A scalable coupled surface–subsurface flow model

Abstract

The coupling of physically-based models for surface and subsurface water flows is a recent concern. The study of their interactions is important both for water resource management and environmental studies. However, despite constant innovation, physically-based simulations of water flows are still time consuming. That is especially problematic for large and/or long-term studies, or to test a large range of parametrizations with an adjoint model. As the current trend in computing sciences is to increase the computational power with additional computational units, new model developments are expected to scale efficiently on parallel infrastructures. This paper describes a coupled surface–subsurface flow model that combines implicit and explicit time discretizations for the surface and subsurface dynamics, respectively. Despite that the surface flow has a faster dynamics than the subsurface flow, we are able to use a unique nearly-optimal time step for each submodel, hence improving the resources use. The surface model is discretized with an implicit control volume finite element method while the subsurface model is solved by means of an explicit discontinuous Galerkin finite element method. The surface and subsurface models are coupled by weakly imposing the continuity of water pressure. By imposing a threshold on the influence coefficients of the control volume finite element method, we can prevent the occurrence of unphysical fluxes in anisotropic elements. The proposed coupling is shown to produce results similar to state-of-the-art models for four different test cases while achieving better strong and weak scalings on up to 192 processors.