alexa Approximate Riemann solutions of the shallow water equations
Bioinformatics & Systems Biology

Bioinformatics & Systems Biology

Journal of Theoretical and Computational Science

Author(s): Paul Glaister

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A 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.

This article was published in Journal of Hydraulic Research and referenced in Journal of Theoretical and Computational Science

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