Accurate fluid-structure interaction computations using elements without mid-side nodes. (English) Zbl 1398.76119

Summary: The paper proposes a new analysis method for fluid-structure problems, which has nodal consistency at the fluid-structure interface and its calculation efficiency and accuracy are high. The incompressible viscous fluid analysis method using the P1-P1 element based on SUPG/PSPG developed by Tezduyar et al. is used for fluid analysis, while the high-accuracy analysis method based on EFMM developed by the authors is adopted for structure analysis. As the common feature of these methods, it is possible to analyze a fluid or a structure rather accurately by using the first-order triangular or tetrahedral elements. In addition, variables are exchanged exactly at the common nodes on the fluid-structure boundary without deteriorating accuracy and calculation efficiency due to the interpolation of variables between nodes. The present method is applied to a fluid-structure interaction problem by simulating the deformation of a red blood cell.


76M10 Finite element methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs


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[1] Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Elsevier, Amsterdam
[2] Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. Prentice Hall, New York · Zbl 0634.73056
[3] Zienkiewicz OC, Taylor RL, Nithiarasu P (2005) The finite element method for fluid dynamics, 6th edn. Elsevier, Amsterdam
[4] 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
[5] Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44 · Zbl 0747.76069
[6] 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
[7] Tezduyar TE (2003) ”Computation of Moving Boundaries and Interfaces and Stabilization Parameters”. Int J Numer Methods Fluids 43: 555–575 · Zbl 1032.76605
[8] 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
[9] 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
[10] 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 43: 39–49 · Zbl 1310.74049
[11] Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46: 17–29 · Zbl 1261.92010
[12] Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space-time finite element computation of arterial fluid-structure interactions. Comput Mech 46: 31–41 · Zbl 1301.92019
[13] Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech. doi: 10.1007/s00466-011-0571-z · Zbl 1398.76128
[14] Yagawa G, Matsubara H (2007) Enriched free mesh method: an accuracy improvement for node-based fem, computational plasticity. Comput Methods Appl Sci 7: 207–219
[15] Yagawa G, Yamada T (1996) Free mesh method a new meshless finite element method. Comput Mech 18: 383–386 · Zbl 0894.73182
[16] Yagawa G, Yamada T (1996) Performance of Parallel computing of free mesh method. In: Proceedings of the 45th National Congress of Theroretical & Applied Mechanics · Zbl 0894.73182
[17] Berg M, Cheong O, Kreveld M, Overmars M (2008) Computational geometry: algorithms and applications, 3rd edn. Springer, New York · Zbl 1140.68069
[18] Inaba M, Fujisawa T, Okuda Y, Yagawa G (2002) Local mesh generation algorithm for free mesh method. The Japan Society of Mechanical Engineers [No. 02-9] Dynamic and Design Conference
[19] Zienkiewicz OC, Taylor RL (1996) Matrix finite element method I (Recision new publication) Kagaku Gijutsu Shuppan, Inc
[20] Newmark NM (1962) A method of computation for structural dynamics, civil engineering. Trans ASCE 127: 1406–1435
[21] Franca LP, Frey SL (1992) Stabilized finite element methods II. The incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 99: 209–233 · Zbl 0765.76048
[22] Zhang S (1997) GPBi-CG generalized product-type methods based on Bi-CG for solving non-symmetriclinear systems. SIAM J Sci Stat Comput 18: 537–551 · Zbl 0872.65023
[23] Thuthu M, Fujino S (2008) Stability of GPBiCG AR method based on minimization of associate residual. ASCM 5081: 108–120 · Zbl 1166.65330
[24] Belytschko T, Flanagan DF, Kennedy JM (1982) Finite element method with user-controlled meshes for fulid-structure interactions. Comput Methods Appl Mech Eng 33: 689–723 · Zbl 0492.73089
[25] Huetra A, Liu WK (1988) Viscous flow with large free surface motion. Comput Methods Appl Mech Eng 69: 277–324 · Zbl 0655.76032
[26] Huetra A, Liu WK (1988) Viscous flow structure interaction. J Press Vessel Technol 110: 15–21
[27] Nitikipaiboon C, Bathe KJ (1993) An arbitrary Lagrangian-Eulerian velocity potential formulation for fluid-structure interaction. Comput Struct 47: 871–891 · Zbl 0800.73296
[28] Bathe KJ, Nitikitpaiboon C, Wang X (1995) A mixed displacement-based finite element formulation for acoustic fluid-structure interaction. Comput Struct 56: 225–237 · Zbl 1002.76536
[29] Bathe KJ, Zhang H, Wang MH (1995) Finite element analysis of incompressible and compressible fluid flows with free interfaces and structural interactions. Comput Struct 56: 193–213 · Zbl 0923.76103
[30] Chakrabarti SK (2007) Fluid structure interaction and moving boundary problems. WIT Press, Southampton
[31] Mittal S, Tezduyar TE (1992) A finite element study of incompressible flows past oscillating cylinders and airfoils. Int J Numer Methods Fluids 15: 1073–1118
[32] 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
[33] 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
[34] Nomura T (1992) Finite element analysis of vortex-induced vibrations of bluff cylinders. J Wind Eng 52: 553
[35] Anagnostopoulos P, Bearman PW (1967) Response characteristics of vortex-exited cylinder at low Reynolds numbers. J Fluids Struct 6: 501–502
[36] Koopman GH (1967) The vortex wakes of vibrating cylinders at low Reynolds numbers. J Fluid Mech 28: 501–502
[37] Tanaka M, Sakamoto T, Sugawara S, Nakajima H, Katahira Y, Ohtsuki S, Kanai H (2008) Blood flow structure and dynamics, and ejection mechanism in the left ventricle. J Cardiol 52: 86–101
[38] Kanno H, Morimoto M, Fujii H, Tsujimura T, Asai H, Noguchi T, Kitamura Y, Miwa S (1995) Primary structure of marine red blood cell-type Pyruvate Kinase (PK) and molecular characterization of PK deficiency identified in the CBA strain. Blood 86: 3205–3210
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