一种用于多物种Boltzmann方程的间断Galerkin快速谱方法
A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equation
AI总结：
本文提出了一种用于多物种Boltzmann碰撞算子的快速傅里叶谱方法，结合了间断Galerkin离散化，以实现高精度求解气体混合物的完整Boltzmann方程，通过数值测试验证了方法的效率和精度。
摘要：
我们介绍了一种用于多物种Boltzmann碰撞算子的快速傅里叶谱方法。该方法保留了单物种快速谱方法（Gamba等人，SIAM J. Sci. Comput., 39 pp. B658--B674 2017）的特性，包括：(a) 谱精度，(b) 相比直接谱方法计算复杂度更低，(c) 预计算中的内存需求更低，以及(d) 适用于通用碰撞核。随后，该快速碰撞算法与物理空间中的间断Galerkin离散化（Jaiswal等人，J. Comp. Phys., 378 pp. 178--208 2019）相结合，从而得到一种高精度的确定性方法（DGFS）用于完整Boltzmann方程。进行了若干数值测试以展示所提方法的效率和精度。研究了各种基准案例，涵盖不同的碰撞核、不同的质量比、动量传输、热传输，特别是扩散传输。结果与直接模拟蒙特卡罗（DSMC）方法直接比较。
英文摘要：
We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674 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. J. Comp. Phys., 378 pp. 178--208 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.
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