Improved treatment of source terms in TVD scheme for shallow water equations

A number of high-resolution schemes have been recently developed to solve the homogeneous form of the shallow water equations. However, most approximate Riemann solvers experience difficulties with natural river applications if the irregular bed topography is not handled correctly. Based on the finite-difference flux-limited total variation diminishing (TVD) scheme, this paper develops a simple approach to handle the source terms for the one-dimensional open channel flow simulation with rapidly varying bed topography. Conclusions on the validity of the operator-splitting approach, the eigenvector-projection approach, and the proposed approach are presented. Analytical solution, experimental data, and available numerical result comparisons are shown to demonstrate the accuracy, robustness, stability, simplicity, and applicability of the proposed model.