Parallel Simulations of Shallow Water Solvers for Modelling Overland Flows

In this paper, we simulate overland flows using a cell-centred finite volume (CCFV) method with three solvers – HLLC, central-upwind, and artificial viscosity schemes – and present their parallel efficiency within the framework of our in-house code called NUFSAW2D. The parallel efficiency is investigated through four explicit time stepping schemes – the first-order Euler and the second, third, and fourth-order Runge Kutta methods. The bed slope terms are solved using a Riemann-solver-free technique and the friction terms are treated semi-implicitly for all time stepping schemes, allowing our model to simulate wet-dry problems with very low water depths on very rough beds. A second-order spatial accuracy is achieved with the Monotonic Upstream-Centred Scheme for Conservation Laws (MUSCL) linear interpolation technique. Since our code is based on an edge-based data structure, the edge-based MinMod limiter function is used to enforce the monotonicity of reconstructed variables. Our code shows accurate results and achieves a good scalability for up to 3.2 million cells or 6.4 million edges using OpenMP parallelisation technique.