ABSTRACT
This chapter examines the numerical solution of transient multidimensional parabolic systems by finite difference methods. There is a large variety of heat or mass transfer problems that are parabolic in nature. The chapter presents the alternating direction implicit (ADI) and alternating direction explicit (ADE) methods as well as the use of explicit and combined methods for finite difference representation of two- and three-dimensional model problems. It also examines purely diffusive systems and advective–diffusive systems with known velocity field. The chapter also presents the use of the simple explicit method and the stability constraints associated with the finite difference representation of typical parabolic problems including: two-dimensional heat diffusion in solids, two-dimensional steady, boundary layer flow, and transient convection–diffusion. It illustrates the application of the combined method for finite difference approximation of multidimensional parabolic systems for a three-dimensional diffusion problem.
