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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