Tensor methods for the Boltzmann-BGK equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:421

Article

Boelens, Arnout M. P.¹  Venturi, Daniele²  Tartakovsky, Daniel M.¹ 

[1] Stanford Univ, Dept Energy Resources Engn, Stanford, CA 94305 USA

[2] UC Santa Cruz, Dept Appl Math, Santa Cruz, CA 95064 USA

关键词: High-dimensional PDE;    Tensor method;    Non-equilibrium;   

DOI  :  10.1016/j.jcp.2020.109744

来源: Elsevier

【 摘 要 】

We present a tensor-decomposition method to solve the Boltzmann transport equation (BTE) in the Bhatnagar-Gross-Krook approximation. The method represents the six-dimensional BTE as a set of six one-dimensional problems, which are solved with the alternating least-squares algorithm and the discrete Fourier transform at N collocation points. We use this method to predict the equilibrium distribution (steady-state simulation) and a non-equilibrium distribution returning to the equilibrium (transient simulation). Our numerical experiments demonstrate N log N scaling. Unlike many BTE-specific numerical techniques, the numerical tensor-decomposition method we propose is a general technique that can be applied to other high-dimensional systems. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free