Computational Fluid Dynamics

Appendix C Explicit and Implicit Methods

The first-order explicit and implicit methods have been described in Chapter 4, Section 4.2.3. Here, we further concentrate on the formulation of the second-order explicit Adams-Bashford and semi-implicit Crank-Nicholson methods as illustrated below.

As illustrated from the sketch in Fig. C.1, the extension of the first-order explicit method to the second-order explicit Adams-Bashford requires the values not only at time level n but also at time level n – 1. The unsteady one-dimensional convection-diffusion of Eq. (4.43) can be recast in the form of:

For the second-order Crank-Nicholson method, this special ...