标题： Burnett谱方法用于空间齐次玻尔兹曼方程 显示英文标题

标题： Burnett Spectral Method for the Spatially Homogeneous Boltzmann Equation

摘要： 我们开发了一种谱方法，用于空间均匀的玻尔兹曼方程，使用 Burnett 多项式作为基函数。 利用碰撞项展开中系数的稀疏性，对于一般的碰撞核，计算成本降低了一个数量级，而对于麦克斯韦分子，计算成本降低了两个数量级。 所提出的方法可以无缝地与 BGK 类型的建模技术结合，使未来的应用变得可行。 详细讨论了算法的实现，包括一个用于准确计算所有系数的数值方案，以及设计数据结构以实现高缓存命中率。 提供了数值示例来展示我们方法的准确性和效率。 显示英文摘要

摘要： We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced by one order of magnitude for general collision kernels and by two orders of magnitude for Maxwell molecules. The proposed method can couple seamlessly with the BGK-type modelling techniques to make future applications affordable. The implementation of the algorithm is discussed in detail, including a numerical scheme to compute all the coefficients accurately, and the design of the data structure to achieve high cache hit ratio. Numerical examples are provided to demonstrate the accuracy and efficiency of our method