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arXiv · 1712.07617

Convergence of a semi-Lagrangian scheme for the ellipsoidal BGK model of the Boltzmann equation

Giovanni Russo·Seok-Bae Yun
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Abstract

The ellipsoidal BGK model is a generalized version of the original BGK model designed to reproduce the physical Prandtl number in the Navier-Stokes limit. In this paper, we propose a new implicit semi-Lagrangian scheme for the ellipsoidal BGK model, which, by exploiting special structures of the ellipsoidal Gaussian, can be transformed into a semi-explicit form, guaranteeing the stability of the implicit methods and the efficiency of the explicit methods at the same time. We then derive an error estimate of this scheme in a weighted $L^{\infty}$ norm. Our convergence estimate holds uniformly in the whole range of relaxation parameter $\nu$ including $\nu=0$, which corresponds to the original BGK model.

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Giovanni Russo, Seok-Bae Yun. 2017-12-20. Convergence of a semi-Lagrangian scheme for the ellipsoidal BGK model of the Boltzmann equation. https://arxiv.org/abs/1712.07617

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