Investigation of fluid-structure interactions using a velocity-linked P2/P1 finite element method and the generalized- α method

International Journal for Numerical Methods in Engineering

Volumn 90, Issue 12, 2012, Pages 1529-1548

  Kang, S ^a   Choi, H G ^b   Yoo, J Y ^c  

^a Seoul National University   (South Korea)

^b Seoul National University of Science and Technology   (South Korea)

^c Seoul National University   (South Korea)

Author keywords

Arbitrary Lagrangian Eulerian; Blood flow; Convergence characteristics; Fluid structure interaction; Velocity linked formulation

Indexed keywords

ARBITRARY LAGRANGIAN EULERIAN; ARBITRARY LAGRANGIAN EULERIAN METHOD; BLOOD FLOW; CONVERGENCE CHARACTERISTICS; COUPLED ALGORITHMS; COUPLED SYSTEMS; DIRECT SOLVERS; FINITE ELEMENT; FLEXIBLE TUBES; FLUID-STRUCTURE INTERFACES; FORCING TERMS; FULLY-COUPLED; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; ITERATIVE SOLVERS; POISSON'S RATIO; PRIMITIVE VARIABLES; STRONG COUPLING; STRUCTURAL EQUATIONS; TEMPORAL DISCRETIZATION; UNSTEADY FLUID-STRUCTURE INTERACTIONS; VELOCITY FIELD; VELOCITY-LINKED FORMULATION;

ALGORITHMS; FLEXIBLE DISPLAYS; FLUID STRUCTURE INTERACTION; NAVIER STOKES EQUATIONS; PIPE FLOW; TUBES (COMPONENTS); VELOCITY;

FINITE ELEMENT METHOD;

EID: 84861576928     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.4252     Document Type: Article

References (38)

1. Wootton DM, Ku DN. Fluid mechanics of vascular systems, diseases, and thrombosis. Annual Review of Biomedical Engineering 1999; 1:299-329.
2. Yamaguchi T, Ishikawa T, Tsubota K, Imai Y, Nakamura M, Fukui T. Computational blood flow analysis - new trends and methods. Journal of Biomechanical Science and Engineering 2006; 1:29-50.
3. Zhang X, Ajaykumar R, Sudharsan NM, Kumar K. Investigation of two-dimensional channel flow with a partially compliant wall using finite volume-finite difference approach. International Journal for Numerical Methods in Fluids 2005; 49:635-655.
4. Figueroa CA, Vignon-Clementel IE, Jansen KE, Hughes TJR, Taylor CA. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Computer Methods in Applied Mechanics and Engineering 2006; 195:5685-5706.
5. Zilian A, Legay A. The enriched space-time finite element method (EST) for simultaneous solution of fluid-structure interaction. International Journal for Numerical Methods in Engineering 2008; 75:305-334.
6. Guidoboni G, Glowinski R, Cavallini N, Canic S. Stable loosely-coupled-type algorithm for fluid-structure interaction in blood flow. Journal of Computational Physics 2009; 228:6916-6937.
7. Lee KW, Xu XY. Modelling of flow and wall behaviour in a mildly stenosed tube. Medical Engineering & Physics 2002; 24:575-586.
8. Kuhl E, Hulshoff S, de Borst R. An arbitrary Lagrangian Eulerian finite-element approach for fluid-structure interaction phenomena. International Journal for Numerical Methods in Engineering 2003; 57:117-142.
9. Greenshields CJ, Weller HG. A unified formulation for continuum mechanics applied to fluid-structure interaction in flexible tubes. International Journal for Numerical Methods in Engineering 2005; 64:1575-1593.
10. Ishihara D, Yoshimura S. A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equation. International Journal for Numerical Methods in Engineering 2005; 64:167-203.
11. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR. Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Computational Mechanics 2006; 38:310-322.
12. Liu WK, Liu Y, Farrell D, Zhang L, Wang XS, Fukui Y, Patankar N, Zhang Y, Bajaj C, Lee J, Hong J, Chen X, Hsu H. Immersed finite element method and its applications to biological systems. Computer Methods in Applied Mechanics and Engineering 2006; 195:1722-1749.
13. Papadakis G. A novel pressure-velocity formulation and solution method for fluid-structure interaction problems. Journal of Computational Physics 2008; 227:3383-3404.
14. Braun AL, Awruch AM. A partitioned model for fluid-structure interaction problems using hexahedral finite elements with one-point quadrature. International Journal for Numerical Methods in Engineering 2009; 79:505-549.
15. Idelsohn SR, Del Pin F, Rossi R, Oñate E, Fluid-structure interaction problems with strong added mass effect. International Journal for Numerical Methods in Engineering 2009; 80:1261-1294.
16. Wang H, Belytschko T. Fluid-structure interaction by the discontinuous-Galerkin method for large deformations. International Journal for Numerical Methods in Engineering 2009; 77:30-49.
17. Barker AT, Cai X-C. Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling. Journal of Computational Physics 2010; 229:642-659.
18. Kim H-G. A new coupling strategy for fluid-solid interaction problems by using the interface element method. International Journal for Numerical Methods in Engineering 2010; 81:403-428.
19. Jog CS, Pal RK. A monolithic strategy for fluid-structure interaction problems. International Journal for Numerical Methods in Engineering 2011; 85:429-460.
20. Zhang Q, Hisada T. Studies of the strong coupling and weak coupling methods in FSI analysis. International Journal for Numerical Methods in Engineering 2004; 60:2013-2029.
21. Jaiman RK, Jiao X, Geubelle PH, Loth E. Assessment of conservative load transfer for fluid-solid interface with non matching meshes. International Journal for Numerical Methods in Engineering 2005; 64:2014-2038.
22. Badia S, Codina R. On some fluid-structure iterative algorithms using pressure segregation methods. Application to aeroelasticity. International Journal for Numerical Methods in Engineering 2007; 72:46-71.
23. Kollmannsberger S, Geller S, Düster A, Tölke J, Sorger C, Krafczyk M, Rank E. Fixed-grid fluid-structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p-FEM approach. International Journal for Numerical Methods in Engineering 2009; 79:817-845.
24. Michler C, Hulshoff SJ, van Brummelen EH, de Borst R. A monolithic approach to fluid-structure interaction. Computers & Fluids 2004; 33:839-848.
25. Causin P, Gerbeau JF, Nobile F. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Computer Methods in Applied Mechanics and Engineering 2005; 194:4506-4527.
26. Gresho PM. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory. International Journal for Numerical Methods in Fluids 1990; 11:587-620.
27. Ramaswamy B, Jue TC. Some recent trends and developments in finite element analysis for incompressible thermal flows. International Journal for Numerical Methods in Engineering 1992; 35:671-707.
28. Choi HG, Choi H, Yoo JY. A fractional four-step finite element formulation of the unsteady incompressible Navier-Stokes equations using SUPG and linear equal-order element methods. Computer Methods in Applied Mechanics and Engineering 1997; 143:333-348.
29. Codina R, Oñate E, Cervera M. The intrinsic time for the streamline upwind/Petrov-Galerkin formulation using quadratic elements. Computer Methods in Applied Mechanics and Engineering 1992; 94:239-262.
30. Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized- α method. Journal of Applied Mechanics 1993; 60:371-375.
31. Jansen KE, Whiting CH, Hulbert GM. A generalized- α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 190:305-319.
32. Kuhl D, Crisfield MA. Energy-conserving and decaying algorithms in non-linear structural dynamics. International Journal for Numerical Methods in Engineering 1999; 45:569-599.
33. Lee SH, Choi HG, Yoo JY. Finite element simulation of blood flow in a flexible carotid artery bifurcation, Proceedings of ASME-JSME-KSME Joint Fluids Engineering Conference 2011, Hamamatsu, Shizuoka, JAPAN, July 24-29, 2011. AJK2011-09020.
34. Wiggert DC, Tijsseling AS. Fluid transients and fluid-structure interaction in flexible liquid-filled piping. Applied Mechanics Reviews 2001; 54:455-481.
35. Tijsseling AS. Water hammer with fluid-structure interaction in thick-walled pipes. Computers & Structures 2007; 85:844-851.
36. Erlicher S, Bonaventura L, Bursi OS. The analysis of the Generalized- α methods for non-linear dynamic problems. Computational Mechanics 2002; 28:83-104.
37. van der Vorst HA. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1992; 13:631-644.
38. Nam YS, Choi HG, Yoo JY. AILU preconditioning for the finite element formulation of the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 2002; 191:4323-4339.