abstract

The previous chapter presented the methodology for solving incompressible flow problem using pressure based algorithms. In this chapter these algorithms are extended to allow for the simulation of compressible flows in the various Mach number regimes, i.e., over the entire spectrum from subsonic to hypersonic speeds. While incompressible flow solutions do not generally require solving the energy equation, compressibility effects couple hydrodynamics and thermodynamics necessitating the simultaneous solution of the continuity, momentum, and energy equations. The dependence of density on pressure and temperature, a relation expressed via an equation of state, further complicates the velocity-pressure coupling present in incompressible flows. The derivation of the pressure correction equation now involves a density correction that introduces to the equation a convection-like term, in addition to the diffusion-like term introduced by the velocity correction. Another difficulty is introduced by the complex boundary conditions that arise in compressible flow problems. Details on resolving all these issues are presented throughout this chapter.