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

TL;DR

This paper introduces a tensor decomposition-based solver for the Boltzmann equation with the S-model collision integral, significantly reducing memory usage and enabling complex 3D kinetic simulations on standard desktops.

Contribution

The paper develops a novel tensor-train based numerical method for solving the Boltzmann equation with the S-model collision integral in 3D, improving efficiency and accessibility.

Findings

Memory usage reduced by up to 30 times

Enables solving complex 3D problems on desktops

Provides a prototype code for kinetic equation simulations

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.