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An Adaptive Dynamical Low Rank Method for the Nonlinear Boltzmann Equation

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Abstract

Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision operator. In this work, we propose a highly efficient adaptive low rank method for the Boltzmann equation, concerning in particular the steady state computation. This method employs the fast Fourier spectral method (for the collision operator) and the dynamical low rank method to obtain computational efficiency. An adaptive strategy is introduced to incorporate the boundary information and control the computational rank in an appropriate way. Using a series of benchmark tests in 1D and 2D, we demonstrate the efficiency and accuracy of the proposed method in comparison to the full tensor grid approach.

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Funding

This work is partially supported under the NSF CAREER grant DMS-2153208, NSF CDS & E grant CBET-1854829, and AFOSR grant FA9550-21-1-0358.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA

    Jingwei Hu

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Yubo Wang

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  1. Jingwei Hu
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  2. Yubo Wang
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Correspondence to Jingwei Hu.

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Hu, J., Wang, Y. An Adaptive Dynamical Low Rank Method for the Nonlinear Boltzmann Equation. J Sci Comput 92, 75 (2022). https://doi.org/10.1007/s10915-022-01934-4

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  • DOI: https://doi.org/10.1007/s10915-022-01934-4

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