A novel pressure-velocity formulation and solution method for fluid-structure interaction problems

Journal of Computational Physics

Volumn 227, Issue 6, 2008, Pages 3383-3404

  Papadakis, George ^a  

^a KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Elastodynamic equations; Finite volume method; Flexible tube; Fluid structure interaction; Pressure wave propagation; SIMPLE algorithm

Indexed keywords

FLUID STRUCTURE INTERACTION; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; WAVE PROPAGATION;

DISPLACEMENT COMPONENTS; ELASTODYNAMIC EQUATION; FINITE-VOLUME METHOD; FLEXIBLE TUBES; FLUID-STRUCTURE INTERACTION; FLUID-STRUCTURE INTERACTION PROBLEM; PRESSURE WAVE PROPAGATION; PRESSURE-VELOCITY; SIMPLE ALGORITHM; SOLUTION METHODS;

FINITE VOLUME METHOD;

EID: 38749146842     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.12.004     Document Type: Article

References (43)

1. Matthies H.G., and Steindorf J. Partitioned but strongly coupled iteration schemes for non-linear fluid-structure interaction problems. Comput. Struct. 80 (2002) 1991-1999
2. Farhat C., and Lesoinne M. Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput. Method Appl. Math. 182 (2000) 499-515
3. Slone A.K., Pericleous K., Bailey C., and Cross M. Dynamic fluid-structure interaction using finite volume unstructured mesh procedures. Comput. Struct. 80 (2002) 371-390
4. Le Tallec P., and Mouro J. Fluid structure interaction with large structural displacements. Comput. Method Appl. Math. 190 (2001) 3039-3067
5. Ahn H.T., and Kallinderis Y. Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes. J. Comput. Phys. 219 (2006) 671-696
6. Bazilevs Y., Calo V.M., Zhang Y., and Hughes T.J.R. Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput. Mech. 38 (2006) 310-322
7. Heil M. An efficient solver for the fully coupled solution of large displacement fluid-structure interaction problems. Comput. Method Appl. Math. 193 (2004) 1-23
8. Tezduyar T.E., Sathe S., and Stein K. Solution techniques for the fully discretised equations in computation of fluid-structure interactions with the space-time formulations. Comput. Method Appl. Math. 195 (2006) 5743-5753
9. Oñate E., Cervera M., and Zienkiewicz O.C. A finite volume format for structural mechanics. Int. J. Numer. Methods Eng. 37 (1994) 181-201
10. Bathe K.J. Finite Element Procedures (1996), Prentice-Hall, Englewood Cliffs, NJ
11. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (2000), Dover Publications Inc., New York
12. Gresho P.M., and Sani R.L. Incompressible Flow and the Finite Element Method vols. 1 and 2 (2000), John Wiley and Sons, Chichester
13. Bailey C., and Cross M. A finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh. Int. J. Numer. Methods Eng. 38 (1995) 1757-1776
14. Ferziger J.H., and Peric M. Computational Methods for Fluid Dynamics (1996), Springer-Verlag, Berlin, Heidelberg
15. Wheel M.A. A geometrically versatile finite volume formulation for plane elastostatic stress analysis. J. Strain Anal. Eng. 31 (1996) 111-116
16. Wheel M.A. A mixed finite volume formulation for determining the small strain deformation of incompressible materials. Int. J. Numer. Methods Eng. 44 (1999) 1843-1861
17. Fallah N.A., Bailey C., Cross M., and Taylor G.A. Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis. Appl. Math. Model. 24 (2000) 439-455
18. Demirdžic I., Muzaferija S., and Peric M. Benchmark solutions of some structural analysis problems using the finite-volume method and multigrid acceleration. Int. J. Numer. Methods Eng. 40 (1997) 1893-1908
19. Jasak H., and Weller H.G. Application of the finite volume method and unstructured meshes to linear elasticity. Int. J. Numer. Methods Eng. 48 (2000) 267-287
20. Greenshields C., Weller H.G., and Ivankovic A. The finite volume method for coupled fluid flow and stress analysis. Comput. Model. Simul. Eng. 4 3 (1999) 213-218
21. Ivankovic A., Karac A., Dendrinos E., and Parker K. Towards early diagnosis of atherosclerosis: the finite volume method for fluid-structure interaction. Biorheology 39 (2002) 401-407
22. Greenshields C., and Weller H.G. A unified formulation for continuum mechanics applied to fluid-structure interaction in flexible tubes. Int. J. Numer. Methods Eng. 64 (2005) 1575-1593
23. A. Karac, Drop impact of fluid-filled polyethylene containers, PhD Thesis, Department of Mechanical Engineering, Imperial College London, 2003.
24. Malvern L.E. Introduction to the Mechanics of a Continuous Medium (1969), Prentice-Hall Inc., New Jersey
25. Lai W.M., Rubin D., and Krempl E. Introduction to Continuum Mechanics. third ed. (1996), Butterworth-Heinemann, Massachusetts
26. Pedley T.J. The Fluid Mechanics of Large Blood Vessels (1980), Cambridge University Press, Cambridge
27. Vardy A.E., and Alsarraj A.T. Method of characteristics analysis of one-dimensional members. J. Sound Vib. 129 (1989) 477-487
28. Lin X., and Ballman J. A numerical scheme for axisymmetric elastic waves in solids. Wave Motion 21 (1995) 115-126
29. Giese G., and Fey M. A genuinely multidimensional high-resolution scheme for the elastic-plastic wave equation. J. Comput. Phys. 181 (2002) 338-353
30. Voinovich P., and Merlen A. Two-dimensional unstructured elastic model for acoustic pulse scattering at solid-liquid interfaces. Shock Waves 13 (2003) 421-429
31. LeVeque R.J. Finite Volume Methods for Hyperbolic Problems (2002), Cambridge University Press, Cambridge
32. Patankar S. Numerical Heat Transfer and Fluid Flow (1980), Hemisphere Publishing Corporation, Washington
33. Versteeg H.K., and Malalasekera W. An Introduction to Computational Fluid Dynamics: The finite Volume method. second ed. (2007), Pearson Education Limited, Harlow, England
34. Issa R.I. Solution of the implicit discretised fluid flow equation by operator-splitting. J. Comput. Phys. 62 (1986) 40-65
35. Rhie C.M., and Chow W.L. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA J. 21 (1983) 1525-1532
36. Yeoh S.L., Papadakis G., and Yianneskis M. Determination of mixing time and degree of homogeneity in stirred vessels with LES. Chem. Eng. Sci. 60 (2005) 2293-2302
37. Liang C., and Papadakis G. Large eddy simulation of pulsating cross-flow over a circular cylinder at subcritical Reynolds number. Comput. Fluids 36 (2007) 299-312
38. Liang C., and Papadakis G. Large eddy simulation of cross flow through a staggered tube bundle at subcritical Reynolds number. J. Fluid Struct. 23 (2007) 1215-1230
39. Atabek H.B. Wave propagation through a viscous fluid contained in a tethered, initially stressed, orthotropic elastic tube. Biophys. J. 8 (1968) 626-649
40. Flügge W. Stresses in Shells (1960), Springer-Verlag, Berlin, Heidelberg
41. Kuiken G.D.C. Wave propagation in a thin-walled liquid-filled initially stressed tube. J. Fluid Mech. 141 (1984) 289-308
42. Struckenbruck S., Wiggert D.C., and Otwell R.S. The influence of pipe motion on acoustic wave propagation. J. Fluids Eng. - Trans. ASME 107 (1985) 518-522
43. Ugural A.C. Stresses in Plates and Shells. second ed. (1999), Mc-Graw Hill, Singapore