Department of Mechanical and Aerospace Engineering

Daniel Tartakovsky › Publications › boelens-2020-tensor

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/j.jcp.2020.109744, 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.

@article{boelens-2020-tensor,

author = {A. M. P. Boelens and D. Venturi and D. M. Tartakovsky},

title = {Tensor methods for the Boltzmann-BGK equation},

year = {2020},

urlpdf = {http://maeresearch.ucsd.edu/Tartakovsky/Papers/boelens-2020-tensor.pdf},

journal = {J. Comput. Phys.},

volume = {421},

doi = {10.1016/j.jcp.2020.109744},

pages = {109744}

}