The simulation of dam-break flows by an improved predictor-corrector TVD scheme

This paper reports a finite difference predictor-corrector TVD (total variation diminishing) scheme for the computation of unsteady one-dimensional dam-break flows. The algorithm modified the widely used MacCormack scheme by implementing a conservative dissipation step to avoid any unphysical oscillation in the vicinity of strong gradients in the numerical solution. A general treatment for satisfying the entropy inequality condition is incorporated. The accuracy and robustness of the numerical scheme are verified with an analytic solution and experimental data. Furthermore, a sensitivity study is carried out to investigate the accuracy of four different versions of the predictor-corrector schemes. It is found that the numerical scheme will have less computational error and higher efficiency when the direction of the predictor-corrector step is the same as the direction of the shock wave propagation.