×

zbMATH — the first resource for mathematics

Unified Lagrangian formulation for elastic solids and incompressible fluids: application to fluid-structure interaction problems via the PFEM. (English) Zbl 1194.74415
Summary: We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and fluid subdomains in a unified manner in fluid-structure interaction (FSI) situations. In our work the FSI problem is solved via the particle finite element method (PFEM). The PFEM is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows, accounting for splashing of waves, large motions of the bodies and frictional contact conditions. Applications of the unified Lagrangian formulation to a number of FSI problems are given.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aubry, R.; Idelsohn, S.R.; Oñate, E., Particle finite element method in fluid mechanics including thermal convection – diffusion, Comp. struct., 83, 17-18, 1459-1475, (2005)
[2] Edelsbrunner, H.; Mucke, E.P., Three dimensional alpha shapes, ACM trans. graphics, 13, 43-72, (1999) · Zbl 0806.68107
[3] S.R. Idelsohn, E. Oñate, F. Del Pin, N. Calvo, Lagrangian formulation: the only way to solve some free-surface fluid mechanics problems, in: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner, (Eds.), Fifth World Congress on Computational Mechanics, Viena, Austria, July 2002, pp. 7-12.
[4] Idelsohn, S.R.; Oñate, E.; Calvo, N.; Del Pin, F., The meshless finite element method, Int. J. num. methods engrg., 58, 6, 893-912, (2003) · Zbl 1035.65129
[5] Idelsohn, S.R.; Oñate, E.; Del Pin, F., A Lagrangian meshless finite element method applied to fluid – structure interaction problems, Comp. struct., 81, 655-671, (2003)
[6] Idelsohn, S.R.; Calvo, N.; Oñate, E., Polyhedrization of an arbitrary point set, Comput. method appl. mech. engrg., 192, 22-24, 2649-2668, (2003) · Zbl 1040.65019
[7] Idelsohn, S.R.; Oñate, E.; Del Pin, F., The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int. J. num. methods engrg., 61, 964-989, (2004) · Zbl 1075.76576
[8] Koshizuka, S.; Tamko, H.; Oka, Y., A particle method for incompressible viscous flow with fluid fragmentation, Comp. fluid dyn. J., 4, 1, 29-46, (1995)
[9] Oñate, E., Derivation of stabilized equations for advective-diffusive transport and fluid flow problems, Comput. methods appl. mech. engrg., 151, 233-267, (1998) · Zbl 0916.76060
[10] Oñate, E., A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation, Comp. methods appl. mech. engrg., 182, 1-2, 355-370, (2000) · Zbl 0977.76050
[11] Oñate, E., Possibilities of finite calculus in computational mechanics, Int. J. num. methods engrg., 60, 1, 255-281, (2004) · Zbl 1060.76576
[12] Oñate, E.; Garcı´a, J., A finite element method for fluid – structure interaction with surface waves using a finite calculus formulation, Comput. methods appl. mech. engrg., 191, 635-660, (2001) · Zbl 0996.76052
[13] Oñate, E.; Idelsohn, S.R.; Del Pin, F., Lagrangian formulation for incompressible fluids using finite calculus and the finite element method, () · Zbl 1075.76576
[14] Oñate, E.; Garcı´a, J.; Idelsohn, S.R., Ship hydrodynamics, ()
[15] Oñate, E.; Idelsohn, S.R.; Del Pin, F.; Aubry, R., The particle finite element method. an overview, Int. J. comput. methods, 1, 2, 267-307, (2004) · Zbl 1182.76901
[16] Farhat, Ch.; Kristoffer, G.; Zee, V.; Geozine, Ph., Probably second-order time accurate loosely-coupled solution algorithm for transient nonlinear computational aeroelasticity, Comput. methods appl. mech. engrg., 195, 17-18, 1973-2001, (2006) · Zbl 1178.76259
[17] Foster, Ch.; Wall, W.A.; Ramm, E., Artificial added mass instabiliting in sequential staggered coupling of nonlinear structures and incompressible flows, Comput. methods appl. mech. engrg., 196, 1278-1293, (2007) · Zbl 1173.74418
[18] R. Lohner, A Parallel Advancing Front Grid Generation Scheme, AIAA, 00-1005, 2000.
[19] Walhorn, E.; Kolke, A.; Hubner, B.; Dinkler, D., Fluid – structure coupling with monolithic model involving free surface flows, Comp. struct., 83, 2100-2111, (2005)
[20] Greenshields, C.J.; Weller, H.G., A unified formulation for continuum mechanics applied to fluid – structure interaction in flexible tubes, Int. J. num. methods engrg., 64, 1575-1593, (2005) · Zbl 1122.74379
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.