Explicit finite volume non-oscillatory schemes for 2D transient free-surface flows

A class of high-resolution non-oscillatory shock-capturing Roe, TVD and ENO explicit schemes in finite volume approach are presented for the computation of 2D unsteady rapidly varied open channel flows. In order to apply these schemes to simulate the hydraulic phenomena in field, the Strang-type operator splitting technique is adopted to treat the flow with bottom slope and friction terms. Verifications of the proposed schemes are made by comparison with analytical solutions or experimental data, and very good agreements are obtained. To illustrate the efficiency and stability of the present algorithms, four typical problems of rapidly varied flows are solved and the results of different schemes are compared. It is demonstrated that the proposed method is accurate, robust and highly stable even in the flows with very strong discontinuites, which need no tuning of any adjustable parameter, such as artificial viscosity coefficient, as other methods do, and is a reliable mathematical modeling for 2D practical hydraulic engineering applications.