Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics

M.R.A. Abdelmalik; Harald van Brummelen

doi:10.1007/978-3-030-30705-9_8

Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics

M.R.A. Abdelmalik, Harald van Brummelen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

In this work we propose numerical approximations of the Boltzmann equation that are consistent with the Euler and Navier–Stoke–Fourier solutions. We conceive of the Euler and the Navier–Stokes–Fourier equations as moment approximations of the Boltzmann equation in renormalized form. Such renormalizations arise from the so-called Chapman-Enskog analysis of the one-particle marginal in the Boltzmann equation. We present a numerical approximation of the Boltzmann equation that is based on the discontinuous Galerkin method in position dependence and on the renormalized-moment method in velocity dependence. We show that the resulting discontinuous Galerkin finite element moment method is entropy stable. Numerical results are presented for turbulent flow in the lid-driven cavity benchmark.

Original language	English
Title of host publication	Numerical Methods for Flows
Subtitle of host publication	FEF 2017 Selected Contributions
Editors	Harald van Brummelen, Alessandro Corsini, Simona Perotto, Gianluigi Rozza
Place of Publication	Cham
Publisher	Springer
Pages	75-95
Number of pages	21
ISBN (Electronic)	978-3-030-30705-9
ISBN (Print)	978-3-030-30704-2
DOIs	https://doi.org/10.1007/978-3-030-30705-9_8
Publication status	Published - 1 Jan 2020
Event	19th International Conference on Finite Elements in Flow Problems, FEF 2017 - Rome, Italy Duration: 5 Apr 2017 → 7 Apr 2017

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	132
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	19th International Conference on Finite Elements in Flow Problems, FEF 2017
Country/Territory	Italy
City	Rome
Period	5/04/17 → 7/04/17

Funding

This work is part of the research programme RARETRANS with project number HTSM-15376, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). The support of ASML of the RARETRANS programme is gratefully acknowledged.

Keywords

Continuum fluid dynamics
Discontinuous Galerkin finite elements
Entropy stability
Moment closure
Moment systems

Access to Document

10.1007/978-3-030-30705-9_8

Cite this

Abdelmalik, M. R. A., & van Brummelen, H. (2020). Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics. In H. van Brummelen, A. Corsini, S. Perotto, & G. Rozza (Eds.), Numerical Methods for Flows: FEF 2017 Selected Contributions (pp. 75-95). (Lecture Notes in Computational Science and Engineering; Vol. 132). Springer. https://doi.org/10.1007/978-3-030-30705-9_8

Abdelmalik, M.R.A. ; van Brummelen, Harald. / Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics. Numerical Methods for Flows: FEF 2017 Selected Contributions. editor / Harald van Brummelen ; Alessandro Corsini ; Simona Perotto ; Gianluigi Rozza. Cham : Springer, 2020. pp. 75-95 (Lecture Notes in Computational Science and Engineering).

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abstract = "In this work we propose numerical approximations of the Boltzmann equation that are consistent with the Euler and Navier–Stoke–Fourier solutions. We conceive of the Euler and the Navier–Stokes–Fourier equations as moment approximations of the Boltzmann equation in renormalized form. Such renormalizations arise from the so-called Chapman-Enskog analysis of the one-particle marginal in the Boltzmann equation. We present a numerical approximation of the Boltzmann equation that is based on the discontinuous Galerkin method in position dependence and on the renormalized-moment method in velocity dependence. We show that the resulting discontinuous Galerkin finite element moment method is entropy stable. Numerical results are presented for turbulent flow in the lid-driven cavity benchmark.",

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Abdelmalik, MRA & van Brummelen, H 2020, Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics. in H van Brummelen, A Corsini, S Perotto & G Rozza (eds), Numerical Methods for Flows: FEF 2017 Selected Contributions. Lecture Notes in Computational Science and Engineering, vol. 132, Springer, Cham, pp. 75-95, 19th International Conference on Finite Elements in Flow Problems, FEF 2017, Rome, Italy, 5/04/17. https://doi.org/10.1007/978-3-030-30705-9_8

Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics. / Abdelmalik, M.R.A.; van Brummelen, Harald.
Numerical Methods for Flows: FEF 2017 Selected Contributions. ed. / Harald van Brummelen; Alessandro Corsini; Simona Perotto; Gianluigi Rozza. Cham: Springer, 2020. p. 75-95 (Lecture Notes in Computational Science and Engineering; Vol. 132).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Abdelmalik, M.R.A.

AU - van Brummelen, Harald

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N2 - In this work we propose numerical approximations of the Boltzmann equation that are consistent with the Euler and Navier–Stoke–Fourier solutions. We conceive of the Euler and the Navier–Stokes–Fourier equations as moment approximations of the Boltzmann equation in renormalized form. Such renormalizations arise from the so-called Chapman-Enskog analysis of the one-particle marginal in the Boltzmann equation. We present a numerical approximation of the Boltzmann equation that is based on the discontinuous Galerkin method in position dependence and on the renormalized-moment method in velocity dependence. We show that the resulting discontinuous Galerkin finite element moment method is entropy stable. Numerical results are presented for turbulent flow in the lid-driven cavity benchmark.

AB - In this work we propose numerical approximations of the Boltzmann equation that are consistent with the Euler and Navier–Stoke–Fourier solutions. We conceive of the Euler and the Navier–Stokes–Fourier equations as moment approximations of the Boltzmann equation in renormalized form. Such renormalizations arise from the so-called Chapman-Enskog analysis of the one-particle marginal in the Boltzmann equation. We present a numerical approximation of the Boltzmann equation that is based on the discontinuous Galerkin method in position dependence and on the renormalized-moment method in velocity dependence. We show that the resulting discontinuous Galerkin finite element moment method is entropy stable. Numerical results are presented for turbulent flow in the lid-driven cavity benchmark.

KW - Continuum fluid dynamics

KW - Discontinuous Galerkin finite elements

KW - Entropy stability

KW - Moment closure

KW - Moment systems

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Abdelmalik MRA , van Brummelen H. Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics. In van Brummelen H, Corsini A, Perotto S, Rozza G, editors, Numerical Methods for Flows: FEF 2017 Selected Contributions. Cham: Springer. 2020. p. 75-95. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-30705-9_8

Entropy stable discontinuous Galerkin finite element moment methods for compressible fluid dynamics

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