Assessment and improvement of mapping algorithms for non-matching meshes and geometries in computational FSI

详细信息    查看全文

• 作者：Tianyang Wang ; Roland Wüchner ; Stefan Sicklinger…
• 关键词：Non ; matching meshes ; Fluid ; structure interaction ; Mortar method ; Dual Lagrange multipliers ; Nonlinear beam FSI
• 刊名：Computational Mechanics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：57
• 期：5
• 页码：793-816
• 全文大小：10,325 KB
• 参考文献：1.Ahrem R, Beckert A, Wendland H (2007) Recovering rotations in aeroelasticity. J Fluids Struct 23(6):874–884CrossRef
  2.Bazilevs Y, Hsu MC, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar T (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65(1–3):207–235CrossRef MATH
  3.Bazilevs Y, Hsu MC, Kiendl J, Wüchner R, Bletzinger KU (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid-structure interaction modeling with composite blades. Int J Numer Methods Fluids 65(1–3):236–253CrossRef MATH
  4.Bazilevs Y, Hsu MC, Scott M (2012) Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249:28–41MathSciNet CrossRef
  5.Bazilevs Y, Hsu MC, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Model Methods Appl Sci 22(supp02):1230002CrossRef MATH
  6.Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, ChichesterCrossRef MATH
  7.Beckert A, Wendland H (2001) Multivariate interpolation for fluid-structure-interaction problems using radial basis functions. Aerosp Sci Technol 5(2):125–134CrossRef MATH
  8.Bernardi C, Maday Y, Patera AT (1994) A new nonconforming approach to domain decomposition: the mortar element method. In: Brezis H, Lions JL (eds) Nonlinear partial differential equations and their applications, vol XI. College de France Seminar. Longman, Harlow, pp 13–51
  9.Blasques JPAA, Bitsche R, Fedorov V, Eder MA (2013) Applications of the beam cross section analysis software (becas). In: Proceedings of the 26th nordic seminar on computational mechanics, pp 46–49
  10.Blom FJ (1998) A monolithical fluid-structure interaction algorithm applied to the piston problem. Comput Methods Appl Mech Eng 167(3):369–391MathSciNet CrossRef MATH
  11.de Boer A, van Zuijlen AH, Bijl H (2008) Comparison of conservative and consistent approaches for the coupling of non-matching meshes. Comput Methods Appl Mech Eng 197(49):4284–4297CrossRef MATH
  12.Bottasso C, Campagnolo F, Croce A, Tibaldi C (2013) Optimization-based study of bend-twist coupled rotor blades for passive and integrated passive/active load alleviation. Wind Energy 16(8):1149–1166
  13.Brenner SC, Scott R (2008) The mathematical theory of finite element methods, vol 15. Springer, New YorkMATH
  14.Chen H, Yu W, Capellaro M (2010) A critical assessment of computer tools for calculating composite wind turbine blade properties. Wind Energy 13(6):497–516CrossRef
  15.Cichosz T, Bischoff M (2011) Consistent treatment of boundaries with mortar contact formulations using dual lagrange multipliers. Comput Methods Appl Mech Eng 200(9):1317–1332MathSciNet CrossRef MATH
  16.Cordero-Gracia M, Gómez M, Valero E (2014) A radial basis function algorithm for simplified fluid-structure data transfer. Int J Numer Methods Eng 99(12):888–905MathSciNet CrossRef
  17.De Rosis A, Falcucci G, Ubertini S, Ubertini F (2013) A coupled lattice boltzmann-finite element approach for two-dimensional fluid-structure interaction. Comput Fluids 86:558–568MathSciNet CrossRef MATH
  18.Degroote J, Bruggeman P, Haelterman R, Vierendeels J (2008) Stability of a coupling technique for partitioned solvers in FSI applications. Comput truct 86(23):2224–2234CrossRef
  19.Farhat C, Lesoinne M, Le Tallec P (1998) Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Comput Methods Appl Mech Eng 157(1):95–114MathSciNet CrossRef MATH
  20.Farhat C, Van der Zee KG, Geuzaine P (2006) Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Comput Methods Appl Mech Eng 195(17):1973–2001MathSciNet CrossRef MATH
  21.Felippa C, Haugen B (2005) A unified formulation of small-strain corotational finite elements: I. theory. Comput Methods Appl Mech Eng 194(21):2285–2335CrossRef MATH
  22.Felippa C, Park K, Ross M (2010) A classification of interface treatments for FSI. In: Bungartz H-J, Mehl M, Schäfer M (eds) Fluid structure interaction II. Springer, Berlin
  23.Fernández MÁ, Moubachir M (2005) A Newton method using exact Jacobians for solving fluid-structure coupling. Comput Struct 83(2):127–142CrossRef
  24.Foley JD, van Dam A, Feiner SK, Hughes JF (1990) Computer graphics: principles and practice, 2nd edn. Addison-Wesley, ReadingMATH
  25.Hansen MOL, Sørensen JN, Voutsinas S, Sørensen N, Madsen HA (2006) State of the art in wind turbine aerodynamics and aeroelasticity. Prog Aerosp Sci 42(4):285–330CrossRef
  26.Hsu MC, Akkerman I, Bazilevs Y (2014) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy 17(3):461–481CrossRef
  27.Hsu MC, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50(6):821–833MathSciNet CrossRef MATH
  28.Jaiman R, Jiao X, Geubelle P, Loth E (2006) Conservative load transfer along curved fluid-solid interface with non-matching meshes. J Comput Phys 218(1):372–397CrossRef MATH
  29.Kindmann R, Kraus M (2004) Steel structures: sesign using FEM. Ernst & Sohn, Berlin
  30.Klöppel T, Popp A, Küttler U, Wall WA (2011) Fluid-structure interaction for non-conforming interfaces based on a dual mortar formulation. Comput Methods Appl Mech Eng 200(45):3111–3126MathSciNet CrossRef MATH
  31.Krenk S (2009) Non-linear modeling and analysis of solids and structures. Cambridge University Press, CambridgeCrossRef MATH
  32.Küttler U, Wall WA (2009) Vector extrapolation for strong coupling fluid-structure interaction solvers. J Appl Mech 76(2):021205CrossRef
  33.Li Z, Vu-Quoc L (2010) A mixed co-rotational 3D beam element formulation for arbitrarily large rotations. Adv Steel Constr 6(2):767–787
  34.Malcolm DJ, Laird DL (2007) Extraction of equivalent beam properties from blade models. Wind Energy 10(2):135–157CrossRef
  35.Michler C, Van Brummelen E, De Borst R (2005) An interface Newton–Krylov solver for fluid-structure interaction. Int J Numer Methods Fluids 47(10–11):1189–1195CrossRef MATH
  36.Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows: fluid-structure interactions. Int J Numer Methods Fluids 21(10):933–953CrossRef MATH
  37.Muja M, Lowe DG (2014) Scalable nearest neighbor algorithms for high dimensional data. Pattern Anal Mach Intell IEEE Trans 36:2227–2240CrossRef
  38.Palacios RS, Cesnik C (2008) Geometrically nonlinear theory of composite beams with deformable cross sections. AIAA J 46(2):439–450CrossRef
  39.Patil MJ, Hodges DH, S Cesnik CE (2001) Nonlinear aeroelasticity and flight dynamics of high-altitude long-endurance aircraft. J Aircr 38(1):88–94CrossRef
  40.Piperno S, Farhat C (2001) Partitioned procedures for the transient solution of coupled aeroelastic problems-Part II: energy transfer analysis and three-dimensional applications. Comput Methods Appl Mech Eng 190(24):3147–3170CrossRef MATH
  41.Popp A, Seitz A, Gee MW, Wall WA (2013) Improved robustness and consistency of 3D contact algorithms based on a dual mortar approach. Comput Methods Appl Mech Eng 264:67–80MathSciNet CrossRef MATH
  42.Press W, Teukolsky S, Vetterline W, Flannery BP (2007) Numerical recipes 3rd edition: the art of scientific computing. Cambridge University Press, CambridgeMATH
  43.Puso MA (2004) A 3D mortar method for solid mechanics. Int J Numer Methods Eng 59(3):315–336CrossRef MATH
  44.Puso MA, Laursen TA (2004) A mortar segment-to-segment frictional contact method for large deformations. Comput Methods Appl Mech Eng 193(45):4891–4913MathSciNet CrossRef MATH
  45.Sicklinger S (2014) Stabilized co-simulation of coupled problems including fields and signals. Ph.D. thesis, Technische Universität München
  46.Sicklinger S, Lerch C, Wüchner R, Bletzinger KU (2015) Fully coupled co-simulation of a wind turbine emergency brake maneuver. J Wind Eng Ind Aerodyn 144:134–145CrossRef
  47.Smith MJ, Cesnik CE, Hodges DH (2000) Evaluation of some data transfer algorithms for noncontiguous meshes. J Aerosp Eng 13(2):52–58CrossRef
  48.Streiner S (2011) Beitrag zur numerischen Simulation der Aerodynamik und Aeroelastik großer Windkraftanlagen mit horizontaler Achse. Verlag Dr. Hut
  49.Takizawa K, Henicke B, Tezduyar TE, Hsu MC, Bazilevs Y (2011) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48(3):333–344CrossRef MATH
  50.Takizawa K, Spielman T, Tezduyar TE (2011) Space-time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech 48(3):345–364CrossRef MATH
  51.Tezduyar T, 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(3):339–351MathSciNet CrossRef MATH
  52.Tezduyar T, 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(3):353–371MathSciNet CrossRef MATH
  53.Tezduyar T, Osawa Y (2001) Fluid-structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191(6):717–726CrossRef MATH
  54.Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Academic Press, San DiegoMATH
  55.Tezduyar TE, Sathe S (2004) Enhanced-discretization space-time technique (EDSTT). Comput Methods Appl Mech Eng 193(15):1385–1401MathSciNet CrossRef MATH
  56.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(17):2002–2027MathSciNet CrossRef MATH
  57.Tezduyar TE, Sathe S, Schwaab M, Pausewang J, Christopher J, Crabtree J (2008) Fluid-structure interaction modeling of ringsail parachutes. Comput Mech 43(1):133–142CrossRef MATH
  58.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(41):5743–5753MathSciNet CrossRef MATH
  59.Unger R, Haupt MC, Horst P (2007) Application of lagrange multipliers for coupled problems in fluid and structural interactions. Comput Struct 85(11):796–809MathSciNet CrossRef
  60.Varello A, Demasi L, Carrera E, Giunta G (2010) An improved beam formulation for aeroelastic applications. In: Proceedings of the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, pp 12–15
  61.Wohlmuth BI (2000) A mortar finite element method using dual spaces for the lagrange multiplier. SIAM J Numer Anal 38(3):989–1012MathSciNet CrossRef MATH
  62.Wüchner R, Kupzok A, Bletzinger KU (2007) A framework for stabilized partitioned analysis of thin membrane-wind interaction. Int J Numer Methods Fluids 54(6–8):945–963MathSciNet CrossRef MATH
  63.Wunderlich W, Kiener G (2004) Statik der Stabtragwerke. Vieweg+Teubner Verlag, BerlinCrossRef
  
• 作者单位：Tianyang Wang (1)
  Roland Wüchner (1)
  Stefan Sicklinger (1)
  Kai-Uwe Bletzinger (1)
  
  1. Chair of Structural Analysis, Technische Universität München, Arcisstr. 21, 80333, München, Germany
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

This paper investigates data mapping between non-matching meshes and geometries in fluid-structure interaction. Mapping algorithms for surface meshes including nearest element interpolation, the standard mortar method and the dual mortar method are studied and comparatively assessed. The inconsistency problem of mortar methods at curved edges of fluid-structure-interfaces is solved by a newly developed enforcing consistency approach, which is robust enough to handle even the case that fluid boundary facets are totally not in contact with structure boundary elements due to high fluid refinement. Besides, tests with representative geometries show that the mortar methods are suitable for conservative mapping but it is better to use the nearest element interpolation in a direct way, and moreover, the dual mortar method can give slight oscillations. This work also develops a co-rotating mapping algorithm for 1D beam elements. Its novelty lies in the ability of handling large displacements and rotations.