A simple and robust shock-capturing approach for discontinuous Galerkin discretizations

Jae Hwan Choi*, Juan J. Alonso, Edwin van der Weide

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

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    Abstract

    The discontinuous Galerkin (DG) method has become popular in Computational Fluid Dynamics mainly due to its ability to achieve high-order solution accuracy on arbitrary grids, its high arithmetic intensity (measured as the ratio of the number of floating point operations to memory references), and the use of a local stencil that makes scalable parallel solutions possible. Despite its advantages, several difficulties hinder widespread use of the DG method, especially in industrial applications. One of the major challenges remaining is the capturing of discontinuities in a robust and accurate way. In our previous work, we have proposed a simple shock detector to identify discontinuities within a flow solution. The detector only utilizes local information to sense a shock/discontinuity ensuring that one of the key advantages of DG methods, their data locality, is not lost in transonic and supersonic flows. In this work, we reexamine the shock detector capabilities to distinguish between smooth and discontinuous solutions. Furthermore, we optimize the functional relationships between the shock detector and the filter strength, and present it in detail for others to use. By utilizing the shock detector and the corresponding filtering-strength relationships, one can robustly and accurately capture discontinuities ranging from very weak to strong shocks. Our method is demonstrated in a number of two-dimensional canonical examples.

    Original languageEnglish
    Article number2651
    JournalEnergies
    Volume12
    Issue number14
    DOIs
    Publication statusPublished - 10 Jul 2019

    Fingerprint

    Shock Capturing
    Discontinuous Galerkin
    Shock
    Discretization
    Detectors
    Galerkin methods
    Detector
    Discontinuity
    Discontinuous Galerkin Method
    Transonic flow
    Supersonic flow
    Data Locality
    Discontinuous Solutions
    Transonic Flow
    Functional Relationship
    Supersonic Flow
    Industrial applications
    Floating point
    Smooth Solution
    Industrial Application

    Keywords

    • CFD
    • Discontinuities
    • Discontinuous Galerkin method
    • High-order methods
    • Shock-capturing

    Cite this

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    title = "A simple and robust shock-capturing approach for discontinuous Galerkin discretizations",
    abstract = "The discontinuous Galerkin (DG) method has become popular in Computational Fluid Dynamics mainly due to its ability to achieve high-order solution accuracy on arbitrary grids, its high arithmetic intensity (measured as the ratio of the number of floating point operations to memory references), and the use of a local stencil that makes scalable parallel solutions possible. Despite its advantages, several difficulties hinder widespread use of the DG method, especially in industrial applications. One of the major challenges remaining is the capturing of discontinuities in a robust and accurate way. In our previous work, we have proposed a simple shock detector to identify discontinuities within a flow solution. The detector only utilizes local information to sense a shock/discontinuity ensuring that one of the key advantages of DG methods, their data locality, is not lost in transonic and supersonic flows. In this work, we reexamine the shock detector capabilities to distinguish between smooth and discontinuous solutions. Furthermore, we optimize the functional relationships between the shock detector and the filter strength, and present it in detail for others to use. By utilizing the shock detector and the corresponding filtering-strength relationships, one can robustly and accurately capture discontinuities ranging from very weak to strong shocks. Our method is demonstrated in a number of two-dimensional canonical examples.",
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    A simple and robust shock-capturing approach for discontinuous Galerkin discretizations. / Choi, Jae Hwan; Alonso, Juan J.; van der Weide, Edwin.

    In: Energies, Vol. 12, No. 14, 2651, 10.07.2019.

    Research output: Contribution to journalArticleAcademicpeer-review

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