ABSTRACT
The computational §uid dynamics (CFD) “frontier” has advanced from the simple to the complex. Generally, the simple methods taxed the available computational power when they occupied the frontier. The evolution proceeded from methods for various forms of the potential and boundarylayer equations to the Euler equations and then to various “parabolized” forms of the Navier-Stokes equations that are the subject of this chapter. Most of the schemes were developed at a time when the use of the full Navier-Stokes equations was prohibitive for many problems because of the large computer memory or CPU time required. If such parabolized schemes were considered economical of computer resources when they were introduced, they are still so. However, the need to save CPU time has diminished in a relative sense because of the incredible reduction in cost per operation experienced in recent times. Numerous numerical strategies will be discussed in this chapter. They all share the common characteristic that the steady form of the governing equations is employed, and the solution is “marched” in space. Some of the solution strategies to be described in this chapter share aspects in common with methods for the full Navier-Stokes equations discussed in Chapter 9.
