Prediction of supercritical flow in open channels

Glaister, P. (1992) Prediction of supercritical flow in open channels. Computers & Mathematics with Applications, 24 (7). pp. 69-75. ISSN 0898-1221 doi: 10.1016/0898-1221(92)90155-B

Abstract/Summary

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, 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. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.