ABSTRACT
The unsteady compressible Navier-Stokes equations are a set of hyperbolic-parabolic equations in time. The unsteady compressible Euler equations constitute an hyperbolic system. In the case of steady state, they become a mixed set of hyperbolic-elliptic equations in the streamwise direction. Problems modelled by hyperbolic equations have application in a variety of fields. For example, low speed compressible flow and its behavior over a long period of time is of interest in meteorology; steady state high speed flow with shocks and turbulence and flow over the boundaries of wings are important in aeronautical applications. In the problems of transient heat conduction in situations involving extremely short time responses (i.e., pico second), extremely high rate of change of heat fluxes or temperatures, or extremely low temperatures approaching absolute zero, the classical heat conduction equation breaks down because the wave nature of thermal transport phenomena becomes dominant. In such cases, the propagation of thermal waves is modelled by the hyperbolic heat conduction equation. In this chapter, we focus attention to the finite-difference approximation of the problems governed by a system of partial differential equations which are hyperbolic in nature.
