English

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

Numerical Analysis 2021-04-13 v2 Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.1912.04582,
  title  = {Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions},
  author = {A. V. Chikitkin and E. K. Kornev and V. A. Titarev},
  journal= {arXiv preprint arXiv:1912.04582},
  year   = {2021}
}
R2 v1 2026-06-23T12:41:08.789Z