Vol. 17, no. 4, 2025
РусскийEnglish
INFORMATION TECHNOLOGIES
Parallel Algorithm for Numerical Solution of the Boltzmann Kinetic Equation with Model Collision Integral Using Tucker Tensor Decomposition
Egor K. Kornev, Vasily I. Golubev
Moscow Institute of Physics and Technology, https://mipt.ru/
Dolgoprudny 141700, Moscow region, Russian Federation
E-mail: kornev.ek@phystech.edu, golubev.vi@mipt.ru
Received June 27, 2025, peer-reviewed July 11, 2025, accepted July 14, 2025, published August 14, 2025
Abstract: This paper presents a dimensionality reduction methodology for the discrete velocity method applied to the numerical solution of the Boltzmann equation with S-model collision integral on unstructured meshes. A low-rank approximation in the Tucker tensor format is used to represent the discrete distribution function within a spatial cell. A shared memory parallel version of the block LU-SGS method is presented for the approximate solution of the linear system arising from the implicit time integration scheme for updating the discrete distribution function. Numerical results are provided for argon flow around a cylinder, including an analysis of the influence of tensor truncation accuracy on the solution, as well as a performance comparison of the parallel method with respect to the number of threads.
Keywords: Boltzmann equation, model collision integral, discrete velocity method, tensor decompositions, Tucker decomposition, rarefied gas dynamics
UDC 004.94
RENSIT, 2025, 17(4):449-454e DOI: 10.17725/j.rensit.2025.17.449
Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/689/17(4)449-454e.pdf