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Numerical methods for subsurface flows and coupling with surface runoff

Pierre Sochala
Abstract : Accurate and robust numerical schemes are proposed to simulate subsurface flows and their coupling with surface runoff. Subsurface flows are modelled by the (unsteady) Richards' equation discretized by a BDF in time and a discontinuous Galerkin method with symmetric interior penalty in space. Infiltration column test cases confirm the robustness of our schemes. Firstly, we consider Signorini conditions for the Richards' equation to model buried drains or the water table reaching the ground surface ; thus we assume that exfiltrated water immediately exits the system. Secondly, runoff flow is taken into account through coupling conditions enforcing water flux equality and pressure continuity at the interface. Overland flows are modelled by the kinematic wave approximation of the shallow water equations, which is discretized by a Godunov method. Both schemes, that for the subsurface flow and that for the overland flow, are mass conservative and can be coupled within a multiple time step procedure. To ensure total water mass conservation for the whole system, interface fluxes must be carefully designed. We specify the form of these fluxes for BDF1 and BDF2. Accuracy and robustness of our schemes are assessed on drainage, exfiltration and hortonian runoff test cases. Finally, we apply the methology to investigate the hydrological behavior of a small-scale drained watershed. keywords : Richards' equation, kinematic wave approximation, discontinuous finite elements, coupling algorithms, mass conservation.
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Submitted on : Monday, January 26, 2009 - 8:00:00 AM
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Pierre Sochala. Numerical methods for subsurface flows and coupling with surface runoff. Mathematics [math]. Ecole des Ponts ParisTech, 2008. English. ⟨pastel-00004625⟩

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