标题： 一种用于格子玻尔兹曼方法的新速度离散化：可压缩流的应用 显示英文标题

标题： A Novel Velocity Discretization for Lattice Boltzmann Method: Application to Compressible Flow

摘要： 粒子分布函数方法（LBM）已成为计算流体动力学和材料科学中的强大工具。 然而，标准的LBM公式对该方法的应用带来了一些限制，特别是在可压缩流体方面。 在本文中，我们引入了一种新的速度离散化方法来克服这些挑战。 在新的公式中，粒子分布使用具有均值和方差的尖峰函数进行离散化。 这引入了足够的独立自由度，以将平衡矩设置为麦克斯韦-玻尔兹曼分布的矩，包括第三阶矩。 因此，正确地恢复了可压缩流体的宏观流体动力学方程。 我们通过多个基准模拟验证了我们的方法。 显示英文摘要

摘要： The Lattice Boltzmann Method (LBM) has emerged as a powerful tool in computational fluid dynamics and material science. However, standard LBM formulation imposes some limitations on the applications of the method, particularly compressible fluids. In this paper, we introduce a new velocity discretization method to overcome some of these challenges. In this new formulation, the particle populations are discretized using a bump function that has a mean and a variance. This introduces enough independent degrees of freedom to set the equilibrium moments to the moments of Maxwell-Boltzmann distribution up to and including the third moments. Consequently, the correct macroscopic fluid dynamics equations for compressible fluids are recovered. We validate our method using several benchmark simulations.