Representation Theory Based Algorithm to Compute Boltzmann’s Bilinear Collision Operator in the Irreducible Spectral Burnett Ansatz Efficiently

被引：0
作者：
Andrea Hanke
Manuel Torrilhon
机构：
[1] RWTH Aachen University,Applied Computational Mathematics
来源：
Journal of Scientific Computing | 2023年 / 95卷
关键词：
Gas dynamics; Particle interactions; Moment equations; Symmetric trace-free tensors; Spherical harmonics; Boltzmann equation;
D O I：
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摘要：
Numerically solving the Boltzmann equation is computationally expensive in part due to the number of variables the distribution function depends upon. Another contributor to the complexity of the Boltzmann Equation is the quadratic collision operator describing changes in the distribution function due to colliding particle pairs. Solving it as efficiently as possible has been a topic of recent research, e.g. Cai and Torrilhon (Phys Fluids 31(12):126105, 2019. https://doi.org/10.1063/1.5127114), Wang and Cai (J Comput Phys 397:108815, 2019. https://doi.org/10.1016/j.jcp.2019.07.014), Cai et al. (Comput Fluids 200:104456, 2020. https://doi.org/10.1016/j.compfluid.2020.104456). In this paper we exploit results from representation theory to find a very efficient algorithm both in terms of memory and computational time for the evaluation of the quadratic collision operator. With this novel approach we are also able to provide a meaningful interpretation of its structure.
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