A Well-Balanced and Non-Negative Numerical Scheme for Solving the Integrated Shallow Water and Solute Transport Equations

Abstract

Based on the recent development in shallow flow modelling, this paper presents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrix system of conservation laws that comprise the shallow water and depth-averaged solute transport equations. The adopted governing equations are derived to preserve exactly the solution of lake at rest so that no special numerical technique is necessary in order to construct a well-balanced scheme. The HLLC approximate Riemann solver is used to evaluate the interface fluxes. Second-order accuracy is achieved using the MUSCL slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is validated against several benchmark tests and the results are in excellent agreement with analytical solutions or other published numerical predictions.