×

Fixed-point fluid-structure interaction solvers with dynamic relaxation. (English) Zbl 1236.74284

Summary: A fixed-point fluid-structure interaction (FSI) solver with dynamic relaxation is revisited. New developments and insights gained in recent years motivated us to present an FSI solver with simplicity and robustness in a wide range of applications. Particular emphasis is placed on the calculation of the relaxation parameter by both Aitken’s \({\Delta^{2}}\) method and the method of steepest descent. These methods have shown to be crucial ingredients for efficient FSI simulations.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Software:

CFX-5
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Badia S, Codina R (2007) On some fluid–structure iterative algorithms using pressure segregation methods. application to aeroelasticity. Int J Numer Methods Eng 72(1): 46–71 · Zbl 1194.74361 · doi:10.1002/nme.1998
[2] Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38(4–5): 310–322 · Zbl 1161.74020 · doi:10.1007/s00466-006-0084-3
[3] Causin P, Gerbeau J-F, Nobile F (2005) Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput Methods Appl Mech Eng 194: 4506–4527 · Zbl 1101.74027 · doi:10.1016/j.cma.2004.12.005
[4] Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized- \({\alpha}\) method. J Appl Math 60: 371–375 · Zbl 0775.73337
[5] Deparis S (2004) Numerical analysis of axisymmetric flows and methods for fluid–structure interaction arising in blood flow simulation. Dissertation, EPFL
[6] Deparis S, Discacciati M, Fourestey G, Quarteroni A (2006) Fluid–structure algorithms based on Steklov-Poincaré operators. Comput Methods Appl Mech Eng 195: 5797–5812 · Zbl 1124.76026 · doi:10.1016/j.cma.2005.09.029
[7] Dettmer WG, 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 · doi:10.1016/j.cma.2005.10.019
[8] Farhat C (2004) CFD-based nonlinear computational aeroelasticity. In: Stein E, De Borst R, Hughes TJR(eds) Encyclopedia of Computational mechanics, vol 3, chap. 13. Wiley, NY
[9] Farhat C, Geuzaine P (2004) Design and analysis of robust ale time-integrators for the solution of unsteady flow problems on moving grids. Comput Methods Appl Mech Eng 193: 4073–4095 · Zbl 1068.76063 · doi:10.1016/j.cma.2003.09.027
[10] Fernández MÁ, Moubachir M (2005) A Newton method using exact jacobians for solving fluid–structure coupling. Comput Struct 83(2–3): 127–142 · doi:10.1016/j.compstruc.2004.04.021
[11] Förster Ch (2007) Robust methods for fluid–structure interaction with stabilised finite elements. Dissertation, Institut für Baustatik und Baudynamik Universität Stuttgart
[12] Förster Ch, Wall WA, Ramm E (2005) On the geometric conservation law in transient flow calculations on deforming domains. Int J Numer Methods Fluids 50: 1369–1379 · Zbl 1097.76049 · doi:10.1002/fld.1093
[13] Förster Ch, Wall WA, Ramm E (2007) Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput Methods Appl Mech Eng 196: 1278–1293 · Zbl 1173.74418 · doi:10.1016/j.cma.2006.09.002
[14] Förster Ch, Wall WA, Ramm E (2008) Stabilized finite element formulation for incompressible flow on distorted meshes. Int J Numer Methods Fluids (in press) · Zbl 1187.76683
[15] Gerbeau J-F, Vidrascu M (2003) A quasi-Newton algorithm based on a reduced model for fluid–structure interaction problems in blood flows. Math Model Numer Anal. Math Model Numer Anal 37(4): 631–647 · Zbl 1070.74047 · doi:10.1051/m2an:2003049
[16] Gerbeau J-F, Vidrascu M, Frey P (2005) Fluid–structure interaction in blood flows on geometries coming from medical imaging. Comput Struct 83: 155–165 · doi:10.1016/j.compstruc.2004.03.083
[17] Golub GH, Van Loan CF (1996) Matrix computations. The Johns Hopkins University Press, Baltimore · Zbl 0865.65009
[18] Heil M (2004) An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems. Comput Methods Appl Mech Eng 193: 1–23 · Zbl 1137.74439 · doi:10.1016/j.cma.2003.09.006
[19] Hübner B, Walhorn E, Dinkler D (2004) A monolithic approach to fluid–structure interaction using space-time finite elements. Comput Methods Appl Mech Eng 193: 2087–2104 · Zbl 1067.74575 · doi:10.1016/j.cma.2004.01.024
[20] Irons B, Tuck RC (1969) A version of the Aitken accelerator for computer implementation. Int J Numer Methods Eng 1: 275–277 · Zbl 0256.65021 · doi:10.1002/nme.1620010306
[21] 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 · doi:10.1016/S0045-7825(00)00204-8
[22] Kelley CT (1995) Iterative Methods for linear and nonlinear equations frontiers in applied mathematics. SIAM
[23] Knoll DA, Keyes DE (2004) Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J Comput Phys 193: 357–397 · Zbl 1036.65045 · doi:10.1016/j.jcp.2003.08.010
[24] Küttler U, Förster Ch, 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 · doi:10.1007/s00466-006-0066-5
[25] Matthies HG, Steindorf J (2003) Partitioned strong coupling algorithms for fluid–structure interaction. Comput Struct 81: 805–812 · doi:10.1016/S0045-7949(02)00409-1
[26] Michler C, Brummelen EH, Borst R (2005) An interface Newton-Krylov solver for fluid–structure interaction. Int J Numer Methods Fluids 47: 1189–1195 · Zbl 1069.76033 · doi:10.1002/fld.850
[27] Mok DP, Wall WA (2001) Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures. In: Wall WA, Bletzinger K-U, Schweitzerhof K (eds) Trends in computational structural mechanics
[28] Park KC, Felippa CA, Ohayon R (2001) Partitioned formulation of internal fluid–structure interaction problems by localized Lagrange multipliers. Comput Methods Appl Mech Eng 190(24–25): 2989–3007 · Zbl 0983.74022 · doi:10.1016/S0045-7825(00)00378-9
[29] Quaini A, Quarteroni A (2007) A semi-implicit approach for fluid–structure interaction based on an algebraic fractional step method. Math Models Methods Appl Sci 17(6): 957–983 · Zbl 1388.74041 · doi:10.1142/S0218202507002170
[30] Le Tallec P, Mouro J (2001) Fluid structure interaction with large structural displacements. Comput Methods Appl Mech Eng 190(24–25): 3039–3067 · Zbl 1001.74040 · doi:10.1016/S0045-7825(00)00381-9
[31] Tezduyar TE (2007) Finite elements in fluids: Special methods and enhanced solution techniques. Comput Fluids 36: 207–223 · Zbl 1177.76203 · doi:10.1016/j.compfluid.2005.02.010
[32] Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206 · Zbl 1177.76202 · doi:10.1016/j.compfluid.2005.02.011
[33] Tezduyar TE, Sathe S (2007) Modelling of fluid–structure interactions with the space-time finite elements: solution techniques. Int J Numer Meth Fluids 54(6–8): 855–900 · Zbl 1144.74044 · doi:10.1002/fld.1430
[34] Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modelling of fluid–structure interactions with the space-time finite elements: arterial fluid mechanics. Int J Numer Meth Fluids 54(6–8): 901–922 · Zbl 1276.76043 · doi:10.1002/fld.1443
[35] 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 · doi:10.1016/j.cma.2004.09.014
[36] 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 · doi:10.1016/j.cma.2005.08.023
[37] Vierendeels J (2005) Implicit coupling of partitioned fluid–structure interaction solvers using a reduced order model. AIAA Fluid Dyn Conf Exhib 35: 1–12 · Zbl 1323.74112
[38] Wall WA (1999) Fluid-Struktur-Interaktion mit stabilisierten Finiten Elementen. Dissertation, Institut für Baustatik, Universität Stuttgart
[39] Wall WA, Gerstenberger A, Gamnitzer P, Förster Ch, Ramm F (2006) Large deformation fluid–structure interaction–advances in ALE methods and new fixed grid approaches. In: Bungartz H-J, Schäfer M(eds) Fluid–structure interaction: modelling, simulation, optimisation, LNCSE. Springer, Heidelberg · Zbl 1323.74097
[40] Wall WA, Mok DP, Ramm E (1999) Partitioned analysis approach of the transient coupled response of viscous fluids and flexible structures. In: Wunderlich W (Ed.), Solids, structures and coupled problems in engineering, proceedings of the European conference on computational mechanics ECCM ’99, Munich
[41] Wüchner R, Kupzok A, Bletzinger K-U (2007) A framework for stabilized partitioned analysis of thin membrane-wind interaction. Int J Numer Methods Fluids 54(6–8) · Zbl 1123.74014
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.