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波动数值模拟中的外推型人工边界条件

邢浩洁 李小军 刘爱文 李鸿晶 周正华 陈苏

邢浩洁, 李小军, 刘爱文, 李鸿晶, 周正华, 陈苏. 波动数值模拟中的外推型人工边界条件[J]. 力学学报, 2021, 53(5): 1480-1495. doi: 10.6052/0459-1879-20-408
引用本文: 邢浩洁, 李小军, 刘爱文, 李鸿晶, 周正华, 陈苏. 波动数值模拟中的外推型人工边界条件[J]. 力学学报, 2021, 53(5): 1480-1495. doi: 10.6052/0459-1879-20-408
Xing Haojie, Li Xiaojun, Liu Aiwen, Li Hongjing, Zhou Zhenghua, Chen Su. EXTRAPOLATION-TYPE ARTIFICIAL BOUNDARY CONDITIONS IN THE NUMERICAL SIMULATION OF WAVE MOTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1480-1495. doi: 10.6052/0459-1879-20-408
Citation: Xing Haojie, Li Xiaojun, Liu Aiwen, Li Hongjing, Zhou Zhenghua, Chen Su. EXTRAPOLATION-TYPE ARTIFICIAL BOUNDARY CONDITIONS IN THE NUMERICAL SIMULATION OF WAVE MOTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1480-1495. doi: 10.6052/0459-1879-20-408

波动数值模拟中的外推型人工边界条件

doi: 10.6052/0459-1879-20-408
基金项目: 1)国家自然科学基金(U1839202);国家自然科学基金(51778588);国家重点研发计划(2017YFC1500400);中国博士后科学基金(2018M641425)
详细信息
    作者简介:

    2)李小军, 教授, 主要研究方向: 地震工程. E-mail: beerli@vip.sina.com

    通讯作者:

    李小军

  • 中图分类号: P315.9,TU435

EXTRAPOLATION-TYPE ARTIFICIAL BOUNDARY CONDITIONS IN THE NUMERICAL SIMULATION OF WAVE MOTION

  • 摘要: 当前波动数值模拟中的人工边界条件(artificial boundary condition, ABC)数量繁多, 但用于串联它们的理论及公式体系还需进一步完善, 以便在复杂波动问题模拟中更准确地选取ABC并评估其性能. 本工作发展一种外推型人工边界条件理论, 将一系列利用临近边界一组节点在前若干时刻的运动来外推人工边界节点运动的经典ABC纳入一个体系. 这些ABC包括廖氏透射边界(multi-transmittig formula, MTF)、旁轴近似边界、Higdon边界以及Givoli-Neta、Hagstrom-Warburton、AWWE辅助变量边界等. 针对现有边界公式存在的不足, 分别提出一种引入多个人工波速进行优化的MTF公式(离散公式)和一种定义在统一局部坐标之上并采用多个人工波速作为控制参数的统一Higdon边界公式(连续公式或微分方程形式ABC), 作为外推型ABC的两个基本公式. 这二者是最简单实用的外推型ABC, 其他同类ABC大多可以由它们转化得到, 或者通过某种等价的中间形式与之相关联. 数值试验证实了理论的正确性, 并初步展示了多人工波速ABC比传统单一人工波速ABC所具有的优势. 研究结果不仅具有重要理论价值, 还为更好地解决具有差异较大的多种物理波速的复杂波动, 如大纵横波速比的软土介质中波动或海洋声学、 气象学中的频散波动等的ABC问题提供了实用方法.

     

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  • 收稿日期:  2020-12-01
  • 刊出日期:  2021-05-18

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