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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2017

01.11.2016

Local Discontinuous Galerkin Method for Incompressible Miscible Displacement Problem in Porous Media

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2017

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Abstract

In this paper, we develop local discontinuous Galerkin method for the two-dimensional coupled system of incompressible miscible displacement problem. Optimal error estimates in \(L^{\infty }(0, T; L^{2})\) for concentration c, \(L^{2}(0, T; L^{2})\) for \(\nabla c\) and \(L^{\infty }(0, T; L^{2})\) for velocity \(\mathbf{u}\) are derived. The main techniques in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method, the nonlinearity, and the coupling of the models. The main difficulty is how to treat the inter-element discontinuities of two independent solution variables (one from the flow equation and the other from the transport equation) at cell interfaces. Numerical experiments are shown to demonstrate the theoretical results.
Vorheriger Artikel Polynomial Preserving Recovery for High Frequency Wave Propagation
Nächster Artikel A New Augmented Singular Transform and its Partial Newton-Correction Method for Finding More Solutions

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Metadaten
Titel
Local Discontinuous Galerkin Method for Incompressible Miscible Displacement Problem in Porous Media
Publikationsdatum
01.11.2016
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0313-7

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