Abstract
Chapter 7 focuses on the computation of one-dimensional channel flow by the numerical method of characteristics. Techniques for construction of the characteristic network are presented. The methods of specified space and time intervals are developed, and are used to solve the dam-break problem. The chapter also addresses the computation of one-dimensional channel flow by finite-difference methods. Conservative and non-conservative formulations are explored. The two-step Lax-Wendroff and Preissmann methods are analyzed. Shock capturing and non-reflecting boundary conditions are described in detail. Fourier analysis of systems of first-order hyperbolic equations is carried out, and the conditions for stability of explicit schemes are examined. Finally, this chapter extends the finite element and finite-volume methods to open-channel flow. The emphasis is on monotonicity preserving methods and shock capturing. The Riemann problem is introduced, and flux limiting is used to construct TVD schemes for open-channel flow.
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