A Large Time Step Scheme For Shallow Water Equations With Application To Sandbar Clogging Simulation

It is difcult to simulate shallow water equations with both high efciency and highaccuracy which afect the reliability of the forecast for flood. This problem is resolved inthis paper by Large Time Step (LTS) scheme which is based on wave propagation methodand Exact Riemann Solver. The LTS scheme is scientifically and practically valuablefor numerical simulation of shallow water equations with high efciency, accuracy andstability. Three important progresses below are made:The traditional Roe scheme of shallow flows is transformed to wave propagationscheme. Then the velocity and the strength of the wave is obtained by Exact RiemannSolver whose structure contains rarefaction naturally which makes the scheme more sta-ble and more convenient to approximate rarefaction with multi waves. The CFL numberis enhanced to5with high efciency and accuracy.The oscillation induced by LTS cannot be eliminated by traditional adding artificialviscosity or WENO due to its special updating procedure. This problem is resolved byRandom Choice Method (RCM) in this paper which enhances CFL number further to25and thus makes the simulation of shallow flows with both high efciency and highaccuracy.The LTS scheme on unstructured grids is then built up to simulate the formation ofthe sandbar owing to confluence of hyper-concentrated flow and to analysis the mecha-nism of the sandbar. The results show the sand bar upstream and deposition downstreambecause of circumfluence. The ditch is found along the belt of the shear flow which isdeferent from the confluence of debris. The sandbar starts from the left bank and to theright bank and deposit with density current. The weak connection of the sandbar is bro-ken through with a large flood in main river, and then the sandbar is separated by severalbreakthroughs until it is vanishes.