In the present work, the Tensor-Train decomposition algorithm is applied to reduce the memory footprint of a stochastic discrete velocity solver for rarefied gas dynamics simulation. An energy-conserving modification to the algorithm is proposed, along with an interleaved collision/convection routine which allows for easy application of higher-order convection schemes. The performance of the developed algorithm is analyzed for several 0- and 1-dimensional model problems in terms of solution error and reduction in memory use requirements.
@article{arxiv.2303.15142,
title = {Use of Tensor-Train Decompositions with a Discrete Velocity Boltzmann Solver},
author = {Georgii Oblapenko},
journal= {arXiv preprint arXiv:2303.15142},
year = {2023}
}