Approximate Riemann solutions of the shallow water equations
1988; Taylor & Francis; Volume: 26; Issue: 3 Linguagem: Inglês
10.1080/00221688809499213
ISSN1814-2079
Autores Tópico(s)Stability and Controllability of Differential Equations
ResumoA finite difference scheme based on flux difference splitting is presented for the solution of the onedimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gasdynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. An extension to the one-dimensional equations with source terms, is included. The scheme for the one-dimensional equations is applied to the dam-break problem, and the approximate solution is compared to the exact solution of ideal fluid flow.
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