An efficient semi-implicit friction source term treatment for modeling overland flow

Abstract

In this study, a new numerical treatment of the friction source term is proposed for modeling shallow water flows over complex bed topography. We design a novel semi-implicit temporal discretization technique based on Taylor series expansion of friction source terms. A well-balanced positivity-preserving finite volume scheme on unstructured triangular grids is used to solve the shallow water model. We present a series of numerical tests to demonstrate the robustness and effectiveness of the proposed numerical model where we used rapidly varying flows over complex topography as well as flows involving small values of water depth and wet/dry zones. The simulation results of the numerical model based on the proposed approach for friction source terms are compared to experimental data and to those obtained by using other existing techniques. The proposed numerical model is stable and second-order accurate and our predictions are in good agreement with experimental observations.