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一种适用于浸入有限元方法的网格自适应方法

张华 白俊强 乔磊 刘艳

张华, 白俊强, 乔磊, 等 . 一种适用于浸入有限元方法的网格自适应方法[J]. 北京航空航天大学学报, 2020, 46(3): 588-597. doi: 10.13700/j.bh.1001-5965.2019.0269
引用本文: 张华, 白俊强, 乔磊, 等 . 一种适用于浸入有限元方法的网格自适应方法[J]. 北京航空航天大学学报, 2020, 46(3): 588-597. doi: 10.13700/j.bh.1001-5965.2019.0269
ZHANG Hua, BAI Junqiang, QIAO Lei, et al. An adaptive mesh refinement method based on immersed finite element method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 588-597. doi: 10.13700/j.bh.1001-5965.2019.0269(in Chinese)
Citation: ZHANG Hua, BAI Junqiang, QIAO Lei, et al. An adaptive mesh refinement method based on immersed finite element method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(3): 588-597. doi: 10.13700/j.bh.1001-5965.2019.0269(in Chinese)

一种适用于浸入有限元方法的网格自适应方法

doi: 10.13700/j.bh.1001-5965.2019.0269
基金项目: 

国家自然科学基金 11802245

国家自然科学基金 11702284

详细信息
    作者简介:

    张华 女, 硕士研究生。主要研究方向:浸入类算法、有限元方法、网格自适应技术

    白俊强 男, 博士, 教授, 博士生导师。主要研究方向:飞行器设计、计算流体力学

    乔磊 男, 博士, 助理研究员。主要研究方向:计算流体力学

    刘艳 女, 博士, 高级工程师。主要研究方向:气动弹性算法

    通讯作者:

    白俊强.E-mail: junqiang@nwpu.edu.cn

  • 中图分类号: V221+.3;TB553

An adaptive mesh refinement method based on immersed finite element method

Funds: 

National Natural Science Foundation of China 11802245

National Natural Science Foundation of China 11702284

More Information
  • 摘要:

    针对动边界流固耦合的数值模拟问题,基于浸入有限元方法提出了一种耦合流场特征和几何特征的笛卡儿网格局部加密自适应方法,克服了单个自适应指示因子无法精确捕捉固体运动的特征的不足。在耦合自适应策略中,分别以流场涡量和固体位置作为流场和几何信息指示因子来驱动网格自适应。通过方腔顶盖驱动圆盘流动算例,以圆盘体积守恒和特征点的运动轨迹验证耦合自适应方法的优势。计算结果表明:仅基于流动特征的自适应不能很好地保证圆盘的体积守恒;仅基于几何特征的自适应无法有效追踪圆盘的轨迹;而耦合自适应策略能同时较好地保证两项指标的计算精度,在保证总体计算自由度不变的情况下,圆盘区域速度散度2-范数降低了一个数量级,圆盘的轨迹误差2-范数降低了2个数量级。

     

  • 图 1  计算域的定义

    Figure 1.  Definition of calculation domain

    图 2  几何自适应示意图

    Figure 2.  Schematic of adaptive refinement based on geometry feature

    图 3  网格悬点形成

    Figure 3.  Hanging point formation of mesh

    图 4  网格自适应流程图

    Figure 4.  Flowchart of mesh adaptation

    图 5  方腔顶盖驱动圆盘问题说明

    Figure 5.  Illustration of disk entrained in a lid-driven cavity flow

    图 6  固体区域网格

    Figure 6.  Mesh of solid area

    图 7  自由度随时间变化

    Figure 7.  Variation of degrees of freedom with time

    图 8  圆盘区域速度散度2-范数随时间的变化

    Figure 8.  Variation of 2-norm of divergence of velocity in disk area with time

    图 9  P1点轨迹x坐标和y坐标误差随时间的变化

    Figure 9.  Variation of error of x and y coordination for point P1 trajectory with time

    图 10  P2点轨迹x坐标和y坐标误差随时间的变化

    Figure 10.  Variation of error of x and y coordination for point P2 trajectory with time

    图 11  P3点轨迹x坐标和y坐标误差随时间的变化

    Figure 11.  Variation of error of x and y coordination for point P3 trajectory with time

    图 12  P4点轨迹x坐标和y坐标误差随时间的变化

    Figure 12.  Variation of error of x and y coordination for point P4 trajectory with time

    图 13  仅设置流场自适应情况下3~6 s的速度云图

    Figure 13.  Velocity contour at t=(3-6) s when setting mesh adaptation based flow features only

    图 14  仅设置几何自适应情况下3~6 s的速度云图

    Figure 14.  Velocity contour at t=(3-6) s when setting mesh adaptation based geometry features only

    图 15  设置耦合自适应情况下3~6 s的速度云图

    Figure 15.  Velocity contour at t=(3-6) s when setting mesh adaptation based on flow and geometry features

    表  1  6种不同形式的网格设置

    Table  1.   Mesh setting for six cases

    Case 初始加密层级 几何自适应 流场自适应 流场加密系数 流场粗化系数 几何加密系数
    Case1 5
    Case2 6
    Case3 7
    Case4 5 0.85 0.1
    Case5 5 1.0
    Case6 5 0.6 0.35 0.4
    下载: 导出CSV

    表  2  初始时刻网格自由度

    Table  2.   Degrees of freedom of mesh at initial time

    初始加密层级 控制体 固体 总自由度
    网格量 自由度 网格量 自由度
    5(Case1, Case4~Case6) 1 024 11 522 320 2 626 14 148
    6(Case2) 4 096 45 570 320 2 626 48 196
    7(Case3) 16 384 181 250 320 2 626 183 876
    下载: 导出CSV

    表  3  速度散度2-范数平均值

    Table  3.   Average value of 2-norm of divergence of velocity

    Case 速度散度2-范数平均值
    Case1 0.022 733
    Case2 0.009 509
    Case3 0.002 129
    Case4 0.017 686
    Case5 0.002 195
    Case6 0.002 242
    下载: 导出CSV

    表  4  四个点的轨迹误差2-范数

    Table  4.   2-norm of trajectory error for four points

    Case P1 P2 P3 P4
    xnorm ynorm xnorm ynorm xnorm ynorm xnorm ynorm
    Case1 0.381 017 0.309 065 0.175 893 0.169 636 0.293 602 0.247 673 0.130 823 0.079 848
    Case2 0.135 22 0.104 793 0.067 734 0.067 368 0.084 943 0.068 042 0.042 763 0.019 129
    Case4 0.044 911 0.033 318 0.022 543 0.016 775 0.041 846 0.024 332 0.029 854 0.025 508
    Case5 0.370 969 0.301 401 0.197 824 0.171 009 0.308 501 0.266 88 0.126 822 0.081 096
    Case6 0.004 382 0.001 385 0.001 874 0.002 688 0.001 667 0.001 309 0.002 096 0.000 906
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-05-31
  • 录用日期:  2019-07-27
  • 刊出日期:  2020-03-20

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