A fully-explicit discontinuous Galerkin hydrodynamic model for variably-saturated porous media

A scalable coupled surface–subsurface flow model

“…(22)-(24) are discretized in time with an explicit Euler scheme. When correctly implemented, explicit schemes can yield a perfect scaling, as shown in [24]. Indeed, their inherent simplicity and the absence of linear system solver limit the communication overhead between processors.…”

“…The subsurface model has been validated in a previous publication [24]. The surface model implementation with the CVFE method is compared with the tilted V-catchment 2D example from [8] that has been extensively used to validate surface models (as for instance [7,36]).…”

“…The identification of the scaling performance for the different parts of the algorithm highlights the source of the poor scaling. Although the solution of subsurface model is the most expensive, it scales optimally as shown in [24]. However, the surface part relies on an implicit solver which requires many inter- Fig.…”

“…The time step of implicit time integration schemes is unrestricted for simple diffusion equations, but the non-linearities of the Richards' equation put an upper limit to it [17]. Recently, De Maet et al [24] have proposed a model using an explicit time integration scheme and a discontinuous Galerkin (DG) finite element (FE) spatial discretization. Such an approach achieves an optimal strong scaling as it does not require linear or non-linear solvers and hence avoids the associated convergence issues.…”

“…In this paper, we present a coupled surface-subsurface flow model that combines an implicit model for the non-inertia shallow water equation and an explicit model for the Richards' equation [24]. Such an approach allows us to use the same time step for both models, as the slow dynamics of the groundwater requires an explicit time step close to the implicit time step required for convergence of the surface flow non-linear solver.…”