Discretization of a model for the formation of longshore sand ridges (Q1903822)

The authors consider a model for the evolution of the bottom topography of the continental shelf. Waves traveling over the bottom are influenced by features of that bottom - like sand ridges. Nonlinear interaction of water waves with the bottom drives the evolution of the topography. This leads to a coupled nonlinear evolutionary model. Changes in the bottom topography occur in a much longer time scale than the typical time scale for the shallow water waves. The system of partial differential equations is solved by a combination of Lax-Wendroff's method and a fixed point iteration. The performance of the numerical methods is carefully studied. In a special case, a two-dimensional model is used for evaluation. A zero-flux condition is imposed to handle the lateral boundaries of the domain without introducing unwanted structures into the solution of the surface equation.