Mathematical foundations of the immersed finite element method

被引：0
作者：
Wing Kam Liu
Do Wan Kim
Shaoqiang Tang
机构：
[1] The Technological Institute Northwestern University,Department of Mechanical Engineering
[2] Sunmoon University,Department of Mathematics
[3] Peking University,LTCS, Department of Mechanics and Engineering Science
来源：
Computational Mechanics | 2007年 / 39卷
关键词：
Fluid-Structure interaction; Euler-Lagrange mapping; Immersed finite element method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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; SIAM J 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
引用
收藏
页码：211 / 222
页数：11
相关论文
共 68 条
  • [1] Babuska I(1971)Error-bounds for finite element method Numer Math 16 322-333
  • [2] Bathe KJ(2004)Finite element developments for general fluid flows with structural interactions Int J Numer Meth Eng 60 213-232
  • [3] Zhang H(1974)On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers RAIRO Anal Numer R- 2 129-151
  • [4] Brezzi F(1982)Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comp Methods Appl Mech Eng 32 199-259
  • [5] Brooks AN(2001)Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique J Comput Phys 169 427-462
  • [6] Hughes TJR(1988)Viscous flow with large free surface motion Comput Methods Appl Mech Eng 69 277-324
  • [7] Hu HH(1986)A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska–Brezzi condition: A stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations Comput Methods Appl Mech Eng 59 85-99
  • [8] Patankar NA(1981)Lagrangian-Eulerian finite element formulations for incompressible viscous flows Comput Methods Appl Mech Eng 29 329-349
  • [9] Zhu MY(1999)Advanced mesh generation and update methods for 3d flow simulations Comput Mech 23 130-143
  • [10] Huerta A(2000)An immersed boundary method with formal second-order accuracy and reduced numerical viscosity J Comput Phys 160 705-719
1234567