ABSTRACT
This chapter focuses on the finite difference approximations of the compressible flow problems that are governed by a system of partial differential equations that are hyperbolic in nature. It provides a simple situation involving the so-called quasi one-dimensional flow and then move to a case involving multidimensional compressible flow. The designation "quasi-one-dimensional flow" refers to a simplified model that applies to compressible flows in pipes and nozzles in which the fluid velocity and properties are assumed to be uniform at the cross section. The chapter illustrates the application of the weighted average flux–total variation diminishing (WAF-TVD) scheme to the compressible axisymmetric flow of a gas, modeled by the time-dependent Euler equations. Euler's equations form a system of nonlinear hyperbolic conservation laws that govern the dynamics of a compressible material, such as gas or liquid at high pressure, for which the effects of body forces, viscous stresses, and heat conduction are neglected.
