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Journal of Scientific Computing

Erschienen in:

09.10.2017

Conservative Local Discontinuous Galerkin Method for Compressible Miscible Displacements in Porous Media

verfasst von: Fan Yu, Hui Guo, Nattaporn Chuenjarern, Yang Yang

Erschienen in: Journal of Scientific Computing | Ausgabe 2-3/2017

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Abstract

In Guo et al. (Appl Math Comput 259:88–105, 2015), a nonconservative local discontinuous Galerkin (LDG) method for both flow and transport equations was introduced for the one-dimensional coupled system of compressible miscible displacement problem. In this paper, we will continue our effort and develop a conservative LDG method for the problem in two space dimensions. Optimal error estimates in \(L^{\infty }(0, T; L^{2})\) norm for not only the solution itself but also the auxiliary variables will be derived. 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 will be given to confirm the accuracy and efficiency of the scheme.

Vorheriger Artikel Discontinuous Galerkin Methods for Relativistic Vlasov–Maxwell System

Nächster Artikel Fourier Type Super Convergence Study on DDGIC and Symmetric DDG Methods

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Titel: Conservative Local Discontinuous Galerkin Method for Compressible Miscible Displacements in Porous Media
verfasst von: Fan Yu
Hui Guo
Nattaporn Chuenjarern
Yang Yang
Publikationsdatum: 09.10.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2-3/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0571-z

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