Mass conservative BDF-discontinuous Galerkin/explicit finite volume schemes for coupling subsurface and overland flows

TL;DR

This paper introduces robust, mass-conservative numerical schemes for accurately simulating coupled subsurface and overland flows, ensuring interface flux continuity and overall mass conservation.

Contribution

It develops a novel coupling approach combining BDF-discontinuous Galerkin and Godunov schemes for subsurface and overland flows, ensuring mass conservation at the interface.

Findings

Schemes are mass conservative individually and when coupled.

Numerical results demonstrate the accuracy and robustness of the algorithms.

The methods effectively simulate coupled flow dynamics in complex scenarios.

Abstract

Robust and accurate schemes are designed to simulate the coupling between subsurface and overland flows. The coupling conditions at the interface enforce the continuity of both the normal flux and the pressure. Richards' equation governing the subsurface flow is discretized using a Backward Differentiation Formula and a symmetric interior penalty Discontinuous Galerkin method. The kinematic wave equation governing the overland flow is discretized using a Godunov scheme. Both schemes individually are mass conservative and can be used within single-step or multi-step coupling algorithms that ensure overall mass conservation owing to a specific design of the interface fluxes in the multi-step case. Numerical results are presented to illustrate the performances of the proposed algorithms.