A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

    Research output: Contribution to journalArticleAcademicpeer-review

    15 Citations (Scopus)

    Abstract

    Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In particular entropy variables can provide numerical methods with attractive properties, e.g. fulfillment of the second law of thermodynamics. We show how a discontinuous Galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids. We also examine which components of the numerical method have to be changed or adapted. Especially, we investigate different possibilities of solving the nonlinear algebraic system with a pseudo-time iteration. Numerical results highlight the applicability of the method for various fluids.
    Original languageUndefined
    Article number10.1016/j.jcp.2008.01.046
    Pages (from-to)5426-5446
    Number of pages21
    JournalJournal of computational physics
    Volume227
    Issue numberWP 08-02/11
    DOIs
    Publication statusPublished - 10 May 2008

    Keywords

    • Discontinuous Galerkin finite element methods
    • Entropy variables
    • Pseudo-time integration methods
    • EWI-14907
    • METIS-255134
    • IR-62699
    • Euler equations
    • Compressible flow
    • Incompressible flow
    • General equations of state

    Cite this

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    title = "A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids",
    abstract = "Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In particular entropy variables can provide numerical methods with attractive properties, e.g. fulfillment of the second law of thermodynamics. We show how a discontinuous Galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids. We also examine which components of the numerical method have to be changed or adapted. Especially, we investigate different possibilities of solving the nonlinear algebraic system with a pseudo-time iteration. Numerical results highlight the applicability of the method for various fluids.",
    keywords = "Discontinuous Galerkin finite element methods, Entropy variables, Pseudo-time integration methods, EWI-14907, METIS-255134, IR-62699, Euler equations, Compressible flow, Incompressible flow, General equations of state",
    author = "L. Pesch and {van der Vegt}, {Jacobus J.W.}",
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    language = "Undefined",
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    issn = "0021-9991",
    publisher = "Academic Press Inc.",
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    A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids. / Pesch, L.; van der Vegt, Jacobus J.W.

    In: Journal of computational physics, Vol. 227, No. WP 08-02/11, 10.1016/j.jcp.2008.01.046, 10.05.2008, p. 5426-5446.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AU - Pesch, L.

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    AB - Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In particular entropy variables can provide numerical methods with attractive properties, e.g. fulfillment of the second law of thermodynamics. We show how a discontinuous Galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids. We also examine which components of the numerical method have to be changed or adapted. Especially, we investigate different possibilities of solving the nonlinear algebraic system with a pseudo-time iteration. Numerical results highlight the applicability of the method for various fluids.

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    KW - Compressible flow

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    KW - General equations of state

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