Numerical Methods for Subsurface Flows and Coupling with Surface Runoff

Abstract

Robust and accurate schemes are proposed to couple subsurface and overland flows by enforcing the continuity of the normal flux and the pressure. Richards’ equation governing the subsurface flow is discretized using a Backward Differentiation Formula in time and a symmetric interior penalty Discontinuous Galerkin method in space. The kinematic wave equation governing the overland flow is discretized using a Godunov scheme. Both schemes are individually mass conservative and can be used within coupling algorithms that ensure overall mass conservation owing to a specific design of the interface fluxes in the multi-step case. For field drainage problems, we also propose a method for representing drain tubes using Signorini type conditions. Numerical results are presented to illustrate the performances of the proposed algorithms.

Keywords: Backward Differentiation Formula, Beavers-Joseph-Saffman condition, field drainage problems, Godunov scheme, high-order initialization, hydraulic conductivity, kinematic wave equation, mass conservative schemes, matrix renumerotation, Richards’ equation, saturated porous media, Signorini type conditions, subsurface flow.