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2014 | OriginalPaper | Buchkapitel

Discontinuous Finite Element Methods for Coupled Surface–Subsurface Flow and Transport Problems

verfasst von : Beatrice Riviere

Erschienen in: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

Verlag: Springer International Publishing

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Abstract

A numerical method is proposed to solve the coupled flow and transport problems in adjacent surface and subsurface regions. The flow problem is characterized by the Navier–Stokes (or Stokes) equations coupled by Darcy equations. In the subsurface, the diffusion coefficient of the transport equation depends on the velocity field in a nonlinear manner. The interior penalty discontinuous Galerkin method is used for the spatial discretization, and the backward Euler technique for the time integration. Convergence of the scheme is theoretically derived. Numerical examples show the robustness of the method for heterogeneous and fractured porous media.

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Titel: Discontinuous Finite Element Methods for Coupled Surface–Subsurface Flow and Transport Problems
verfasst von: Beatrice Riviere
Verlag: Springer International Publishing
Buch: Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations
Print ISBN: 978-3-319-01817-1

Electronic ISBN: 978-3-319-01818-8

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-319-01818-8_11

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