An explicit Discontinuous-Galerkin surface-subsurface water flow model

De Maet, Thomas [UCL] Hanert, Emmanuel [UCL]

In this paper, we present a terrestrial hydrological model that explicitly couples the subsurface and surface hydrodynamics. The use of an explicit time integration scheme allows for an optimal par- allel scaling and an efficient coupling between surface and subsurface components. The saturated- unsaturated subsurface module solves Richards equation with a mixed discontinuous-Galerkin (DG) finite element formulation, using both the pressure head h and the water content θ as prognostic vari- ables. θ is used for the unsaturated zone, where it is know to be more efficient, and h is used for the saturated zone, where θ is constant. In the saturated zone, an un-converged false transient method is used in order to replace the elliptic equation by a parabolic one. To allow physical discontinuities between different types of soils, we make use of a modified jump term in the DG formulation for the variable θ. The diffusive wave approximation is applied to the shallow water equation for surface flows including runoff, lakes and small rivers. The surface-subsurface coupling is ensured through a flux continuity constraint The latter is determined by the subsurface model for which a Dirichlet boundary condition is applied, equalizing surface and subsurface pressures. The resulting model is robust and fully conservative.