A fast spectral method for the inelastic Boltzmann collision operator and application to heated granular gases

JOURNAL OF COMPUTATIONAL PHYSICS

卷:385

Article

Hu, Jingwei¹  Ma, Zheng¹ 

[1] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

关键词: Inelastic collision operator;    Inelastic Boltzmann equation with a heating source;    Granular gas;    Haff's cooling law;    Fast Fourier spectral method;    Spherical design;   

DOI  :  10.1016/j.jcp.2019.01.049

来源: Elsevier

【 摘 要 】

In this paper, we propose a simple fast Fourier spectral method for the inelastic Boltzmann collision operator, with its application to one of the widely used models of granular gases, the inelastic Boltzmann equation with a heating source. Compared to the direct Fourier spectral method, our fast algorithm reduces the computational complexity from O (N-6) to O (MN4 logN) per evaluation of the collision operator in three dimensions, where N is the number of discretization points in each velocity dimension and M << N-2 is the number of quadrature points used on the unit sphere. We test the numerical accuracy and efficiency of the proposed method in both two dimensional and three dimensional examples, where in the latter case the famous Haff's cooling law for granular flows is successfully recovered. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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