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Original Articles

Possibilities of the particle finite element method for fluid-structure interaction problems with free surface waves

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Pages 637-666 | Published online: 26 Apr 2012

References

  • Aubry , R. , Idelsohn , S. R. and Oñate , E. 2004 . “ Particle finite element method in fluid mechanics including thermal convection-diffusion ” . In Computer & Structures submitted
  • Chorin , A. J. 1967 . A numerical solution for solving incompressible viscous flow problems . J. Comp. Phys. , 2 : 12 – 26 .
  • Codina , R. 2002 . Stabilized finite element approximation of transient incompressible flows using orthogonal subscales . Comp. Meth. Appl. Mech. Engng. , 191 : 4295 – 4321 .
  • Codina , R. , Vazquez , M. and Zienkiewicz , O. C. 1998 . A general algorithm for compressible and incompressible flow - Part III. The semi-implicit form . Int. J. Num. Meth. in Fluids , 27 : 13 – 32 .
  • Codina , R. and Blasco , J. 2000 . Stabilized finite element method for the transient Navier- Stokes equations based on a pressure gradient operator . Comp. Meth. in Appl. Mech. Engng. , 182 : 277 – 301 .
  • Codina , R. and Zienkiewicz , O. C. 2002 . CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of the time step as stabilization parameter . Communications in Numerical Methods in Engineering , 18 : 99 – 112 .
  • Cruchaga , M. A. and Oñate , E. 1997 . A finite element formulation for incompressible flow problems using a generalized streamline operator . Comp. Meth. Appl. Mech. Engng. , 143 : 49 – 67 .
  • Cruchaga , M. A. and Oñate , E. 1999 . A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces . Comp. Meth. Appl. Mech. Engng. , 173 : 241 – 255 .
  • Donea , J. and Huerta , A. 2003 . Finite element method for flow problems , J. Wiley .
  • Edelsbrunner , H. and Mucke , E. P. 1999 . Three-dimensional alpha shapes . ACM Trans. Graphics , 13 : 43 – 72 .
  • Franca , L. P. and Frey , S. L. 1992 . Stabilized finite element methods: II. The incompressible Navier-Stokes equations . Comp. Meth. Appl. Mech. Engng. , 99 : 209 – 233 .
  • García , J. and Oñate , E. 2003 . An unstructured finite element solver for ship hydrodynamic problems . J. Appl. Mech. , 70 : 18 – 26 .
  • 2004 . GID. The personal pre/postprocessor , Barcelona : CIMNE . www.gidhome.com
  • Hansbo , P. and Szepessy , A. 1990 . A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations . Comp. Meth. Appl. Mech. Engng. , 84 : 175 – 192 .
  • Hughes , T. J. R. , Franca , L. P. and Balestra , M. 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 accomodating equal order interpolations . Comp. Meth. Appl. Mech. Engng. , 59 : 85 – 89 .
  • Hughes , T. J. R. , Franca , L. P. and Hulbert , G. M. 1989 . A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations . Comp. Meth. Appl. Mech. Engng. , 73 : 173 – 189 .
  • Hughes , T. J. R. , Hauke , G. and Jansen , K. 1994 . “ Stabilized finite element methods in fluids: Inspirations, origins, status and recent developments ” . In Recent Developments in Finite Element Analysis , Edited by: Hughes , T. J. R. , Oñate , E. and Zienkiewicz , O. C. 272 – 292 . Barcelona , , Spain : CIMNE . A Book Dedicated to Robert L. Taylor
  • Idelsohn , S. R. , Oñate , E. , Del Pin , F. and Calvo , N. Lagrangian formulation: the only way to solve some free-surface fluid mechanics problems . Fith World Congress on Computational Mechanics . Edited by: Mang , H. A. , Rammerstorfer , F. G. and Eberhardsteiner , J. Vienna , , Austria
  • Idelsohn , S. R. , Oñate , E. , Calvo , N. and Del Pin , F. 2003 . The meshless finite element method . Int. J. Num. Meth. Engng. , 58 : 893 – 912 .
  • Idelsohn , S. R. , Oñate , E. and Del Pin , F. 2003 . A lagrangian meshless finite element method applied to fluid-structure interaction problems . Computer and Structures , 81 : 655 – 671 .
  • Idelsohn , S. R. , Calvo , N. and Oñate , E. 2003 . Polyhedrization of an arbitrary point set . Comp. Meth. Appl. Mech. Engng. , 192 : 2649 – 2668 .
  • Idelsohn , S. R. , Oñate , E. and Del Pin , F. 2004 . The particle finite element method, a powerful tool to solve incompressible flows with free-surfaces and breaking waves . Int. J. Num. Meth. Engng. , submitted
  • Koshizuka , S. and Oka , Y. 1996 . Moving particle semi-implicit method for fragmentation of incompressible fluid . Nuclear Engng. Science , 123 : 421 – 434 .
  • Laitone , E. V. 1960 . The second approximation to cnoidal waves . J. Fluids Mech. , 9 : 430
  • Oñate , E. 1998 . Derivation of stabilized equations for advective-diffusive transport and fluid flow problems . Comp. Meth. Appl. Mech. Engng. , 151 : 233 – 267 .
  • Oñate , E. and Idelsohn , S. R. 1998 . A mesh free finite point method for advectivediffusive transport and fluid flow problems . Comp. Mech. , 21 : 283 – 292 .
  • Oñate , E. 2000 . A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation . Comp. Meth. Appl. Mech. Engng. , 182 : 355 – 370 .
  • Oñate , E. , Sacco , C. and Idelsohn , S. R. 2000 . A finite point method for incompressible flow problems . Comput. and Visual. in Science , 2 : 67 – 75 .
  • Oñate , E. and García , J. 2001 . A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation . Comp. Meth. Appl. Mech. Engng. , 191 : 635 – 660 .
  • Oñate , E. , Idelsohn , S. R. and Del Pin , F. 2003 . “ Lagrangian formulation for incompressible fluids using finite calculus and the finite element method ” . In Numerical Methods for Scientific Computing Variational Problems and Applications , Edited by: Kuznetsov , Y. , Neittanmaki , P. and Pironneau , O. Barcelona : CIMNE .
  • Oñate , E. 2004 . Possibilities of finite calculus in computational mechanics . Int. J. Num. Meth. Engng. , 60 : 255 – 281 .
  • Oñate , E. , Rojek , J. , Taylor , R. L. and Zienkiewicz , O. C. 2004 . Finite calculus formulation for incompressible solids using linear triangles and tetraedra . Int. J. Num. Meth. Engng. , 59 : 1473 – 1500 .
  • Oñate , E. , García , J. and Idelsohn , S. R. 2004 . “ Ship hydrodynamics ” . In Encyclopedia of Computational Mechanics , Edited by: Stein , E. , de Borst , R. and Hughes , T. J. R. J. Wiley .
  • Radovitzki , R. and Ortiz , M. 1998 . Lagrangian finite element analysis of Newtonian flows . Int. J. Num. Meth. Engng. , 43 : 607 – 619 .
  • Sheng , C. , Taylor , L. K. and Whitfield , D. L. 1996 . Implicit lower-upper / approximatefactorization schemes for incompressible flows . J. Comp. Phys. , 128 : 32 – 42 .
  • Storti , M. , Nigro , N. and Idelsohn , S. R. 1995 . Steady state incompressible flows using explicit schemes with an optimal local preconditioning . Comp. Meth. Appl. Mech. Engng. , 124 : 231 – 252 .
  • Tezduyar , T. E. , Mittal , S. , Ray , S. E. and Shih , R. 1992 . Incompressible flow computations with stabilized bilinear and linear equal order interpolation velocity–pressure elements . Comput. Methods Appl. Mech. Engng. , 95 : 221 – 242 .
  • Zienkiewicz , O. C. and Taylor , R. L. 2000 . The finite element method , 5th Edition , Butterworth–Heinemann . 3 Volumes

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