A high-precision two-dimensional flow-transport coupled model based on Godunov’s schemes

Numerical solution of flow-transport equations usually has to handle complex surface topography, numerical damping effect and numerical oscillation. In order to solve these problems, a high-performance Godunov-type finite volume model is proposed. An approximate Harten-Lax-van Leer-Contact (HLLC) Riemann solver for the integration of transport convection terms is used in the model development to calculate the mass fluxes and transport fluxes. The model can capture shock waves, reduce the numerical damping effect and overcome the numerical oscillation problems. A weighted surface-depth gradient method and the Minmod limiter are used for water depth's reconstruction to improve the model accuracy. Moreover, the Hancock predictor-corrector method is adopted for time stepping. Numerical results show that the proposed model is highly accurate and stable, and can significantly reduce the numerical damping effect. Thus, the model is suitable for simulating the transport problems in complex water flow and has a wide range of application potentials.