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Modeling of fluid-structure interactions with the space-time finite elements: Contact problems. (English) Zbl 1297.74129

Summary: Fluid-structure interaction computations based on interface-tracking (moving-mesh) techniques are often hindered if the structural surfaces come in contact with each other. As the distance between two structural surfaces tends to zero, the fluid mesh in between distorts severely and eventually becomes invalid. Our objective is to develop a technique for modeling problems where the contacting structural surfaces would otherwise inhibit flow modeling or even fluid-mesh update. In this paper, we present our contact tracking technique that detects impending contact and maintains a minimum distance between the contacting structural surfaces. Our Surface-Edge-Node Contact Tracking (SENCT) technique conducts a topologically hierarchical search to detect contact between each node and the elements (“surfaces”), edges and other nodes. To keep the contacting surfaces apart by a small distance, we apply to the contacted nodes penalty forces in SENCT-Force (SENCT-F) and displacement restrictions in SENCT-Displacement (SENCT-D). By keeping a minimum distance between the contacting surfaces, we are able to update the fluid mesh in between and model the flow accurately.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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[1] Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26: 27–36 · Zbl 05090697
[2] Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119: 157–177 · Zbl 0848.76040
[3] Mittal S, Tezduyar TE (1994) Massively parallel finite element computation of incompressible flows involving fluid-body interactions. Comput Methods Appl Mech Eng 112: 253–282 · Zbl 0846.76048
[4] Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows–Fluid–structure interactions. Int J Numer Methods Fluids 21: 933–953 · Zbl 0873.76047
[5] Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23: 130–143 · Zbl 0949.76049
[6] Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190: 321–332 · Zbl 0993.76044
[7] Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D Computation. Comput Methods Appl Mech Eng 190: 373–386 · Zbl 0973.76055
[8] Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191: 717–726 · Zbl 1113.76407
[9] Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190: 3009–3019 · Zbl 0971.74032
[10] Tezduyar TE, Sathe S, Keedy R, Stein K (2004) Space–time techniques for finite element computation of flows with moving boundaries and interfaces. In: Gallegos S, Herrera I, Botello S, Zarate F, Ayala G (eds) Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Science. CD-ROM, Monterrey, Mexico
[11] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulation. Jpn Soc Mech Eng J A 70:1224–1231 (in Japanese)
[12] van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid–structure interaction problem. SIAM J Sci Comput 27: 599–621 · Zbl 1136.65334
[13] Michler C, van Brummelen EH, de Borst R (2005) An interface Newton–Krylov solver for fluid–structure interaction. Int J Numer Methods Fluids 47: 1189–1195 · Zbl 1069.76033
[14] Gerbeau J-F, Vidrascu M, Frey P (2005) Fluid–structure interaction in blood flow on geometries based on medical images. Comput Struct 83: 155–165
[15] Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027 · Zbl 1118.74052
[16] Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195: 5743–5753 · Zbl 1123.76035
[17] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the Deforming-Spatial-Domain/Stabilized Space–Time formulation. Comput Methods Appl Mech Eng 195: 1885–1895 · Zbl 1178.76241
[18] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38: 482–490 · Zbl 1160.76061
[19] Dettmer W, Peric D (2006) A computational framework for fluid–structure interaction: Finite element formulation and applications. Comput Methods Appl Mech Eng 195: 5754–5779 · Zbl 1155.76354
[20] Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322 · Zbl 1161.74020
[21] Khurram RA, Masud A (2006) A multiscale/stabilized formulation of the incompressible Navier–Stokes equations for moving boundary flows and fluid–structure interaction. Comput Mech 38: 403–416 · Zbl 1184.76720
[22] Kuttler U, Forster C, Wall WA (2006) A solution for the incompressibility dilemma in partitioned fluid–structure interaction with pure Dirichlet fluid domains. Comput Mech 38: 417–429 · Zbl 1166.74046
[23] Lohner R, Cebral JR, Yang C, Baum JD, Mestreau EL, Soto O (2006) Extending the range of applicability of the loose coupling approach for FSI simulations. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, pp 82–100 · Zbl 1323.74091
[24] Bletzinger K-U, Wuchner R, Kupzok A (2006) Algorithmic treatment of shells and free form-membranes in FSI. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, pp 336–355 · Zbl 1323.74078
[25] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36: 160–168 · Zbl 1113.76105
[26] Masud A, Bhanabhagvanwala M, Khurram RA (2007) An adaptive mesh rezoning scheme for moving boundary flows and fluid–structure interaction. Comput Fluids 36: 77–91 · Zbl 1181.76108
[27] Sawada T, Hisada T (2007) Fuid–structure interaction analysis of the two dimensional flag-in-wind problem by an interface tracking ALE finite element method. Comput Fluids 36: 136–146 · Zbl 1181.76099
[28] Wall WA, Genkinger S, Ramm E (2007) A strong coupling partitioned approach for fluid–structure interaction with free surfaces. Comput Fluids 36: 169–183 · Zbl 1181.76147
[29] Idelsohn SR, Marti J, Souto-Iglesias A, Onate E (2008) Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM. Comput Mech, published online. doi: 10.1007/s00466-008-0245-7 , February 2008 · Zbl 1177.74140
[30] Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech, published online. doi: 10.1007/s00466-008-0254-6 , February 2008
[31] Kuttler U, Wall WA (2008) Fixed-point fluid–structure interaction solvers with dynamic relaxation. Comput Mech, published online. doi: 10.1007/s00466-008-0255-5 , February 2008
[32] Heil M, Hazel AL, Boyle J (2008) Solvers for large-displacement fluid–structure interaction problems: segregated versus monolithic approaches. Comput Mech, published online. doi: 10.1007/s00466-008-0270-6 , March 2008 · Zbl 1309.76126
[33] Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech, published online. doi: 10.1007/s00466-008-0277-z , April 2008
[34] Manguoglu M, Sameh AH, Tezduyar TE, Sathe S (2008) A nested iterative scheme for computation of incompressible flows in long domains. Comput Mech, published online. doi: 10.1007/s00466-008-0276-0 , April 2008 · Zbl 1279.76024
[35] Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) A fully-integrated approach to fluid–structure interaction. Comput Mech (in preparation)
[36] Tezduyar TE, Sathe S, Stein K, Aureli L (2006) Modeling of fluid–structure interactions with the space–time techniques. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction, Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, pp 50–81 · Zbl 1323.74096
[37] Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: Solution techniques. Int J Numer Methods Fluids 54: 855–900 · Zbl 1144.74044
[38] Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics. Int J Numer Methods Fluids 54: 901–922 · Zbl 1276.76043
[39] Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2007) Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique. Int J Numer Methods Fluids, published online. doi: 10.1002/fld.1633 , October 2007 · Zbl 1230.76054
[40] Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods. Comput Mech, published online. doi: 10.1007/s00466-008-0261-7 , March 2008 · Zbl 1310.74049
[41] Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech, published online. doi: 10.1007/s00466-008-0260-8 , March 2008 · Zbl 1209.74022
[42] Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44 · Zbl 0747.76069
[43] Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces–the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94: 339–351 · Zbl 0745.76044
[44] Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94: 353–371 · Zbl 0745.76045
[45] Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575 · Zbl 1032.76605
[46] Hughes TJR, Brooks AN (1979) A multi-dimensional upwind scheme with no crosswind diffusion. In: Hughes TJR(eds) Finite Element Methods for Convection Dominated Flows, AMD-Vol 34. ASME, New York, pp 19–35
[47] Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32: 199–259 · Zbl 0497.76041
[48] Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242 · Zbl 0756.76048
[49] Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška–Brezzi condition: A stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59: 85–99 · Zbl 0622.76077
[50] Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430 · Zbl 0973.76057
[51] Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, De Borst R, Hughes TJR (eds) Encyclopedia of Computational Mechanics, vol 3: Fluids, Chap 17. Wiley, New York
[52] Tezduyar TE (2007) Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206 · Zbl 1177.76202
[53] Lo A (1982) Nonlinear dynamic analysis of cable and membrane structure. Ph.D. thesis, Department of Civil Engineering, Oregon State University
[54] Benney RJ, Stein KR, Leonard JW, Accorsi ML (1997) Current 3-D structural dynamic finite element modeling capabilities. In: Proceedings of AIAA 14th Aerodynamic Decelerator Systems Technology Conference, AIAA Paper 97-1506. San Francisco, California
[55] Tezduyar TE (2003) Stabilized finite element methods for computation of flows with moving boundaries and interfaces. In: Lecture Notes on Finite Element Simulation of Flow Problems (Basic–Advanced Course), Japan Society of Computational Engineering and Sciences, Tokyo, Japan
[56] Tezduyar TE (2003) Stabilized finite element methods for flows with moving boundaries and interfaces. HERMIS: Int J Comput Math Appl 4: 63–88 · Zbl 1309.76135
[57] Tezduyar TE (2007) Finite elements in fluids: Special methods and enhanced solution techniques. Comput Fluids 36: 207–223 · Zbl 1177.76203
[58] Saad Y, Schultz M (1986) GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7: 856–869 · Zbl 0599.65018
[59] Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods–space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol.246/AMD-Vol.143. ASME, New York, pp 7–24
[60] Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119: 73–94 · Zbl 0848.76036
[61] Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8: 83–130 · Zbl 1039.76037
[62] Tezduyar T (2001) Finite element interface-tracking and interface-capturing techniques for flows with moving boundaries and interfaces. In: Proceedings of the ASME Symposium on Fluid-Physics and Heat Transfer for Macro- and Micro-Scale Gas-Liquid and Phase-Change Flows (CD-ROM), ASME Paper IMECE2001/HTD-24206, ASME, New York
[63] Tezduyar TE (2003) Stabilized finite element formulations and interface-tracking and interface-capturing techniques for incompressible flows. In: Hafez MM(eds) Numerical Simulations of Incompressible Flows. World Scientific, New Jersey, pp 221–239 · Zbl 1059.76038
[64] Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70: 58–63 · Zbl 1110.74689
[65] Tezduyar TE, Sathe S, Senga M, Aureli L, Stein K, Griffin B (2005) Finite element modeling of fluid–structure interactions with space–time and advanced mesh update techniques. In: Proceedings of the 10th International Conference on Numerical Methods in Continuum Mechanics (CD-ROM), Zilina, Slovakia
[66] Karypis G, Kumar V (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20: 359–392 · Zbl 0915.68129
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