Approximate Riemann solutions of the two-dimensional shallow-water equations

Glaister, P. (1990) Approximate Riemann solutions of the two-dimensional shallow-water equations. Journal of Engineering Mathematics, 24 (1). pp. 45-53. ISSN 1573-2703 doi: 10.1007/BF00128845

Abstract/Summary

A finite-difference scheme based on flux difference splitting is presented for the solution of the two-dimensional 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 two-dimensional equations with source terms, is included. The scheme is applied to a dam-break problem with cylindrical symmetry.