A tensorized version of LU-SGS solver for discrete velocity method for Boltzmann kinetic equation with model collision integral

This paper presents a new solver for numerical solution of Boltzmann kinetic equation with S-model collision integral in 3D case with utilization of Tensor-Train decomposition. We take into account the good mathematical properties of numeric arrays (tensors) arising in the problem and use different tensor representation to noticeably compress the data and make the code more memory-efficient. We adopt the known implicit numerical method and adapt it for the new tensor format. The tests show good accuracy and satisfactory rate of convergence.