Tensor Decompositions for the Numerical Simulation of Rarefied Gas Flows in 3D Domains

The numerical simulation of rarefied gas flows governed by kinetic equations typically involves high-dimensional phase spaces and substantial computational costs. A major challenge of direct approaches is the significant memory demand resulting from the high dimensionality of the problem. In this work, to numerically solve the S-model kinetic equation, a modified discrete velocity method coupled with a finite-volume formulation is used, in which the distribution function of the gas is represented using tensor decompositions. Specifically, the Tucker decomposition is employed to compress and manipulate multidimensional data, significantly reducing memory consumption while introducing additional algorithmic complexity. The method was successfully applied to a three-dimensional problem of gas outflow from a pipe over a range of Knudsen numbers, demonstrating substantial memory compression without loss of solution quality. The presented method can be further extended to other three-dimensional problems and provides a framework for efficient large-scale simulations of rarefied gas dynamics.