A geometric multigrid solver for the free-surface equation in environmental models featuring irregular coastlines

Abstract

A recently developed multigrid method (Botto, 2013), based on the concept of volume fraction, has been tested for the inversion of the Helmholz-type equation for the free surface in the environmental public domain code COHERENS. The volume fraction concept is particularly interesting for coarse grid cells that are agglomerated from both dry and wet fine grid cells at irregular coastlines. At these locations, modifying the prolongation operator and the coarse grid discretization, using the volume fraction, results in better convergence. However, as convergence deteriorates in the case of small, elongated islands that tend to disappear by the multigrid coarsening procedure, a correction is proposed, yielding good convergence rates, irrespective of the presence of small or large islands. The method is tested extensively for the inversion of the academic Poisson equation. Larger test cases, solving the Helmholz-type equation, prove the applicability for real-life applications of environmental flows.