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

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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 languageEnglish
Title of host publicationNumerical Methods for Flows
Subtitle of host publicationFEF 2017 Selected Contributions
EditorsHarald van Brummelen, Alessandro Corsini, Simona Perotto, Gianluigi Rozza
Place of PublicationCham
PublisherSpringer
Pages75-95
Number of pages21
ISBN (Electronic)978-3-030-30705-9
ISBN (Print)978-3-030-30704-2
DOIs
Publication statusPublished - 1 Jan 2020
Event19th International Conference on Finite Elements in Flow Problems, FEF 2017 - Rome, Italy
Duration: 5 Apr 20177 Apr 2017

Publication series

NameLecture Notes in Computational Science and Engineering
Volume132
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference19th International Conference on Finite Elements in Flow Problems, FEF 2017
CountryItaly
CityRome
Period5/04/177/04/17

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Keywords

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

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). Cham: Springer. https://doi.org/10.1007/978-3-030-30705-9_8