论文标题
多原子Boltzmann--BGK方程
A positivity-preserving and conservative high-order flux reconstruction method for the polyatomic Boltzmann--BGK equation
论文作者
论文摘要
在这项工作中，我们提出了一种具有阳性的高阶重建方法，用于多原子Boltzmann--BGK方程增强，并具有离散速度模型，以确保该方案是保守的。通过对内部自由度进行建模，该方法进一步扩展到多原子分子，并可以包含任意的本构定律。该方法在一系列大型复杂数值实验上进行了验证，从在非结构化网格上计算出的冲击主导流到直接对三维可压缩湍流的数值模拟，后者是通过直接求解Boltzmann方程来计算的该流量的第一个实例。结果表明，该方案在没有任何临时数值减震方法的情况下直接解决冲击结构的能力，并以一致的方式与流体动力方程保持一致的方式正确近似湍流现象。
In this work, we present a positivity-preserving high-order flux reconstruction method for the polyatomic Boltzmann--BGK equation augmented with a discrete velocity model that ensures the scheme is discretely conservative. Through modeling the internal degrees of freedom, the approach is further extended to polyatomic molecules and can encompass arbitrary constitutive laws. The approach is validated on a series of large-scale complex numerical experiments, ranging from shock-dominated flows computed on unstructured grids to direct numerical simulation of three-dimensional compressible turbulent flows, the latter of which is the first instance of such a flow computed by directly solving the Boltzmann equation. The results show the ability of the scheme to directly resolve shock structures without any ad hoc numerical shock capturing method and correctly approximate turbulent flow phenomena in a consistent manner with the hydrodynamic equations.
