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arXiv · 2301.05850

Hermite spectral method for the inelastic Boltzmann equation

Ruo Li·Yixiao Lu·Yanli Wang
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Abstract

We propose a Hermite spectral method for the inelastic Boltzmann equation, which makes two-dimensional periodic problem computation affordable by the hardware nowadays. The new algorithm is based on a Hermite expansion, where the expansion coefficients for the VHS model are reduced into several summations and can be derived exactly. Moreover, a new collision model is built with a combination of the quadratic collision operator and a linearized collision operator, which helps us to balance the computational cost and the accuracy. Various numerical experiments, including spatially two-dimensional simulations, demonstrate the accuracy and efficiency of this numerical scheme.

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Ruo Li, Yixiao Lu, Yanli Wang. 2023-01-14. Hermite spectral method for the inelastic Boltzmann equation. https://arxiv.org/abs/2301.05850

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