Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems. (1st May 2019)

• Record Type: Journal Article
• Authors: Reuter, Balthasar; Rupp, Andreas; Aizinger, Vadym; Knabner, Peter
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 9(2019)
• Page Start: 2291
• Page End: 2309
• Publication Date: 2019-05-01
• Subjects: Darcy flow -- Hydrostatic equations -- Three-dimensional shallow water equations with free surface -- Coupled model -- Local discontinuous Galerkin method -- Discrete energy stability analysis; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.12.020
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We formulate a coupled surface/subsurface flow model that relies on hydrostatic equations with free surface in the free flow domain and on Darcy's law in the subsurface. The model is discretized using the local discontinuous Galerkin method, and a statement of discrete energy stability is proved for the fully non-linear coupled system. The performance of the proposed scheme is illustrated by a numerical convergence study and a realistic example.