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We formulate a coupled surface/subsurface flow model that relies onhydrostatic equations with free surface in the free flow domain and on theDarcy model in the subsurface part. The model is discretized using the localdiscontinuous Galerkin method, and a statement of discrete energy stability isproved for the fully non-linear coupled system.

Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems