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High-Order Cut-Cell Discontinuous Galerkin Difference Discretization

Rensselaer Polytechnic Institute, Troy, New York 12180

*Graduate Student, Department of Mechanical, Aerospace and Nuclear Engineering; . Student Member AIAA (Corresponding Author).

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Ge Yan

Rensselaer Polytechnic Institute, Troy, New York 12180

†Graduate Student, Department of Mechanical, Aerospace and Nuclear Engineering.

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and

Jason E. Hicken

https://orcid.org/0000-0002-8523-6455

Rensselaer Polytechnic Institute, Troy, New York 12180

‡Associate Professor, Department of Mechanical, Aerospace and Nuclear Engineering; . Associate Fellow AIAA.

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Published Online:26 Jun 2023https://doi.org/10.2514/1.J062990

Abstract

We present a high-order cut-cell method based on the discontinuous Galerkin difference (DGD) discretization. We leverage the inherent properties of the DGD basis functions to construct a cut-cell discretization that does not require special treatment to mitigate the small-cell problem. The paper describes how the DGD discretization can be constructed from an existing discontinuous Galerkin (DG) discretization, and we highlight differences between the DG and DGD methods. By performing condition-number studies on one- and two-dimensional model problems, we demonstrate that cut-cell DGD discretization remains well conditioned even when the cut-cell volume is orders of magnitude smaller than neighboring cells. We verify the high-order accuracy of the discretization by solving the two-dimensional steady-state Euler equations.

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Volume 61, Number 10October 2023

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Copyright © 2023 by Sharanjeet Kaur, Ge Yan, and Jason Hicken. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-385X to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp.

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Acknowledgments

S. Kaur was partially supported by the National Science Foundation under grant no. 1825991, and G. Yan was partially supported by the National Science Foundation under grant no. 1554253. The authors gratefully acknowledge this support. We are also thankful to Rensselaer Polytechnic Institute’s Scientific Computation Research Center for the use of computer facilities.

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Received11 March 2023
Accepted30 May 2023
Published online26 June 2023

High-Order Cut-Cell Discontinuous Galerkin Difference Discretization

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