Mathematical foundations of the immersed finite element method
Mathematical foundations of the immersed finite element method
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DOI：
10.1007/s00466-005-0018-5
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发表时间：
2007-02-01
影响因子：
4.1
通讯作者：
Tang, Shaoqiang
中科院分区：
文献类型：
--
作者：
Liu, Wing Kam;Kim, Do Wan;Tang, Shaoqiang
本文提出了一种有效处理流固耦合问题的浸入式固体系统方法。在移动固体域中增加流体，我们引入体积力以获得流体和结构的正确动力学。我们进一步定义了一个欧拉-拉格朗日映射来描述浸没固体的运动。一个弱制定（WF），然后构造和证明是等价的FSI和ISS在一定的规律性假设。弱公式（WF）可以通过具有有限元法的隐式算法和流线迎风/Petrov-Galerkin方法进行数值计算。与Peskin等人成功的浸入边界法（IBM）进行了比较（J Comput Phys 160：705-719，2000; Acta Numerica 11：479-517，2002; SIAMJ Sci Stat Comput 13（6）：1361-1376，1992）ISS方法适用于具有非均匀网格的更一般的几何形状，并且避免了近似狄拉克δ函数的不准确性。
In this paper, we propose an immersed solid system (ISS) method to efficiently treat the fluid-structure interaction (FSI) problems. Augmenting a fluid in the moving solid domain, we introduce a volumetric force to obtain the correct dynamics for both the fluid and the structure. We further define an Euler-Lagrange mapping to describe the motion of the immersed solid. A weak formulation (WF) is then constructed and shown to be equivalent to both the FSI and the ISS under certain regularity assumptions. The weak formulation (WF) may be computed numerically by an implicit algorithm with the finite element method, and the streamline upwind/Petrov-Galerkin method. Compared with the successful immersed boundary method (IBM) by Peskin and co-workers (J Comput Phys 160: 705-719, 2000; Acta Numerica 11: 479-517, 2002; SIAMJ Sci Stat Comput 13(6): 1361-1376, 1992) the ISS method applies to more general geometries with non-uniform grids and avoids the inaccuracy in approximating the Dirac delta function.