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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Acknowledgements
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.
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Abdelmalik, M.R.A., van Brummelen, H. (2020). Entropy Stable Discontinuous Galerkin Finite Element Moment Methods for Compressible Fluid Dynamics. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_8
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DOI: https://doi.org/10.1007/978-3-030-30705-9_8
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