×

Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method. (English) Zbl 1529.76049

Summary: The combined interface boundary condition (CIBC) method has been recently proposed for fluid-structure interaction. The CIBC method employs a Gauss-Seidel-like procedure to transform traditional interface conditions into velocity and traction corrections whose effect is controlled by a dimensional parameter. However, the original CIBC method has to invoke the uncorrected traction when forming the traction correction. This process limits its application to fluid-rigid body interaction. To repair this drawback, a new formulation of the CIBC method has been developed by using a new coupling parameter. The reconstruction is simple and the structural traction is removed completely. Two partitioned subiterative coupling versions of the CIBC method are developed. The first scheme is an implicit strategy while the second one is a semi-implicit strategy. Iterative loops are actualised by the fixed-point algorithm with Aitken accelerator. The obtained results agree with the well-documented data, and some famous flow phenomena have been successfully detected.

MSC:

76G25 General aerodynamics and subsonic flows
Full Text: DOI

References:

[1] Abdullah, M. M.; Walsh, K. K.; Grady, S.; Wesson, G. D., Modeling Flow Around Bluff Bodies, Journal of Computing in Civil Engineering-ASCE, 19, 1, 104-107 (2005)
[2] Ahn, H. T.; Kallinderis, Y., Strongly Coupled Flow/Structure Interactions with a Geometrically Conservative ALE Scheme on General Hybrid Meshes, Journal of Computational Physics, 219, 2, 671-696 (2006) · Zbl 1189.74035
[3] Anagnostopoulos, P., Numerical Investigation of Response and Wake Characteristics of a Vortex-Excited Cylinder in a Uniform Stream, Journal of Fluids and Structures, 8, 4, 367-390 (1994)
[4] Anagnostopoulos, P.; Bearman, P. W., Response Characteristics of a Vortex-Excited Cylinder at Low Reynolds Numbers, Journal of Fluids and Structures, 6, 1, 39-50 (1992)
[5] Anju, A.; Maruoka, A.; Kawahara, M., 2-D Fluid-Structure Interaction Problems by an Arbitrary Lagrangian-Eulerian Finite Element Method, International Journal of Computational Fluid Dynamics, 8, 1, 1-9 (1997) · Zbl 0895.76041
[6] Badia, S.; Codina, R., On Some Fluid-Structure Iterative Algorithms Using Pressure Segregation Methods. Application to Aeroelasticity, International Journal for Numerical Methods in Engineering, 72, 1, 46-71 (2007) · Zbl 1194.74361
[7] Badia, S.; Nobile, F.; Vergara, C., Fluid-Structure Partitioned Procedures Based on Robin Transmission Conditions, Journal of Computational Physics, 227, 14, 7027-7051 (2008) · Zbl 1140.74010
[8] Bahmani, M. H.; Akbari, M. H., Effects of Mass and Damping Ratios on VIV of a Circular Cylinder, Ocean Engineering, 37, 5-6, 511-519 (2010)
[9] Barrero-Gil, A.; Sanz-Andres, A.; Roura, M., Transverse Galloping at Low Reynolds Numbers, Journal of Fluids and Structures, 25, 7, 1236-1242 (2009)
[10] Bearman, P. W., Vortex Shedding from Oscillating Bluff Bodies, Annual Review of Fluid Mechanics, 16, 1, 195-222 (1984) · Zbl 0605.76045
[11] Blevins, R. D., Flow-Induced Vibration (1990), New York: Van Nostrand Reinhold, New York
[12] Blom, F. J., A Monolithical Fluid-Structure Interaction Algorithm Applied to the Piston Problem, Computer Methods in Applied Mechanics and Engineering, 167, 3-4, 369-391 (1998) · Zbl 0948.76046
[13] Breuer, M.; De Nayer, G.; Münsch, M.; Gallinger, T.; Wüchner, R., Fluid-Structure Interaction Using a Partitioned Semi-implicit Predictor-Corrector Coupling Scheme for the Application of Large-Eddy Simulation, Journal of Fluids and Structures, 29, 107-130 (2012)
[14] Causin, P.; Gerbeau, J. F.; Nobile, F., Added-Mass Effect in the Design of Partitioned Algorithms for Fluid-Structure Problems, Computer Methods in Applied Mechanics and Engineering, 194, 42-44, 4506-4527 (2005) · Zbl 1101.74027
[17] Chen, X. Y.; Zha, G. C., Fully Coupled Fluid-Structural Interactions Using an Efficient High Resolution Upwind Scheme, Journal of Fluids and Structures, 20, 8, 1105-1125 (2005)
[18] Chorin, A. J., Numerical Solution of the Navier-Stokes Equations, Mathematics of Computation, 22, 104, 745-762 (1968) · Zbl 0198.50103
[19] Codina, R.; Vázquez, M.; Zienkiewicz, O. C., A General Algorithm for Compressible and Incompressible Flows. Part III: The Semi-implicit Form, International Journal for Numerical Methods in Fluids, 27, 1-4, 13-32 (1998) · Zbl 0914.76050
[20] Degroote, J.; Haelterman, R.; Annerel, S.; Bruggeman, P.; Vierendeels, J., Performance of Partitioned Procedures in Fluid-Structure Interaction, Computers and Structures, 88, 7-8, 446-457 (2010)
[21] Dettmer, W.; Perić, D., A Computational Framework for Fluid-Rigid Body Interaction: Finite Element Formulation and Applications, Computer Methods in Applied Mechanics and Engineering, 195, 13-16, 1633-1666 (2006) · Zbl 1123.76029
[22] Donea, J.; Huerta, A.; Ponthot, J. -P.; Rodriguez-Ferran, A.; Stein, Erwin; de Borst, René; Hughes, Thomas J. R., Chapter 14: Arbitrary Lagrangian-Eulerian Methods, Encyclopedia of Computational Mechanics, 413-438 (2004), Chichester: Wiley, Chichester
[23] Farhat, C.; Lesoinne, M., Two Efficient Staggered Algorithms for the Serial and Parallel Solution of Three-Dimensional Nonlinear Transient Aeroelastic Problems, Computer Methods in Applied Mechanics and Engineering, 182, 3-4, 499-515 (2000) · Zbl 0991.74069
[24] Farhat, C.; Lesoinne, M.; Maman, N., Mixed Explicit/Implicit Time Integration of Coupled Aeroelastic Problems: Three-Field Formulation, Geometric Conservation and Distributed Solution, International Journal for Numerical Methods in Fluids, 21, 10, 807-835 (1995) · Zbl 0865.76038
[25] Felippa, C. A.; Park, K. C.; Farhat, C., Partitioned Analysis of Coupled Mechanical Systems, Computer Methods in Applied Mechanics and Engineering, 190, 24-25, 3247-3270 (2001) · Zbl 0985.76075
[26] Feng, X., Analysis of Finite Element Methods and Domain Decomposition Algorithms for a Fluid-Solid Interaction Problem, SIAM Journal on Numerical Analysis, 38, 4, 1312-1336 (2000) · Zbl 0984.76046
[27] Feng, X.; Lee, P.; Wei, Y., Formulation and Mathematical Analysis of a Fluid-Solid Interaction Problem, Technical Report (1997), Minneapolis, MN: Institute of Mathematics and Application, University of Minnesota, Minneapolis, MN
[28] Fernández, M. A.; Gerbeau, J. F.; Grandmont, C., A Projection Semi-implicit Scheme for the Coupling of an Elastic Structure with an Incompressible Fluid, International Journal for Numerical Methods in Engineering, 69, 4, 794-821 (2007) · Zbl 1194.74393
[29] Förster, C.; Wall, W. A.; Ramm, E., Artificial Added Mass Instabilities in Sequential Staggered Coupling of Nonlinear Structures and Incompressible Viscous Flows, Computer Methods in Applied Mechanics and Engineering, 196, 7, 1278-1293 (2007) · Zbl 1173.74418
[30] Govardhan, R.; Williamson, C. H. K., Modes of Vortex Formation and Frequency Response of a Freely Vibrating Cylinder, Journal of Fluid Mechanics, 420, 85-130 (2000) · Zbl 0988.76027
[31] He, T.; Zhou, D.; Bao, Y., Combined Interface Boundary Condition Method for Fluid-Rigid Body Interaction, Computer Methods in Applied Mechanics and Engineering, 223-224, 81-102 (2012) · Zbl 1253.74034
[32] Hou, G.; Wang, J.; Layton, A., Numerical Methods for Fluid-Structure Interaction: A Review, Communications in Computational Physics, 12, 2, 337-377 (2012) · Zbl 1373.76001
[33] Jaiman, R. K., Advances in ALE Based Fluid-Structure Interaction Modeling for Offshore Engineering Applications, Paper presented at the Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) (2012), Vienna
[34] Jaiman, R.; Geubelle, P.; Loth, E.; Jiao, X., Combined Interface Boundary Condition Method for Unsteady Fluid-Structure Interaction, Computer Methods in Applied Mechanics and Engineering, 200, 1-4, 27-39 (2011) · Zbl 1225.74091
[35] Jaiman, R.; Geubelle, P.; Loth, E.; Jiao, X., Transient Fluid-Structure Interaction with Non-matching Spatial and Temporal Discretizations, Computers & Fluids, 50, 1, 120-135 (2011) · Zbl 1271.76242
[37] Jaiman, R. K.; Jiao, X.; Geubelle, P. H.; Loth, E., Conservative Load Transfer Along Curved Fluid-Solid Interface with Non-matching Meshes, Journal of Computational Physics, 218, 1, 372-397 (2006) · Zbl 1158.76405
[39] Jan, Y. J.; Sheu, T. W. H., Finite Element Analysis of Vortex Shedding Oscillations from Cylinders in the Straight Channel, Computational Mechanics, 33, 2, 81-94 (2004) · Zbl 1067.76569
[40] Joly, A.; Etienne, S.; Pelletier, D., Galloping of Square Cylinders in Cross-Flow at Low Reynolds Numbers, Journal of Fluids and Structures, 28, 232-243 (2012)
[41] Küttler, U.; Wall, W., Fixed-Point Fluid-Structure Interaction Solvers with Dynamic Relaxation, Computational Mechanics, 43, 1, 61-72 (2008) · Zbl 1236.74284
[42] Le Tallec, P.; Mouro, J., Fluid Structure Interaction with Large Structural Displacements, Computer Methods in Applied Mechanics and Engineering, 190, 24-25, 3039-3067 (2001) · Zbl 1001.74040
[43] Lefrançois, E., A Simple Mesh Deformation Technique for Fluid-Structure Interaction Based on a Submesh Approach, International Journal for Numerical Methods in Engineering, 75, 9, 1085-1101 (2008) · Zbl 1195.74185
[44] Lesoinne, M.; Farhat, C., Geometric Conservation Laws for Flow Problems with Moving Boundaries and Deformable Meshes, and Their Impact on Aeroelastic Computations, Computer Methods in Applied Mechanics and Engineering, 134, 1-2, 71-90 (1996) · Zbl 0896.76044
[45] Li, L.; Sherwin, S. J.; Bearman, P. W., A Moving Frame of Reference Algorithm for Fluid/Structure Interaction of Rotating and Translating Bodies, International Journal for Numerical Methods in Fluids, 38, 2, 187-206 (2002) · Zbl 1009.76055
[46] Liang, C.; DeJong, A. S., Massively Parallel Spectral Difference Solver for Simulating Vortex-Induced Vibrations of Circular Cylinders, Proceedings of ASME 2012 International Mechanical Engineering Congress and Exposition (2012), Houston, TX
[47] Liu, X. Q.; Qin, N.; Xia, H., Fast Dynamic Grid Deformation Based on Delaunay Graph Mapping, Journal of Computational Physics, 211, 2, 405-423 (2006) · Zbl 1138.76405
[48] Markou, G. A.; Mouroutis, Z. S.; Charmpis, D. C.; Papadrakakis, M., The Ortho-semi-torsional (OST) Spring Analogy Method for 3D Mesh Moving Boundary Problems, Computer Methods in Applied Mechanics and Engineering, 196, 4-6, 747-765 (2007) · Zbl 1121.74482
[49] Matsumoto, M.; Daito, Y.; Yoshizumi, F.; Ichikawa, Y.; Yabutani, T., Torsional Flutter of Bluff Bodies, Journal of Wind Engineering and Industrial Aerodynamics, 69-71, 871-882 (1997)
[50] Murea, C. M.; Sy, S., A Fast Method for Solving Fluid-Structure Interaction Problems Numerically, International Journal for Numerical Methods in Fluids, 60, 10, 1149-1172 (2009) · Zbl 1419.74114
[51] Nagaoka, S.; Nakabayashi, Y.; Yagawa, G.; Kim, Y., Accurate Fluid-Structure Interaction Computations Using Elements Without Mid-side Nodes, Computational Mechanics, 48, 3, 269-276 (2011) · Zbl 1398.76119
[52] Nithiarasu, P., A Matrix Free Fractional Step Method for Static and Dynamic Incompressible Solid Mechanics, International Journal for Computational Methods in Engineering Science and Mechanics, 7, 5, 369-380 (2006) · Zbl 1431.74105
[53] Nithiarasu, P.; Zienkiewicz, O. C., On stabilization of the CBS Algorithm: Internal and External Time Steps, International Journal for Numerical Methods in Engineering, 48, 6, 875-880 (2000) · Zbl 0986.76046
[54] Nomura, T., ALE Finite Element Computations of Fluid-Structure Interaction Problems, Computer Methods in Applied Mechanics and Engineering, 112, 1-4, 291-308 (1994) · Zbl 0845.76049
[55] Nomura, T.; Hughes, T. J. R., An Arbitrary Lagrangian-Eulerian Finite Element Method for Interaction of Fluid and a Rigid Body, Computer Methods in Applied Mechanics and Engineering, 95, 1, 115-138 (1992) · Zbl 0756.76047
[57] Parkinson, G. V.; Smith, J. D., The Square Prism as an Aeroelastic Non-linear Oscillator, The Quarterly Journal of Mechanics and Applied Mathematics, 17, 2, 225-239 (1964) · Zbl 0133.19102
[58] Piperno, S., Explicit/Implicit Fluid/Structure Staggered Procedures with a Structural Predictor and Fluid Subcycling for 2D Inviscid Aeroelastic Simulations, International Journal for Numerical Methods in Fluids, 25, 10, 1207-1226 (1997) · Zbl 0910.76065
[59] Prasanth, T. K.; Mittal, S., Vortex-Induced Vibrations of a Circular Cylinder at Low Reynolds Numbers, Journal of Fluid Mechanics, 594, 463-491 (2008) · Zbl 1159.76316
[60] Robertson, I.; Li, L.; Sherwin, S. J.; Bearman, P. W., A Numerical Study of Rotational and Transverse Galloping Rectangular Bodies, Journal of Fluids and Structures, 17, 5, 681-699 (2003)
[61] Roe, B.; Jaiman, R.; Haselbacher, A.; Geubelle, P. H., Combined Interface Boundary Condition Method for Coupled Thermal Simulations, International Journal for Numerical Methods in Fluids, 57, 3, 329-354 (2008) · Zbl 1241.80009
[62] Roshko, A., On the Development of Turbulent Wakes from Vortex Streets, Technical Report, NACA TN 1191 (1954), National Advisory Committee for Aeronautics
[63] Rossi, R.; Oñate, E., Analysis of Some Partitioned Algorithms for Fluid-Structure Interaction, Engineering Computations, 27, 1, 20-56 (2010) · Zbl 1284.74143
[64] Sarpkaya, T., A Critical Review of the Intrinsic Nature of Vortex-Induced Vibrations, Journal of Fluids and Structures, 19, 4, 389-447 (2004)
[65] Schulz, K. W.; Kallinderis, Y., Unsteady Flow Structure Interaction for Incompressible Flows Using Deformable Hybrid Grids, Journal of Computational Physics, 143, 2, 569-597 (1998) · Zbl 0935.76052
[66] Sen, S.; Mittal, S., Free Vibration of a Square Cylinder at Low Reynolds Numbers, Journal of Fluids and Structures, 27, 5-6, 875-884 (2011)
[67] Sen, S.; Mittal, S.; Biswas, G., Flow Past a Square Cylinder at Low Reynolds Numbers, International Journal for Numerical Methods in Fluids, 67, 9, 1160-1174 (2011) · Zbl 1426.76303
[68] Shen, Y. Q.; Zha, G. C.; Chen, X. Y., High Order Conservative Differencing for Viscous Terms and the Application to Vortex-Induced Vibration Flows, Journal of Computational Physics, 228, 22, 8283-8300 (2009) · Zbl 1422.76138
[69] Sy, S.; Murea, C. M., A Stable Time Advancing Scheme for Solving Fluid-Structure Interaction Problem at Small Structural Displacements, Computer Methods in Applied Mechanics and Engineering, 198, 2, 210-222 (2008) · Zbl 1194.74475
[70] Témam, R., A method to approximate the solutions of Navier-Stokes equations, Bulletin de la Societe Mathematique de France, 96, 115-152 (1968) · Zbl 0181.18903
[71] van Brummelen, E. H., Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction, Journal of Applied Mechanics-ASME, 76, 2, 1-7 (2009)
[74] Wei, R.; Sekine, A.; Shimura, M., Numerical Analysis of 2D Vortex-Induced Oscillations of a Circular Cylinder, International Journal for Numerical Methods in Fluids, 21, 10, 993-1005 (1995) · Zbl 0862.76040
[75] Williamson, C. H. K.; Govardhan, R., Vortex-Induced Vibrations, Annual Review of Fluid Mechanics, 36, 1, 413-455 (2004) · Zbl 1125.74323
[76] Williamson, C. H. K.; Roshko, A., Vortex Formation in the Wake of an Oscillating Cylinder, Journal of Fluids and Structures, 2, 4, 355-381 (1988)
[77] Yang, F. L.; Chen, C. H.; Young, D. L., A Novel Mesh Regeneration Algorithm for 2D FEM Simulations of Flows with Moving Boundary, Journal of Computational Physics, 230, 9, 3276-3301 (2011) · Zbl 1316.76053
[78] Yang, J.; Preidikman, S.; Balaras, E., A Strongly Coupled, Embedded-Boundary Method for Fluid-Structure Interactions of Elastically Mounted Rigid Bodies, Journal of Fluids and Structures, 24, 2, 167-182 (2008)
[79] Zeng, D. H.; Ethier, C. R., A Semi-torsional Spring Analogy Model for Updating Unstructured Meshes in 3D Moving Domains, Finite Elements in Analysis and Design, 41, 11-12, 1118-1139 (2005)
[80] Zienkiewicz, O. C.; Codina, R., A General Algorithm for Compressible and Incompressible Flow. Part I: The Split, Characteristic-Based Scheme, International Journal for Numerical Methods in Fluids, 20, 8-9, 869-885 (1995) · Zbl 0837.76043
[81] Zienkiewicz, O. C.; Morgan, K.; Sai, B. V. K. S.; Codina, R.; Vasquez, M., A General Algorithm for Compressible and Incompressible Flow. Part II: Tests on the Explicit Form, International Journal for Numerical Methods in Fluids, 20, 8-9, 887-913 (1995) · Zbl 0837.76044
[82] Zienkiewicz, O. C.; Nithiarasu, P.; Codina, R.; Vázquez, M.; Ortiz, P., The Characteristic-Based-Split Procedure: An Efficient and Accurate Algorithm for Fluid Problems, International Journal for Numerical Methods in Fluids, 31, 1, 359-392 (1999) · Zbl 0985.76069
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.