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

✍ Scribed by P. Glaister

• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 366 KB
• Volume: 24
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00128845

✦ Synopsis

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.