Wetting and drying numerical treatments for the Roe Riemann scheme

Abstract

Accurate characterization of wetting-drying fronts in free surface flows is challenging because it is difficult and computationally demanding to track the exact position of the interface. This work presents a novel numerical treatment of the wetting-drying fronts applied to an approximate Roe Riemann solver and compares it to four other approaches. The numerical treatments were implemented both for the shallow water equations and for the local inertial equations. The results of this comparison overall showed a good agreement. For the tests conducted it was verified that element removal numerical treatments with global distributing of water can introduce errors and degenerate the solution introducing or displacing water upstream. Local correction and flux restricting numerical treatments show the best results. The negative depth numerical treatments provided similar results to the local correction and flux restricting numerical treatment, although with mass conservation errors.