A numerical method, called the Random Choice Method, is used to solve benchmark problem 3. It is based on the the shallow water wave equations. This method is capable of preserving a shock, i.e abrupt spatial changes in the flow conditions. This means that wave breaking can be modeled without any special treatment for numerical instabilities at the bore front. The method is unconditionally stable provided that the Courant-Friedrichs-Lewy condition is fulfilled. The solution is advanced in time by a series of operations which inclues solving a Riemann problem at each gridpoint at each timestep. The Riemann problem is computationally expensive so considerable efforts were made on speeding up the solution procedure. This scheme was originally developed by Chorin~1 based on the theory by Glimm~4 to solve the euler equations.
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