虚拟解法分析浸入边界法的精度

宫兆新; 鲁传敬; 黄华雄

doi:10.3879/j.issn.1000-0887.2010.10.001

虚拟解法分析浸入边界法的精度

doi: 10.3879/j.issn.1000-0887.2010.10.001

1.
上海交通大学力学系, 上海 200240;2.海洋工程国家重点实验室,上海 200030;3.多伦多约克大学数学统计系,M3J 1P3, 加拿大

基金项目: 国家自然科学基金资助项目(10472070)

详细信息

作者简介:
宫兆新(1982- ),女,黑龙江人,博士生(E-mail:jackyff@sjtu.edu.cn);鲁传敬,教授(联系人.E-mail:cjlu@mail.sjtu.edu.cn).

中图分类号: O368;O241.82
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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-06-17
- 刊出日期: 2010-10-15

Accuracy Analysis of the Immersed Boundary Method Using the Method of Manufactured Solutions

1.
Department of Mechanics, Shanghai Jiaotong University, Shanghai 200240, P. R. China;

摘要

摘要: 浸入边界法是对流固耦合系统进行建模和模拟的有效工具，在生物力学领域的应用尤为广泛．该文的工作主要包含两个部分：程序验证和精度分析．前者证明了程序的正确性，后者给出了浸入边界法的精度．两部分工作均使用虚拟解法作为研究工具．在程序验证部分，使用二阶空间离散格式进行数值计算，通过分析各种变量的离散误差，得到的程序计算精度阶是二阶，与理论精度阶一致，证明了数值计算所使用程序的正确性．精度分析部分工作在此基础上展开．引入压强跳跃，在动量方程中加入相应源项，通过分析带有源项的控制方程中各物理量的离散误差，证明浸入边界法只具有一阶精度．同时可以得出以下结论：粗网格无法敏感地捕捉浸入边界的影响；当Euler网格固定时，增加Lagrange标志点的数目并不会改善计算误差．
- 虚拟解 /
- 浸入边界法 /
- 精度阶 /
- 程序验证 /
- 离散误差
Abstract: The immersed boundary method is an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics.The principle work was to analyze the accuracy of the immersed boundary method.The whole procedure contained two parts:code verification and accuracy analysis.The code verification part provided the confidence that the code used here was mistake free and the accuracy analysis part gave the order of accuracy of the immersed boundary method.The method of manufactured solutions was taken as the research means for both parts.In the first part, the numerical code employed a second order discretization scheme, i.e., the theoretical order of accuracy was second order.It was matched by the calculated order of accuracy obtained by numerical calculation for all variables.This meant that the code contained no mistake, which was the premise of the following work.The second part introduced a jump in the manufactured solution for pressure and added corresponding singular forcing terms in the momentum equations.By analyzing the discretization errors, the accuracy of the immersed boundary method was proved to be first order, even though the discretization scheme was second order.In the meantime, it was found that the coarser mesh might be not sensitive enough to capture the influence of the immersed boundary and that refinement on the Lagrangian markers barely had any effects on the numerical calculation.
- manufactured solutions /
- immersed boundary method /
- order of accuracy /
- codeveri-fication /
- discretization error

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参考文献(29)

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虚拟解法分析浸入边界法的精度

doi: 10.3879/j.issn.1000-0887.2010.10.001

作者简介:
宫兆新(1982- ),女,黑龙江人,博士生(E-mail:jackyff@sjtu.edu.cn);鲁传敬,教授(联系人.E-mail:cjlu@mail.sjtu.edu.cn).

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Accuracy Analysis of the Immersed Boundary Method Using the Method of Manufactured Solutions

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虚拟解法分析浸入边界法的精度

doi: 10.3879/j.issn.1000-0887.2010.10.001

作者简介: 宫兆新(1982- ),女,黑龙江人,博士生(E-mail:jackyff@sjtu.edu.cn);鲁传敬,教授(联系人.E-mail:cjlu@mail.sjtu.edu.cn).

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出版历程

Accuracy Analysis of the Immersed Boundary Method Using the Method of Manufactured Solutions

计量

出版历程

目录

作者简介:
宫兆新(1982- ),女,黑龙江人,博士生(E-mail:jackyff@sjtu.edu.cn);鲁传敬,教授(联系人.E-mail:cjlu@mail.sjtu.edu.cn).