Numerical solution of surface flow equations by finite differences

Abstract

Abstract This chapter discusses finite difference methods applied to the solution of surface flow equations. The examples chosen are those which can be solved by fairly simple methods. They are arranged in the order in which they occur in Table 1.1.1. The first, lateral velocity distribution across a channel, is an example of an ordinary differential equation boundary value problem. The box scheme, introduced in section 3.8, is applied in section 4.2 to the non-linear hyperbolic kinematic wave equation. Section 4.3 includes the box scheme and the Abbott scheme applied to the solution of the St Venant equations. Section 4.4 discusses the limitations on the use of these schemes and section 4.5 lists some alternatives. Section 4.5 describes in outline only some more sophisticated methods for the problem of vertically integrated two-dimensional surface flow.