不可压缩流动的高精度非标准格子玻尔兹曼方法

马超; 吴杰

doi:10.7638/kqdlxxb-2021.0243

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不可压缩流动的高精度非标准格子玻尔兹曼方法

专栏——格子玻尔兹曼方法及应用 | 更新时间：2026-05-28

- 不可压缩流动的高精度非标准格子玻尔兹曼方法
- A high-order off-lattice Boltzmann method for incompressible flows
- 空气动力学学报 2022年40卷第3期页码：65-74
- 作者机构：
  
  南京航空航天大学航空学院,南京,210016
- 作者简介：
  
  马超（1994-），男，江苏扬州人，博士研究生，研究方向：高精度格子玻尔兹曼方法. E-mail：machaosxm@163.com
  吴杰*（1979-），男，江苏宜兴人，教授，研究方向：计算空气动力学. E-mail: wuj@nuaa.edu.cn
- 基金信息：
  
  国家自然科学基金（12072158）
- DOI：10.7638/kqdlxxb-2021.0243
  中图分类号： O357.1
- 纸质出版：2022
- 稿件说明：
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马超, 吴杰. 不可压缩流动的高精度非标准格子玻尔兹曼方法[J]. 空气动力学学报, 2022, 40(3): 65−74.

MA Chao, WU Jie. A high-order off-lattice Boltzmann method for incompressible flows[J]. 2022, 40(3): 65-74.
马超, 吴杰. 不可压缩流动的高精度非标准格子玻尔兹曼方法[J]. 空气动力学学报, 2022, 40(3): 65−74. DOI： 10.7638/kqdlxxb-2021.0243

MA Chao, WU Jie. A high-order off-lattice Boltzmann method for incompressible flows[J]. 2022, 40(3): 65-74. DOI： 10.7638/kqdlxxb-2021.0243.

摘要

首先回顾了高精度非标准格子玻尔兹曼方法的发展历程，基于高精度通量重构格式，发展了一种通量重构格子玻尔兹曼方法（FRLBM）。采用两种求解方法：一种是将碰撞项隐式处理，直接求解离散速度玻尔兹曼方程（直接法）；另一种是先执行碰撞步，再求解纯对流方程（分步法）。通过收敛性研究，比较了这两种方法的精度和稳定性。研究结果表明，在小时间步长下两种方法误差近似，都能取得高阶精度；然而当时间步长增大，直接法误差几乎不变，分步法误差出现明显上升。由此表明，当取得近似误差时，直接法可以采用较大时间步长，计算效率更高，且直接法的稳定性略占优。接着通过模拟顶盖驱动方腔流验证了FRLBM捕捉流场细节的能力，并且比较了基于半隐格式的显式方法和一阶、二阶及三阶隐式-显式Runge-Kutta格式的时间离散，在不同雷诺数下的最大允许Courant-Friedrichs-Lewy数，数值结果表明二阶隐式-显式Runge-Kutta格式效果最优。最后数值模拟了圆柱绕流，验证了FRLBM计算复杂外形绕流的可靠性。

Abstract

This paper firstly reviews the development of the high-order off-lattice Boltzmann method (OLBM). Based on the high-order flux reconstruction scheme (FR)

we develop a high-order flux reconstruction lattice Boltzmann method (FRLBM). Two numerical methods are adapted. One is to directly solve the discrete velocity Boltzmann equation with collision term treated implicitly (direct method) and the other is to sequencially implement collision step and the convection term (two-step method). Through the convergence study

the accuracy and stability of the two methods are compared. It is found that

when the time step is small

the errors of the two methods are in similar order

and the high-order accuracy can be obtained. However

when the time step is increased

the error of the direct method is almost unchanged

while the error of the two-step method increases significantly. The results indicate that the direct method can use a larger time step to obtain higher accuracy to abtain the reasonable accuracy in comparing with two step method. Meanwhile

the direct method also has better stability. Then

the ability of FRLBM to capture the details of the flow field is verified by simulating the lid-driven cavity flow. In addition

we compare the maximum Courant-Friedrichs-Lewy (CFL) numbers at different Reynolds numbers by semi-implicit time-marching scheme

first

second and third-order implicit-explicit (IMEX) Runge-Kutta schemes

respectively. The numerical results indicate the second-order IMEX performs best. Finally

the numerical simulation of the flow over a circular cylinder verifies the reliability of the FRLBM for calculation of the flow around the body with complex geometry.

关键词

Keywords

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