A stable 2D unstructured shallow flow model for simulations of wetting and drying over rough terrains

Abstract

This paper proposes a 2D unstructured finite volume Godunov-type shallow water model to simulate complex flows involving wet–dry interfaces over irregular terrains. In this model, the MUSCL linear reconstruction is used to compute the values of variables at cell edges. These values are then modified with a non-negative reconstruction method to preserve non-negative edge water depths and the C-property. The modified values are then employed to evaluate the fluxes and the slope source terms using the Harten, Lax and van Leer approximate Riemann solver with the contact wave restored (HLLC) and the slope flux method, respectively. The friction source terms are solved by a splitting point-implicit method. The novel aspect of the model is an efficient approach to eliminate spurious edge velocities with high local extreme values caused by MUSCL reconstruction of the conservative variables near wet–dry interfaces. This approach is crucial to preserve the numerical stability of the model when simulating wetting and drying. The proposed model is tested against exact solutions, laboratory experiments and a real dam-break case. The results show that the proposed model is accurate and stable for handling complex flows with moving wet–dry interfaces over complex beds on unstructured grids.