A high-resolution numerical method for solving the shallow water equations based on the modified CABARET scheme

A numerical method based on the CABARET scheme for modeling unsteady flow over arbitrary topography in the shallow water approximation is developed. The method allows simulating a wide range of flow conditions, including transcritical. To model transcritical transitions, a hybrid approach is used based on solving the local Riemann problem, as is done in Godunov-type schemes. The presented numerical method has a well-balance condition-the fulfillment of the condition of hydrostatic equilibrium or the condition of a fluid at rest on an uneven bottom topography. A robust technique is used to simulate the movement of wet/dry fronts caused by flooding or recession. A number of physical processes are taken into account, such as bed friction and rain. Numerical results are compared with analytical solutions and data from the dam-break experiment.