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

Abstract

The paper presents a new solver for the numerical solution of the Boltzmann kinetic equation with the Shakhov model collision integral (S-model) for arbitrary spatial domains. The numerical method utilizes the Tucker decomposition, which reduces the required computer memory for up to 100 times, even on a moderate velocity grid. This improvement is achieved by representing the distribution function values on a structured velocity grid as a 3D tensor in the Tucker 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 the numerical solution of kinetic equations in 3D domains using a discrete velocity method. Program summaryProgram Title: Boltzmann-TCPC Library link to program files:https://doi.org/10.17632/29wv8nmbgn.1Developer’s repository link:https://github.com/chikitkin/Boltzmann-TuckerLicensing provisions: MITProgramming language: Python 3External libraries: Solver is based on the customized version of the tucker3d library [1]Nature of problem: Numerical solution of the Boltzmann kinetic equation with the S-model collision integral in an arbitrary 3D spatial domainSolution method: Discrete velocity method utilizing tensor decomposition for memory reductionAdditional comments including restrictions and unusual features: At present, 1st order advection scheme is used, solver supports unstructured hexagonal meshes written in StarCD ASCII formatReference tucker3d (https://github.com/rakhuba/tucker3d) library contains Python implementations of several important procedures for working with tensors in the Tucker format.