Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions

Paper presents a new solver for numerical solution of the Boltzmann kinetic equation with Shakhov model collision integral (S-model) for arbitrary spatial domains. Numerical method utilizes Tensor-Train decomposition, which allows to reduce required computer memory for up to 30 times even on a moder...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Chikitkin, A V, Kornev, E K, Titarev, V A
Format: Article
Language:English
Subjects:
Boltzmann transport equation
Computer simulation
Decomposition
Distribution functions
Domains
Finite element method
Integrals
Kinetic equations
Mathematical analysis
Mathematical models
Numerical analysis
Numerical methods
Personal computers
Tensors
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Summary:Paper presents a new solver for numerical solution of the Boltzmann kinetic equation with Shakhov model collision integral (S-model) for arbitrary spatial domains. Numerical method utilizes Tensor-Train decomposition, which allows to reduce required computer memory for up to 30 times even on a moderate velocity mesh. This improvement is achieved by representing values of distribution function on the structured velocity mesh as a 3D tensor in Tensor-Train format. The resulting numerical method makes it possible to solve complex 3D problems on modern desktop computers. Our implementation may serve as a prototype code for researchers concerned with numerical solution of the kinetic equations in 3D domains by the discrete velocity method.
ISSN:2331-8422
DOI:10.48550/arxiv.1912.04582