Topography discretization techniques for Godunov-type shallow water numerical models: a comparative study

This paper compares various topography discretization approaches for Godunov-type shallow water numerical models. Many different approaches have emerged popular with Godunov-type water wave models. To date, literature lacks an investigative study distinguishing their pros and the cons, and assessing their reliability relating to issues of practical interest. To address this gap, this work reviews and assesses five standard topography discretization methods that consist of the Upwind, the surface gradient method (SGM), the mathematically balanced set of the SWE (Etta-SWE), the hydrostatic reconstruction technique (Hydr-Rec) and the RKDG2 model. The study further considers mix-mode approaches that incorporate wetting and drying together with the topography discretization. Steady and transient hydraulic tests are employed to measure the performance of the approaches relating to the issues of mesh size, topography’s differentiability, accuracy-order of the numerical scheme, and impact of wetting and drying.