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求解三维流固耦合问题的一种全隐全耦合区域分解并行算法

邓小毛 廖子菊

邓小毛, 廖子菊. 求解三维流固耦合问题的一种全隐全耦合区域分解并行算法. 力学学报, 2022, 54(12): 3513-3523 doi: 10.6052/0459-1879-22-398
引用本文: 邓小毛, 廖子菊. 求解三维流固耦合问题的一种全隐全耦合区域分解并行算法. 力学学报, 2022, 54(12): 3513-3523 doi: 10.6052/0459-1879-22-398
Deng Xiaomao, Liao Ziju. A fully implicit and monolithic parallel decomposition method for 3D fluid-solid interaction problems. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3513-3523 doi: 10.6052/0459-1879-22-398
Citation: Deng Xiaomao, Liao Ziju. A fully implicit and monolithic parallel decomposition method for 3D fluid-solid interaction problems. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3513-3523 doi: 10.6052/0459-1879-22-398

求解三维流固耦合问题的一种全隐全耦合区域分解并行算法

doi: 10.6052/0459-1879-22-398
基金项目: 国家自然科学基金 (11602282) 和广东省自然科学基金 (2020A1515010704, 2021A1515012366) 资助项目
详细信息
    作者简介:

    廖子菊, 讲师, 主要研究方向: 计算流体力学. E-mail: liaozj@jnu.edu.cn

  • 中图分类号: O357.1

A FULLY IMPLICIT AND MONOLITHIC PARALLEL DECOMPOSITION METHOD FOR 3D FLUID-SOLID INTERACTION PROBLEMS

  • 摘要: 三维流固耦合问题的非结构网格数值算法在很多工程领域都有重要应用, 目前现有的数值方法主要基于分区算法, 即流体和固体区域分别进行求解, 因此存在收敛速度较慢以及附加质量导致的稳定性问题, 此外, 该类算法的并行可扩展性不高, 在大规模应用计算方面也受到一定限制.本文针对三维非定常流固耦合问题, 提出一种基于区域分解的全隐全耦合可扩展并行算法.首先基于任意拉格朗日−欧拉框架建立流固耦合控制方程, 然后时间方向采用二阶向后差分隐式格式、空间方向采用非结构稳定化有限元方法进行离散.对于大规模非线性离散系统, 构造一种结合非精确Newton法、Krylov子空间迭代法与区域分解Schwarz预条件子的Newton-Krylov-Schwarz (NKS) 并行求解算法, 实现流体、固体和动网格方程的一次性整体求解.采用弹性障碍物绕流的标准测试算例对数值方法的准确性进行了验证, 数值性能测试结果显示本文构造的全隐全耦合算法具有良好的稳定性, 在不同的物理参数下具有良好的鲁棒性, 在“天河二号”超级计算机上, 当并行规模从192增加到3072个处理器核时获得了91%的并行效率.性能测试结果表明本文构造的NKS算法有望应用于复杂区域流固耦合问题的大规模数值模拟研究中.

     

  • 图  1  ALE框架

    Figure  1.  ALE configuration

    图  2  计算区域

    Figure  2.  Computational domain

    图  3  不同杨氏模量下的弹性变形及速度分布图

    Figure  3.  Deformation and velocity distribution with different Young's modulus

    图  4  算法加速比

    Figure  4.  Parallel speedup of the algorithm

    表  1  计算网格

    Table  1.   Computational meshes

    Mesh1234
    cells1.89 × 1041.30 × 1051.08 × 1066.03 × 106
    DoF2.90 × 1041.78 × 1051.47 × 1068.11 × 106
    np244896192
    memory/MB51.86141.5453.81140
    Newton2.02.02.02.0
    GMRES11.617.028.240.4
    time step/s1.184.1519.8877.72
    下载: 导出CSV

    表  2  观测点${{P}}1\;(0.4,\;0.2,\; - 0.2)$处的位移

    Table  2.   Displacements at point ${P}1\;(0.4,\;0.2,\; - 0.2)$

    $d_x^{}$/m$d_y^{}$/m$d_z^{}$/m
    mesh 11.984 × 10−35.152 × 10−4−9.431 × 10−5
    mesh 21.729 × 10−35.052 × 10−4−6.124 × 10−5
    mesh 31.602 × 10−34.832 × 10−4−5.775 × 10−5
    mesh 41.598 × 10−34.847 × 10−4−6.785 × 10−5
    Ref. [22]1.63 × 10−35.05 × 10−4−1.22 × 10−4
    下载: 导出CSV

    表  3  观测点${{P2}}\;(0.5,\;0.2,\; - 0.2)$处的位移

    Table  3.   Displacements at point ${{P2}}\;(0.5,\;0.2,\; - 0.2)$

    $d_x^{}$/m$d_y^{}$/m$d_z^{}$/m
    mesh 11.964 × 10−3−5.377 × 10−4−4.855 × 10−5
    mesh 21.700 × 10−3−4.683 × 10−4−7.854 × 10−5
    mesh 31.563 × 10−3−4.251 × 10−4−7.185 × 10−5
    mesh 41.550 × 10−3−4.240 × 10−4−7.216 × 10−5
    Ref. [22]1.54 × 10−3−4.65 × 10−4−3.13 × 10−5
    下载: 导出CSV

    表  4  子区域的重叠层数及子问题求解器对算法性能的影响

    Table  4.   Impact of the overlapping size and the subsolver on the NKS algorithm

    $\delta $SubsolverNewtonGMRESTime/s
    1ILU(0)2.062.318.07
    1ILU(1)2.040.018.15
    1ILU(2)2.031.219.34
    1ILU(3)2.029.234.98
    2ILU(0)2.054.317.40
    2ILU(1)2.034.418.23
    2ILU(2)2.028.219.88
    2ILU(3)2.024.537.50
    下载: 导出CSV

    表  5  不同时间步长对NKS算法收敛性能的影响

    Table  5.   Performance of NKS with respect to $\Delta t$

    $\Delta t$NewtonGMRESTime/s
    0.0012.019.521.34
    0.0022.022.621.54
    0.0042.026.221.97
    0.0082.039.022.96
    0.0162.047.223.99
    0.0322.055.924.25
    0.0642.671.832.98
    0.1283.070.438.17
    下载: 导出CSV

    表  6  关于流体黏性系数的算法鲁棒性测试

    Table  6.   Robustness of the algorithm with respect to the fluid viscosity

    ${\mu ^f}$NewtonGMRESTime/s
    1.02.026.221.97
    0.12.026.622.04
    0.012.026.821.98
    下载: 导出CSV

    表  7  关于固体密度的算法鲁棒性测试

    Table  7.   Robustness of the algorithm with respect to the solid density

    ${\rho ^s}$NewtonGMRESTime/s
    12.060.825.29
    102.053.224.41
    1002.045.623.75
    10002.026.221.97
    20002.022.421.13
    40002.014.020.85
    下载: 导出CSV

    表  8  关于杨氏模量和Poisson比的算法鲁棒性测试

    Table  8.   Robustness of the algorithm with respect to the Young’s modulus and Poisson’s ratio

    ${E^s}$${\nu ^s}$NewtonGMRESTime/s
    1.4 × 1060.12.025.021.62
    1.4 × 1060.22.025.721.87
    1.4 × 1060.32.025.821.96
    1.4 × 1060.42.026.221.97
    1.4 × 1060.482.041.423.39
    1.4 × 1060.42.026.221.97
    7.0 × 1050.42.022.921.67
    3.5 × 1050.42.020.221.44
    1.75 × 1050.42.018.021.21
    8.75 × 1040.42.016.821.05
    下载: 导出CSV

    表  9  算法并行可扩展性测试

    Table  9.   Parallel performance and scalability of the algorithm

    ${n_p}$19238476815363072
    Newton2.02.02.02.02.0
    GMRES45.747.049.352.453.5
    time83.4135.0717.209.655.73
    speedup12.384.858.6414.56
    ideal124816
    efficiency100%119%121%108%91%
    下载: 导出CSV

    表  10  本文算法与其他文献算法的性能比较

    Table  10.   Comparison of different numerical approaches found in literature

    SolverDofsNewton stepsRatio*CPU coresParallel efficiencySource
    Ref. [22]Newton-Block LDU14 000 0006 ~ 9109.916 ~ 25641%Fig.14, Fig.15
    Ref. [28]Newton-Krylov-
    Multigrid-Richardson
    120 902411391Tab. 1, Tab. 12
    Ref. [29]Newton-Multigrid3 531 3045.15450.31 ~ 3231%Tab. 6, Tab. 9, Fig. 7
    this workNewton-Krylov-
    Schwarz
    8 110 0002543.5192 ~ 307291%Tab. 1, Tab. 9
    *Note: Here the “Ratio” indicates the degree of freedom persecond computed with one CPU core for each time step
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-08-29
  • 录用日期:  2022-11-01
  • 网络出版日期:  2022-11-02
  • 刊出日期:  2022-12-15

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