An extended finite element method based approach for large deformation fluid-structure interaction

This paper illustrates aspects of an ongoing eort to develop a fixed grid fluid-structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow. After presenting a list of requirements for future fixed grid methods, an eXtended Finite Element Method (XFEM) based fixed grid method is proposed. It will allow the simulation of large deformations of thin and bulky structures. The extended Eulerian fluid field and the Lagrangian structural field are coupled using an partitioned, iterative approach. Finally, first results illustrating the essential capabilities are presented.

[1]  Ted Belytschko,et al.  Quasi-Eulerian Finite Element Formulation for Fluid-Structure Interaction , 1980 .

[2]  Lucy T. Zhang,et al.  Immersed finite element method , 2004 .

[3]  P. Steinmann,et al.  A finite element method for the computational modelling of cohesive cracks , 2005 .

[4]  Ekkehard Ramm,et al.  Large deformation fluid structure interaction - advances in ALE methods and new fixed grid approaches , 2006 .

[5]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[6]  Thomas J. R. Hughes,et al.  A comparative study of different sets of variables for solving compressible and incompressible flows , 1998 .

[7]  P. Tallec,et al.  Fluid structure interaction with large structural displacements , 2001 .

[8]  W. F. Noh,et al.  CEL: A TIME-DEPENDENT, TWO-SPACE-DIMENSIONAL, COUPLED EULERIAN-LAGRANGE CODE , 1963 .

[9]  Randall J. LeVeque,et al.  Cartesian Grid Methods for Fluid Flow in Complex Geometries , 2001 .

[10]  Tayfun E. Tezduyar,et al.  Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces , 2006 .

[11]  F. Baaijens A fictitious domain/mortar element method for fluid-structure interaction , 2001 .

[12]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[13]  A. U.S.,et al.  A LAGRANGIAN-EULERIAN SHELL-FLUID COUPLING ALGORITHM BASED ON LEVEL SETS , 2006 .

[14]  Patrick Patrick Anderson,et al.  Fluid-solid interactions: modeling, simulation, bio-mechanical applications A three-dimensional fluid-structure interaction method for heart valve modelling , 2005 .

[15]  C. W. Hirt,et al.  An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , 1997 .

[16]  Wing Kam Liu,et al.  Particulate flow simulations using lubrication theory solution enrichment , 2003 .

[17]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[18]  T. Belytschko,et al.  An Eulerian–Lagrangian method for fluid–structure interaction based on level sets , 2006 .

[19]  Gianluca Iaccarino,et al.  IMMERSED BOUNDARY METHODS , 2005 .

[20]  Daniel Pinyen Mok Partitionierte Lösungsansätze in der Strukturdynamik und der Fluid-Struktur-Interaktion , 2001 .

[21]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[22]  R. Glowinski,et al.  A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations , 1994 .

[23]  Wing Kam Liu,et al.  Extended immersed boundary method using FEM and RKPM , 2004 .

[24]  R. Glowinski,et al.  A distributed Lagrange multiplier/fictitious domain method for particulate flows , 1999 .

[25]  Zhaosheng Yu A DLM/FD method for fluid/flexible-body interactions , 2005 .

[26]  C. Peskin The immersed boundary method , 2002, Acta Numerica.

[27]  Randall J. LeVeque,et al.  An Immersed Interface Method for Incompressible Navier-Stokes Equations , 2003, SIAM J. Sci. Comput..

[28]  G. G. Peters,et al.  A two-dimensional fluid–structure interaction model of the aortic value , 2000 .

[29]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[30]  Julien Réthoré,et al.  An energy‐conserving scheme for dynamic crack growth using the eXtended finite element method , 2005 .

[31]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[32]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[33]  Wolfgang A. Wall Fluid-Struktur-Interaktion mit stabilisierten Finiten Elementen , 1999 .

[34]  C. Peskin Numerical analysis of blood flow in the heart , 1977 .

[35]  E. Ramm,et al.  Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows , 2007 .

[36]  P. Hansbo,et al.  A finite element method for the simulation of strong and weak discontinuities in solid mechanics , 2004 .

[37]  Bruce M. Irons,et al.  A version of the Aitken accelerator for computer iteration , 1969 .

[38]  S. Giuliani,et al.  Lagrangian and Eulerian Finite Element Techniques for Transient Fluid-Structure Interaction Problems , 1977 .

[39]  Ted Belytschko,et al.  COMPUTER MODELS FOR SUBASSEMBLY SIMULATION , 1978 .