Asymptotic method for entropic multiple relaxation time model in lattice Boltzmann method
Asymptotic method for entropic multiple relaxation time model in lattice Boltzmann method
复制标题
格子玻尔兹曼法中熵多重弛豫时间模型的渐近方法
DOI：
10.1103/physreve.106.015303
复制
发表时间：
2022
影响因子：
2.4
通讯作者：
Oztekin, Alparslan
中科院分区：
文献类型：
--
作者：
Tang, Xiangshuo;Yu, Yue;Oztekin, Alparslan
为了提高格子Boltzmann方法的数值稳定性，Karlinet al. [Phys.Rev.E90，031302（R）（2014）10.1103/PhysRevE.90.031302]提出了熵多重弛豫时间（EMRT）碰撞模型。EMRT背后的思想是通过最大化其局部熵值来构造最佳碰撞后状态。EMRT模型的关键步骤是在一定的约束条件下求解熵最大化问题，这通常是计算昂贵的，甚至是不可行的。在本文中，我们建议利用微扰理论并获得最大熵状态的渐进解。通过对放松约束条件下的特殊情况的数学分析，我们得到了原问题的无扰形式，并导出了渐近解。我们表明，渐近解很好地逼近最优状态，因此，我们的方法提供了一种有效的方法来解决EMRT模型中的约束最大熵问题。此外，我们使用相同的想法EMRT模型的分布函数的初始条件，并提出离开熵函数，以确定在初始节点的丢失信息。最后，我们数值验证了通过微扰理论得到的EMRT模型的模拟结果与泰勒-格林涡问题的精确解吻合得很好。此外，我们还证明了EMRT模型具有良好的稳定性性能，在双周期剪切层流问题的低分辨率模拟。
To improve the numerical stability of the lattice Boltzmann method, Karlinet al.[Phys. Rev. E 90, 031302(R) (2014)10.1103/PhysRevE.90.031302] proposed the entropic multiple relaxation time (EMRT) collision model. The idea behind EMRT is to construct an optimal postcollision state by maximizing its local entropy value. The critical step of the EMRT model is to solve the entropy maximization problem under certain constraints, which is often computationally expensive and even not feasible. In this paper, we propose to employ perturbation theory and obtain an asymptotic solution to the maximum entropy state. With mathematical analysis of particular cases under relaxed constraints, we obtain the unperturbed form of the original problem and derive the asymptotic solution. We show that the asymptotic solution well approximates the optimal states; thus, our approach provides an efficient way to solve the constrained maximum entropy problem in the EMRT model. Also, we use the same idea of the EMRT model for the initial condition of the distribution function and propose to leave the entropy function to determine the missing information at the initial nodes. Finally, we numerically verify that the simulation results of the EMRT model obtained via the perturbation theory agree well with the exact solution to the Taylor-Green vortex problem. Furthermore, we also demonstrate that the EMRT model exhibits excellent stability performance for under-resolved simulations in the doubly periodic shear layer flow problem.