Large structure simulation for landscape evolution models

Abstract

The aim of this paper is to discuss the efficiency of a new methodology to maintain the accuracy of numerical solutions obtained from our landscape evolution model (LEM). As in every LEM, the tricky part is the coupling between water and sediment flows that drives the nonlinear self-amplification mechanisms. But this coupling is also responsible for the emergence and amplification of numerical errors, as we illustrate here. These numerical instabilities being strongly reminiscent of turbulence-induced instabilities in computational fluid dynamics (CFD), we introduce a “large structure simulation” (LSS) approach for LEM, mimicking the large eddy simulation (LESs) used for turbulent CFD. In practice, this treatment consists in a filtering strategy that controls small-scale perturbations in the solution. We demonstrate the accuracy of the LSS approach in the context of our LEM.