论文标题
有限元离散的玻尔兹曼方法，用于高knudsen数字流量
A finite element discrete Boltzmann method for high Knudsen number flows
论文作者
论文摘要
离散的Boltzmann Bhatnagar-krook（BGK）方程的模拟是了解非智能方案中流体动力学的重要工具。在这里，我们介绍了一种不连续的Galerkin有限元法（DG-FEM），用于用于具有Knudsen数字（KN〜O（1））的等温流的离散玻尔兹曼方程的空间离散化。结合高阶runge-kutta时间行进方案，该方法能够在空间和时间上达到高阶精度，同时保持紧凑的模板。我们在二维的cOUETTE流中验证了该方案的精确度的空间顺序，而KN = 1和D2Q16速度离散化。然后，我们将该方案应用于KN = 1、2和8处的盖子驱动的微型腔流，并比较高斯 - 热矿（GH）和Newton-cotes（NC）速度集的能力，以捕获流场的高非线性。虽然GH正交提供更高的集成强度，但较少的点，但NC正交的分布得更均匀，重量大于机器零，有助于避免所谓的射线效应。从广义上讲，我们预计这项工作的洞察力将有助于促进有效实施和应用高阶数值方法，以实现复杂的高纳德森数量流。
Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook (BGK) equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method (DG-FEM) for spatial discretization of the discrete Boltzmann equation for isothermal flows with Knudsen numbers (Kn~O(1)). In conjunction with a high-order Runge-Kutta time marching scheme, this method is capable of achieving high-order accuracy in both space and time, while maintaining a compact stencil. We validate the spatial order of accuracy of the scheme on a two-dimensional Couette flow with Kn = 1 and the D2Q16 velocity discretization. We then apply the scheme to lid-driven micro-cavity flow at Kn = 1, 2, and 8, and we compare the ability of Gauss-Hermite (GH) and Newton-Cotes (NC) velocity sets to capture the high non-linearity of the flow-field. While GH quadrature provides higher integration strength with fewer points, the NC quadrature has more uniformly distributed nodes with weights greater than machine-zero, helping to avoid the so-called ray-effect. Broadly speaking, we anticipate that the insights from this work will help facilitate the efficient implementation and application of high-order numerical methods for complex high Knudsen number flows.
