ABSTRACT
Digital simulation of fluid mechanics and heat transfer problems depends upon computing solutions to partial differential equations (PDEs). In this chapter, a brief introduction to the different types of equations is given and their mathematical classification is included. The mathematical classification into elliptic, parabolic, and hyperbolic PDEs is presented using a general second-order PDE. This is followed by example problems illustrating the behavior of the solutions inherent to each class. Further information based on physical behavior and expected type of governing equation is presented. The classification of equations is extended to systems showing a limited number of cases where this classification is clear. A number of classical PDEs that govern numerous physical processes are included and are used to illustrate solution techniques throughout the text.
