A Simple and Robust Shock-Capturing Approach for Discontinuous Galerkin Discretizations

Jae Hwan Choi, Juan J. Alonso and Edwin van der Weide
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Jae Hwan Choi: Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA
Juan J. Alonso: Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA
Edwin van der Weide: Department of Mechanical Engineering, University of Twente, 7522 NB Enschede, The Netherlands

Energies, 2019, vol. 12, issue 14, 1-19

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.

Keywords: discontinuous Galerkin method; shock-capturing; discontinuities; high-order methods; CFD (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
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