Saint–Venant equations simulation by finite volume method and ULTIMATE strategy

A wide range of natural phenomena can be mathematically modeled by the Saint–Venant equations, such as flood routing. The rapid change of dependent variables, that occurs during a flood event, could cause unphysical oscillations in the model results and invalidates the simulation. In this study, the dynamic wave model was discretized by the finite volume method. Additionally, the polynomial schemes and ULTIMATE strategy were set up to prevent spurious numerical oscillation in the proposed model. Then a solution flowchart was introduced for solving the discretized equations set. Finally, the introduced model was evaluated compared to the finite difference method and HEC-RAS computer program results. The comparison of the results indicated that the proposed numerical model was correct, and the solution flowchart was well established.