×

zbMATH — the first resource for mathematics

A smoothed particle hydrodynamics-peridynamics coupling strategy for modeling fluid-structure interaction problems. (English) Zbl 07337943
Summary: Fluid-structure interaction (FSI) is a multiphysics problem with diverse application scenarios ranging from the aeroelasticity of aircraft wings and the structural response of marine platforms, to blood circulation through aortic valves. Solving the FSI problems is challenging, predominantly because of the complex time-variant geometry in the fluid-structure interface. To alleviate the difficulties encountered by the grid-based methods in tracking and meshing the fluid-structure interface involving large deformation and structure failures, in this study, we propose a meshfree framework that couples smoothed particle hydrodynamics (SPH) with peridynamics (PD) for the numerical modeling of FSI problems. This SPH-PD framework involves a four-step partitioned coupling procedure, where the key point is utilizing the SPH moving ghost particles as a medium. An original data transfer scheme is developed based on the partnerships built between the SPH moving ghost particles and the PD particles. The structure failures are incorporated in the PD model by adopting a damage law of maximum bond stretch. The SPH-PD method is validated against existing experimental and numerical data. Through the use of this model, we successfully simulate the low-velocity fluid-structure impact and capture the large deformation with local failures.
MSC:
76-XX Fluid mechanics
74-XX Mechanics of deformable solids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kamakoti, R.; Shyy, W., Fluid-structure interaction for aeroelastic applications, Prog. Aerosp. Sci., 40, 535-558 (2004)
[2] Colagrossi, A., A meshless Lagrangian method for free-surface and interface flows with fragmentation, (These (2005), Universita di Roma), 82-84
[3] Marom, G., Numerical methods for fluid-structure interaction models of aortic valves, Arch. Comput. Methods Eng., 22, 595-620 (2014) · Zbl 1348.74099
[4] Rebouillat, S.; Liksonov, D., Fluid-structure interaction in partially filled liquid containers: A comparative review of numerical approaches, Comput. & Fluids, 39, 739-746 (2010) · Zbl 1242.76004
[5] Khor, C. Y.; Abdullah, M. Z.; Lau, C.-S.; Azid, I. A., Recent fluid-structure interaction modeling challenges in IC encapsulation-A review, Microelectron. Reliab., 54, 1511-1526 (2014)
[6] Liew, K. M.; Pan, Z.; Zhang, L.-W., The recent progress of functionally graded CNT reinforced composites and structures, Sci. China Phys. Mech. Astron., 63, Article 234601 pp. (2020)
[7] Hou, G.; Wang, J.; Layton, A., Numerical methods for fluid-structure interaction—a review, Commun. Comput. Phys., 12, 337-377 (2012) · Zbl 1373.76001
[8] Degroote, J., Partitioned simulation of fluid-structure interaction, Arch. Comput. Methods Eng., 20, 185-238 (2013) · Zbl 1354.74066
[9] Farhat, C.; Lesoinne, M.; Le Tallec, P., 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. Engrg., 157, 95-114 (1998) · Zbl 0951.74015
[10] Souli, M.; Ouahsine, A.; Lewin, L., ALE formulation for fluid-structure interaction problems, Comput. Methods Appl. Mech. Engrg., 190, 659-675 (2000) · Zbl 1012.76051
[11] Basting, S.; Quaini, A.; Čanić, S.; Glowinski, R., Extended ALE method for fluid-structure interaction problems with large structural displacements, J. Comput. Phys., 331, 312-336 (2017) · Zbl 1378.74020
[12] Peskin, C. S., The immersed boundary method, Acta Numer., 11, 479-517 (2003) · Zbl 1123.74309
[13] Borazjani, I.; Ge, L.; Sotiropoulos, F., Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies, J. Comput. Phys., 227, 7587-7620 (2008) · Zbl 1213.76129
[14] Kamensky, D.; Hsu, M.-C.; Schillinger, D.; Evans, J. A.; Aggarwal, A.; Bazilevs, Y.; Sacks, M. S.; Hughes, T. J.R., An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves, Comput. Methods Appl. Mech. Engrg., 284, 1005-1053 (2015) · Zbl 1423.74273
[15] Bazilevs, Y.; Hsu, M. C.; Kiendl, J.; Wüchner, R.; Bletzinger, K. U., 3D simulation of wind turbine rotors at full scale. Part II: Fluid-structure interaction modeling with composite blades, Internat. J. Numer. Methods Fluids, 65, 236-253 (2011) · Zbl 1428.76087
[16] Tallec, P. L.; Mouro, J., Fluid structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., 190, 3039-3067 (2001) · Zbl 1001.74040
[17] Wick, T., Coupling fluid-structure interaction with phase-field fracture, J. Comput. Phys., 327, 67-96 (2016) · Zbl 1373.74043
[18] Zheng, C.-J.; Bi, C.-X.; Zhang, C.; Gao, H.-F.; Chen, H.-B., Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver, J. Comput. Phys., 359, 183-198 (2018) · Zbl 1383.74090
[19] Monaghan, J. J., Smoothed particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 543-574 (1992)
[20] Lucy, L. B., Numerical approach to testing the fission hypothesis, Astron. J., 82, 1013-1024 (1977)
[21] Gingold, R. A.; Monaghan, J. J., Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. R. Astron. Soc., 181, 375-389 (1977) · Zbl 0421.76032
[22] Monaghan, J. J., Simulating free surface flows with SPH, J. Comput. Phys., 110, 399-406 (1994) · Zbl 0794.76073
[23] Morris, J. P.; Fox, P. J.; Zhu, Y., Modeling low Reynolds number incompressible flows using SPH, J. Comput. Phys., 136, 214-226 (1997) · Zbl 0889.76066
[24] Meng, Z.-F.; Wang, P.-P.; Zhang, A. M.; Ming, F.-R.; Sun, P.-N., A multiphase SPH model based on Roe’s approximate Riemann solver for hydraulic flows with complex interface, Comput. Methods Appl. Mech. Engrg., 365, Article 112999 pp. (2020) · Zbl 1442.76087
[25] Sun, P.; Ming, F.; Zhang, A., Numerical simulation of interactions between free surface and rigid body using a robust SPH method, Ocean Eng., 98, 32-49 (2015)
[26] Zhang, A.; Sun, P.; Ming, F., An SPH modeling of bubble rising and coalescing in three dimensions, Comput. Methods Appl. Mech. Engrg., 294, 189-209 (2015) · Zbl 1423.76378
[27] Zhang, L. W.; Ademiloye, A. S.; Liew, K. M., Meshfree and particle methods in biomechanics: Prospects and challenges, Arch. Comput. Methods Eng., 26, 1547-1576 (2019)
[28] Gray, J. P.; Monaghan, J. J.; Swift, R. P., SPH elastic dynamics, Comput. Methods Appl. Mech. Engrg., 190, 6641-6662 (2001) · Zbl 1021.74050
[29] Antoci, C.; Gallati, M.; Sibilla, S., Numerical simulation of fluid-structure interaction by SPH, Comput. Struct., 85, 879-890 (2007)
[30] Rafiee, A.; Thiagarajan, K. P., An SPH projection method for simulating fluid-hypoelastic structure interaction, Comput. Methods Appl. Mech. Engrg., 198, 2785-2795 (2009) · Zbl 1228.76117
[31] Liu, M.; Zhang, Z., Smoothed particle hydrodynamics (SPH) for modeling fluid-structure interactions, Sci. China Phys. Mech. Astron., 62, Article 984701 pp. (2019)
[32] Silling, S. A., Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids, 48, 175-209 (2000) · Zbl 0970.74030
[33] Silling, S. A.; Askari, E., A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct., 83, 1526-1535 (2005)
[34] Silling, S. A.; Epton, M.; Weckner, O.; Xu, J.; Askari, E., Peridynamic states and constitutive modeling, J. Elast., 88, 151-184 (2007) · Zbl 1120.74003
[35] W. Gerstle, N. Sau, S.A. Silling, Peridynamic modeling of plain and reinforced concrete structures, in: SMiRT18: 18th International Conference on Structural Mechanics in Reactor Technology, Beijing, 2005.
[36] Ghajari, M.; Iannucci, L.; Curtis, P., A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media, Comput. Methods Appl. Mech. Engrg., 276, 431-452 (2014) · Zbl 1423.74882
[37] Oterkus, S.; Madenci, E.; Oterkus, E., Fully coupled poroelastic peridynamic formulation for fluid-filled fractures, Eng. Geol., 225, 19-28 (2017)
[38] Lai, X.; Liu, L.; Li, S.; Zeleke, M.; Liu, Q.; Wang, Z., A non-ordinary state-based peridynamics modeling of fractures in quasi-brittle materials, Int. J. Impact Eng., 111, 130-146 (2018)
[39] Fan, H.; Bergel, G. L.; Li, S., A hybrid peridynamics-SPH simulation of soil fragmentation by blast loads of buried explosive, Int. J. Impact Eng., 87, 14-27 (2016)
[40] Fan, H.; Li, S., A peridynamics-SPH modeling and simulation of blast fragmentation of soil under buried explosive loads, Comput. Methods Appl. Mech. Engrg., 318, 349-381 (2017) · Zbl 1439.74187
[41] Ren, B.; Fan, H.; Bergel, G. L.; Regueiro, R. A.; Lai, X.; Li, S., A peridynamics-SPH coupling approach to simulate soil fragmentation induced by shock waves, Comput. Mech., 55, 287-302 (2014) · Zbl 1398.74395
[42] Ye, T.; Pan, D.; Huang, C.; Liu, M., Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications, Phys. Fluids, 31, Article 011301 pp. (2019)
[43] Sun, P. N.; Colagrossi, A.; Le Touzé, D.; Zhang, A. M., Extension of the \(\delta \)-plus-SPH model for simulating vortex-induced-vibration problems, J. Fluids Struct., 90, 19-42 (2019)
[44] Fu, L.; Han, L.; Hu, X. Y.; Adams, N. A., An isotropic unstructured mesh generation method based on a fluid relaxation analogy, Comput. Methods Appl. Mech. Engrg., 350, 396-431 (2019) · Zbl 1441.65075
[45] Ji, Z.; Fu, L.; Hu, X.; Adams, N., A consistent parallel isotropic unstructured mesh generation method based on multi-phase SPH, Comput. Methods Appl. Mech. Engrg., 363, Article 112881 pp. (2020) · Zbl 1436.65201
[46] Ji, Z.; Fu, L.; Hu, X. Y.; Adams, N. A., A new multi-resolution parallel framework for SPH, Comput. Methods Appl. Mech. Engrg., 346, 1156-1178 (2019) · Zbl 1440.76112
[47] Cheng, H.; Peng, M.; Cheng, Y., The dimension splitting and improved complex variable element-free Galerkin method for 3-dimensional transient heat conduction problems, Internat. J. Numer. Methods Engrg., 114, 321-345 (2018)
[48] Cheng, H.; Peng, M. J.; Cheng, Y. M., Analyzing wave propagation problems with the improved complex variable element-free Galerkin method, Eng. Anal. Bound. Elem., 100, 80-87 (2019) · Zbl 1464.65116
[49] Meng, Z.; Cheng, H.; Ma, L.; Cheng, Y., The hybrid element-free Galerkin method for three-dimensional wave propagation problems, Internat. J. Numer. Methods Engrg., 117, 15-37 (2019)
[50] Martin, J. C.; Moyce, W. J., Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane, Phil. Trans. R. Soc. A, 244, 312-324 (1952)
[51] Ritter, A., Die fortpflanzung der wasserwellen, Z. Vereines Deutsch. Ing., 36, 947-954 (1892)
[52] Ghia, U.; Ghia, K. N.; Shin, C., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48, 387-411 (1982) · Zbl 0511.76031
[53] Wan, D. C.; Patnaik, B. S.V.; Wei, G. W., Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows, J. Comput. Phys., 180, 229-255 (2002) · Zbl 1130.76403
[54] Wan, D. C.; Patnaik, B. S.V.; Wei, G. W., A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution, Numer. Heat Transfer B, 40, 199-228 (2001)
[55] Sun, W.; Xu, Y.; Hu, C.; Liu, X., Effect of film-hole configuration on creep rupture behavior of a second generation nickel-based single crystal superalloys, Mater. Charact., 130, 298-310 (2017)
[56] Zhang, Z. L.; Long, T.; Chang, J. Z.; Liu, M. B., A smoothed particle element method (SPEM) for modeling fluid-structure interaction problems with large fluid deformations, Comput. Methods Appl. Mech. Engrg., 356, 261-293 (2019) · Zbl 1441.76097
[57] Walhorn, E.; Kölke, A.; Hübner, B.; Dinkler, D., Fluid-structure coupling within a monolithic model involving free surface flows, Comput. Struct., 83, 2100-2111 (2005)
[58] Idelsohn, S. R.; Marti, J.; Limache, A.; Oñate, E., Unified Lagrangian formulation for elastic solids and incompressible fluids: application to fluid-structure interaction problems via the PFEM, Comput. Methods Appl. Mech. Engrg., 197, 1762-1776 (2008) · Zbl 1194.74415
[59] Marti, J. M.; Idelsohn, S. R.; Limache, A. C.; Calvo, N. A.; D’elia, J., A fully coupled particle method for quasi incompressible fluid-hypoelastic structure interactions, Mec. Comput., 25, 809-827 (2006)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.