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

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