在有限变形的流体结构接口中,不匹配的离散的变量合
Soonpil Kang1, JaeHyuk Kwack2, Arif Masud1
1Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
概括
这项研究引入了一种新的多尺度不连续的Galerkin (VMDG) 方法,用于流体结构相互作用. VMDG方法有效地将粘性流体和变形固体在不匹配的网格上结合起来,提高了模拟的准确性.
科学领域:
- 计算力学 计算力学 计算力学
- 流体结构相互作用 (FSI)
- 数学方法 数学方法
背景情况:
- 在许多工程应用中,精确模拟流体结构相互作用至关重要.
- 将不可压缩的粘性流体与具有有限变形的弹性固体相结合,带来了重大的数值挑战,特别是在不匹配的界面网格上.
- 现有的方法往往在流体-固体界面的稳定性和准确性方面扎.
研究的目的:
- 提出一种稳定型单立体方法,用于将不可压缩的粘性流体与有限变形的弹性固体相合.
- 开发一个强大的数值框架,有效地处理不匹配的接口网格.
- 引入一个系统的程序来导出接口稳定术语.
主要方法:
- 拟议的变量多尺度不连续的加勒金 (VMDG) 方法在变量多尺度 (VMS) 框架内结合了不连续的加勒金 (DG) 思想.
- 控制方程是用适当的框架 (固体的拉格朗日方程,流体的任意拉格朗日-欧勒方程) 制定的,以管理大型接口运动.
- 接口合术语是通过局部解决微量变量方程和分析确定引拉格朗日乘数来得出的.
主要成果:
- 一个新的接口稳定张量被系统地导出,从VMDG配方中自然出现.
- 稳定张量表现出面积平均和应力平均属性,并随着界面的非线性场而演变.
- 使用基准问题的数值验证证实了该方法对有限变形流体结构接口的准确性和稳定性.
结论:
- VMDG方法为单体流体结构相互作用模拟提供了稳定而准确的方法.
- 衍生的接口稳定张量有效地解决了与不匹配的网格和大变形相关的挑战.
- 该方法在复杂的流体结构相互作用场景中显示出强大的性能.
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