Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems

TL;DR

This paper develops a coupled hydrostatic free surface and saturated subsurface flow model using a discontinuous Galerkin method, proving its discrete energy stability for the nonlinear system.

Contribution

It introduces a novel coupled model with a discontinuous Galerkin discretization and provides a proof of discrete energy stability for the nonlinear system.

Findings

Model achieves discrete energy stability

Coupled system effectively integrates surface and subsurface flows

Discontinuous Galerkin method is suitable for nonlinear coupled systems

Abstract

We formulate a coupled surface/subsurface flow model that relies on hydrostatic equations with free surface in the free flow domain and on the Darcy model in the subsurface part. The model is discretized using the local discontinuous Galerkin method, and a statement of discrete energy stability is proved for the fully non-linear coupled system.