A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equation
A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equation
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DOI：
10.1016/j.cma.2019.04.015
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发表时间：
2019-03
影响因子：
7.2
通讯作者：
S. Jaiswal;Alina A. Alexeenko;Jingwei Hu
中科院分区：
文献类型：
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作者：
S. Jaiswal;Alina A. Alexeenko;Jingwei Hu
介绍了一种快速傅立叶谱法求解多种玻尔兹曼碰撞算子。该方法保留了单物种快速光谱方法Gamba et al.（2017）的优点，包括：(a)光谱精度，(b)与直接光谱方法相比降低了计算复杂度，(c)减少了预计算中的内存需求，以及(d)适用于一般碰撞核。然后，将快速碰撞算法与物理空间Jaiswal等（2019）中的不连续伽辽金离散相结合，得到了气体混合物全玻尔兹曼方程的高精度确定性方法（DGFS）。通过一系列数值试验验证了该方法的有效性和准确性。研究了不同碰撞核、不同质量比、动量传递、传热，特别是扩散输运的各种基准。结果与直接模拟蒙特卡罗（DSMC）方法进行了比较。
We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the advantages of the single-species fast spectral method Gamba et al. (2017) including: (a) spectral accuracy, (b) reduced computational complexity compared to direct spectral method, (c) reduced memory requirement in the precomputation, and (d) applicability to general collision kernels. The fast collision algorithm is then coupled with discontinuous Galerkin discretization in the physical space Jaiswal et al. (2019) to result in a highly accurate deterministic method (DGFS) for the full Boltzmann equation of gas mixtures. A series of numerical tests is performed to illustrate the efficiency and accuracy of the proposed method. Various benchmarks highlighting different collision kernels, different mass ratios, momentum transfer, heat transfer, and in particular the diffusive transport have been studied. The results are directly compared with the direct simulation Monte Carlo (DSMC) method.