基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

佟莹; 夏健; 陈龙; 薛浩天

doi:10.6052/0459-1879-21-315

基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

doi: 10.6052/0459-1879-21-315

佟莹^*,
夏健^*,
陈龙^*,,
薛浩天^*

南京航空航天大学航空学院非定常空气动力学与流动控制工业和信息化部重点实验室, 南京 210016

基金项目: 江苏高校优势学科建设工程资助项目

详细信息

作者简介:
陈龙, 讲师, 主要研究方向: 流固耦合动力学数值计算方法 . E-mail: lchen@nuaa.edu.cn

中图分类号: O355
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- 被引次数: 0
出版历程
- 收稿日期: 2021-06-30
- 录用日期: 2021-09-27
- 网络出版日期: 2021-09-28
- 刊出日期: 2022-01-05

AN IMMERSED BOUNDARY LATTICE BOLTZMANN METHOD BASED ON IMPLICIT DIFFUSE DIRECT-FORCING SCHEME

Key Laboratory of Unsteady Aerodynamics and Flow Control of Ministry of Industry and Information Technology, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要: 采用浸没边界格子Boltzmann (immersed boundary-lattice Boltzmann, IB-LB)模型执行动边界绕流数值模拟时, 信息交互界面和边界力计算格式直接影响流动求解器的数值精度和计算效率. 基于隐式扩散界面, 一种改进的直接力格式IB-LB模型被提出. 边界力表达式基于欧拉/拉格朗日变量同一性准则推导, 转换矩阵描述的信息交互界面耦合了拉格朗日节点间的非同步运动. 采用Richardson迭代数值求解关联边界力与无滑移速度约束的线性方程组, 不仅克服了传统速度修正格式中矩阵求逆引起的计算效率问题, 而且摆脱了算法稳定性对拉格朗日点分布的依赖. 根据解析解已知的Taylor-Green涡流评估本文模型的数值模拟精度, 结果表明改进的IB模型能够完整保留背景LB模型的二阶数值精度. 静止圆柱和振荡圆柱绕流数值实验结果表明, 当前模型在涉及复杂外形和运动界面的流动模拟中能够提供可靠的数值预测, 满足力同一性的IB-LB模型能够有效抑制非定常流体力的伪物理震荡. 波动翼型绕流模拟验证了当前模型的实用性, 可在大变形柔性体流固耦合动力学问题中进一步推广.
- 格子Boltzmann方法 /
- 浸没边界方法 /
- 隐式扩散界面 /
- 直接力格式 /
- 可变形运动边界
Abstract: When the immersed boundary-lattice Boltzmann (IB-LB) model with the direct-forcing scheme is used to analyze the viscous fluid dynamics of the flow around a moving boundary, the interaction interface and the boundary force format directly affect the numerical accuracy and computational efficiency of the flow solver. Based on the implicit diffuse interface, an improved IB-LB model with the direct-forcing scheme was presented. The boundary force expression is derived based on Eulerian/Lagrangian variable identities. The interaction interface described by the transfer matrix couples the asynchronous movement between Lagrangian points. Use Richardson iteration to numerically solve the linear equations related to the boundary force and the non-slip velocity constraint. It not only overcomes the calculation efficiency problem caused by matrix inversion in the traditional velocity correction scheme, but also gets rid of the dependence of algorithm stability and Lagrangian point distribution. According to the Taylor-Green flow with analytical solution, the numerical accuracy of the present model is evaluated. The results show that the improved IB model can retain the second-order numerical accuracy of the background LB model. The numerical results of the flow over a stationary cylinder and an oscillating cylinder show that the model can provide reliable numerical predictions in the flow simulation involving complex geometries and moving interfaces. The IB-LB model yielded the force identity can effectively suppress the non-physical oscillation of the predicted hydrodynamic forces. The simulation of the flow around the undulating airfoil verifies the practicability of the current model, and can be further popularized in the fluid-structure coupling simulation of large-deformation flexible bodies.
- lattice Boltzmann model /
- immersed boundary model /
- implicit diffuse interface /
- direct-forcing scheme /
- deformable moving boundary

HTML全文

图 1 浸没边界方法原理图. ○ 代表拉格朗日边界节点; ●代表欧拉流体节点

Figure 1. Schematic diagram of the immersed boundary method. ○ indicate the Lagrangian boundary point; ● indicate the Eulerian fluid node

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图 2 直接力格式IB-LB模型算法流程图. 浅灰色框指明物面参数输出子步骤

Figure 2. An overview of one cycle of the IB-LB algorithm with the direct force scheme. The light grey box shows the output sub-step of the surface variables

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图 3 对数坐标下的速度误差L₂与网格尺度h

Figure 3. Numerical error L₂ of velocity versus mesh spacing h for Taylor-Green flow using the present IB-LB model with different φ and the standard LB model

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图 4 圆柱表面压强系数与方向角关系曲线

Figure 4. Pressure coefficient curve of cylinder versus the orientation angle

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图 5 圆柱周围流线分布

Figure 5. Streamline distribution near the cylinder.

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图 6 振荡圆柱阻力系数与圆柱中心位移的关系

Figure 6. Drag coefficient acting on the oscillation cylinder versus the position of the cylinder center

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图 7 波动翼型的时间相关推力系数

Figure 7. Time-dependent thrust coefficient acting on the undulatory foil

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图 8 波动翼型的时间相关运动功率系数、阻力功率系数和总功率系数

Figure 8. Time-dependent kinematic power coefficient, overcome drag power coefficient, and total power coefficient required by the undulatory foil

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图 9 均匀流动中复合运动翼型周围涡量云图

Figure 9. Vortex contour near the swimming foil in a uniform flow

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表 1 Re = 20和40时规则区长度和阻力系数与已有文献结果的比较

Table 1. Comparison of the obtained recirculating length, the drag coefficient with the previous results at Re = 20 and 40

Re	Refs.	2L_w/D	C_D
20	Ref. [21]	1.87	2.022
	Ref. [15]	1.86	2.091
	Ref. [17]	1.92	2.084
	Ref. [19]	2.03	2.213
	present (30D×15D)	1.90	2.266
	present (40D×40D)	1.92	2.096
40	Ref. [21]	4.67	1.495
	Ref. [15]	4.62	1.565
	Ref. [17]	4.72	1.560
	Ref. [19]	4.82	1.660
	present (30D×15D)	4.57	1.680
	present (40D×40D)	4.60	1.572

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表 2 Re = 100的当前模型与其他方法的流动特征参数比较

Table 2. Comparison between the present model and other methods at Re = 100

Refs.	$\overline{ {C}_{ {\rm{D} } } }$	$ {C}_{{\rm{L}}}^{{\rm{max}}} $	St
Ref. [30]	1.420	0.365	0.165
Ref. [31]	1.25	−	0.167
Ref. [15]	1.364	0.344	0.163
Ref. [17]	1.368	0.346	0.162
Ref. [19]	1.418	0.367	0.166
present	1.445	0.359	0.163

下载: 导出CSV

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