Beyond One-Dimensional Transport

Abstract

The basic properties of finite-difference methods were explored in Chap. 3 by applying each scheme to simple prototype problems involving advection and diffusion in one spatial dimension. The equations governing wavelike geophysical flows include additional complexities. In particular, the flow may depend on several unknown functions that are related by a system of partial differential equations, the unknowns may be functions of more than two independent variables, and the equations may be nonlinear. In this chapter we will examine some of the additional considerations that arise in the design and analysis of finite-difference schemes for the approximation of these more general problems.