Tensor methods for the Boltzmann-BGK equation

[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.

[发布日期] 2020-11-15

[关键词] High-dimensional PDE;Tensor method;Non-equilibrium