Beyond the One-Way Wave Equation
The basic properties of finite-difference methods were explored in Chapter 2 by applying each scheme to a simple prototype problem: the one-way wave equation (or, equivalently, the one-dimensional constant-wind-speed advection equation). The equations governing wave-like 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. It may also be necessary to account for weak dissipation, sources, and sinks. 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.
KeywordsAmplification Factor Average Scheme Advection Equation Nonlinear Instability Aliasing Error
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