Large deformation fluid structure interaction - advances in ALE methods and new fixed grid approaches

This contribution focusses on computational approaches for fluid structure interaction problems from several perspectives. Common driving force is the desire to handle even the large deformation case in a robust, efficient and straightforward way. In order to meet these requirements main subjects are on the one hand necessary improvements on coupling issues as well as on Arbitrary Lagrangian Eulerian (ALE) approaches. On the other hand, we discuss pros and cons of avail-able fixed grid approaches and start the development of new such approaches. Some numerical examples are provided along the paper.

[1]  Charbel Farhat,et al.  Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes , 1999 .

[2]  V. Parthasarathy,et al.  A fully automated Chimera methodology for multiple moving body problems , 2000 .

[3]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part II: Level set update , 2002 .

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

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

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

[7]  Charbel Farhat,et al.  The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids , 2001 .

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

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

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

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

[12]  S. Turek,et al.  Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow , 2006 .

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

[14]  Patrick Patrick Anderson,et al.  A combined fictitious domain/adaptive meshing method for fluid–structure interaction in heart valves , 2004 .

[15]  Guillaume Houzeaux,et al.  A Chimera method based on a Dirichlet/Neumann(Robin) coupling for the Navier–Stokes equations , 2003 .

[16]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model , 2002 .

[17]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[18]  T. Belytschko,et al.  Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment , 2003 .

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

[20]  T. Belytschko,et al.  An Extended Finite Element Method for Two-Phase Fluids , 2003 .

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

[22]  Charbel Farhat,et al.  On the significance of the geometric conservation law for flow computations on moving meshes , 2000 .

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

[24]  E. Ramm,et al.  Models and finite elements for thin-walled structures , 2004 .

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

[26]  Shay Gueron,et al.  Computational modeling in biological fluid dynamics , 2001 .

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

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

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

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

[31]  Ekkehard Ramm,et al.  Shell structures—a sensitive interrelation between physics and numerics , 2004 .

[32]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

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

[34]  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 .

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

[36]  R. Rannacher,et al.  Benchmark Computations of Laminar Flow Around a Cylinder , 1996 .

[37]  Ekkehard Ramm,et al.  On the geometric conservation law in transient flow calculations on deforming domains , 2006 .

[38]  Charbel Farhat,et al.  Design and analysis of robust ALE time-integrators for the solution of unsteady flow problems on moving grids , 2004 .

[39]  R. Meakin.  Unsteady aerodynamic simulation of multiple bodies in relative motion: A prototype method , 1989 .

[40]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[41]  Wolfgang A. Wall,et al.  Parallel multilevel solution of nonlinear shell structures , 2005 .

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

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

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

[45]  Fehmi Cirak,et al.  A Lagrangian-Eulerian shell-fluid coupling algorithm based on level sets , 2003 .

[46]  K. Kussmaul,et al.  STRUCTURAL MECHANICS IN REACTOR TECHNOLOGY , 1993 .

[47]  Daniele Boffi,et al.  Stability and geometric conservation laws for ALE formulations , 2004 .

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

[49]  P. Tallec,et al.  Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity , 1998 .

[50]  Thomas J. R. Hughes,et al.  The Continuous Galerkin Method Is Locally Conservative , 2000 .

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

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

[53]  Charbel Farhat,et al.  Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations , 2003 .

[54]  Fabio Nobile,et al.  Added-mass effect in the design of partitioned algorithms for fluid-structure problems , 2005 .

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

[56]  Eugenio Oñate,et al.  A Lagrangian meshless finite element method applied to fluid-structure interaction problems , 2003 .

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

[58]  Thomas J. R. Hughes,et al.  Encyclopedia of computational mechanics , 2004 .