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Cite Details

A. M. P. Boelens, D. Venturi and D. M. Tartakovsky, "Tensor methods for the Boltzmann-BGK equation", J. Comput. Phys., vol. 421, doi:10.1016/, pp. 109744, 2020


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.

BibTeX Entry

author = {A. M. P. Boelens and D. Venturi and D. M. Tartakovsky},
title = {Tensor methods for the Boltzmann-BGK equation},
year = {2020},
urlpdf = {},
journal = {J. Comput. Phys.},
volume = {421},
doi = {10.1016/},
pages = {109744}