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一种用于声学传播模拟的简化线性化格子玻尔兹曼方法。

A Simplified Linearized Lattice Boltzmann Method for Acoustic Propagation Simulation.

作者信息

Song Qiaochu, Chen Rongqian, Cao Shuqi, Lou Jinhua, Zhan Ningyu, You Yancheng

机构信息

School of Aerospace Engineering, Xiamen University, Xiamen 361005, China.

出版信息

Entropy (Basel). 2022 Nov 8;24(11):1622. doi: 10.3390/e24111622.

DOI:10.3390/e24111622
PMID:36359712
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9689581/
Abstract

A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman-Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was first recovered to linearized macroscopic equations. Then, using the fractional-step calculation technique, the solution of these linearized equations was divided into two steps: a predictor step and corrector step. Next, the evolution of the perturbation distribution function was transformed into the evolution of the perturbation equilibrium distribution function using second-order interpolation approximation of the latter at other positions and times to represent the nonequilibrium part of the former; additionally, the calculation formulas of SLLBM were deduced. SLLBM inherits the advantages of the linearized lattice Boltzmann method (LLBM), calculating acoustic disturbance and the mean flow separately so that macroscopic variables of the mean flow do not affect the calculation of acoustic disturbance. At the same time, it has other advantages: the calculation process is simpler, and the cost of computing memory is reduced. In addition, to simulate the acoustic scattering problem caused by the acoustic waves encountering objects, the immersed boundary method (IBM) and SLLBM were further combined so that the method can simulate the influence of complex geometries. Several cases were used to validate the feasibility of SLLBM for simulation of acoustic wave propagation under the mean flow.

摘要

本文提出了一种适用于模拟流体中声波传播的简化线性化格子玻尔兹曼方法（SLLBM）。通过查普曼-恩斯科格展开分析，首先将线性化格子玻尔兹曼方程（LLBE）恢复为线性化宏观方程。然后，利用分步计算技术，将这些线性化方程的求解分为两步：预测步和校正步。接着，利用扰动平衡分布函数在其他位置和时间的二阶插值近似来表示扰动分布函数的非平衡部分，将扰动分布函数的演化转化为扰动平衡分布函数的演化；此外，推导了SLLBM的计算公式。SLLBM继承了线性化格子玻尔兹曼方法（LLBM）的优点，将声扰动和平均流分别计算，使得平均流的宏观变量不影响声扰动的计算。同时，它还有其他优点：计算过程更简单，降低了计算内存成本。此外，为了模拟声波遇到物体时引起的声散射问题，将浸入边界法（IBM）与SLLBM进一步结合，使该方法能够模拟复杂几何形状的影响。通过几个案例验证了SLLBM在平均流下模拟声波传播的可行性。

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