×

zbMATH — the first resource for mathematics

A smoothed particle element method (SPEM) for modeling fluid-structure interaction problems with large fluid deformations. (English) Zbl 1441.76097
Summary: Fluid-structure interaction (FSI) problems with large fluid deformations can be a great challenge for numerical simulations using conventional methods. In this paper, we propose a novel hybrid approach of an improved Smoothed Particle hydrodynamics and smoothed finite Element Method (SPEM) for modeling FSI problems. In SPEM, the edge-based smoothed finite element method (S-FEM) is developed in Lagrangian frame and is used for the first time to model both elastic structures and incompressible flows. For fluid regions with large deformations, the associated finite elements are adaptively converted into particles and the corresponding regions are subsequently modeled using the decoupled finite particle method (DFPM), which is an improved smoothed particle hydrodynamics (SPH) method suitable for modeling incompressible flows with free surfaces. A ghost particle-based interface algorithm to couple existing S-FEM elements and DFPM particles is developed in SPEM to implement the modeling of FSI problems. As the smoothed FEM and decoupled FPM are enhanced FEM and SPH respectively and DFPM is only used for local fluid regions with large deformations, it is expected that SPEM is more accurate and more efficient than the existing coupling approaches of conventional FEM and SPH. Five numerical examples are tested using the proposed SPEM and the comparative studies with results from other sources reveal that SPEM is an effective approach for modeling FSI problems with large fluid deformations.

MSC:
76M28 Particle methods and lattice-gas methods
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Bxx Incompressible inviscid fluids
76Dxx Incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dowell, E. H.; Hall, K. C., Modeling of fluid – structure interaction, Annu. Rev. Fluid Mech., 33, 445-490 (2001)
[2] Hou, G.; Wang, J.; Layton, A., Numerical methods for fluid – structure interaction – a review, Commun. Comput. Phys., 12, 337-377 (2012)
[3] Fadlun, E. A.; Verzicco, R.; Orlandi, P.; Mohd-Yusof, J., Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations, J. Comput. Phys., 161, 35-60 (2000)
[4] Cho, J. R.; Lee, H. W., Numerical study on liquid sloshing in baffled tank by nonlinear finite element method, Comput. Methods Appl. Mech. Engrg., 193, 2581-2598 (2004)
[5] Kim, J.; Kim, D.; Choi, H., An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171, 132-150 (2001)
[6] Hirt, C. W.; Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201-225 (1981)
[7] Peng, D. P.; Merriman, B.; Osher, S.; Zhao, H.; Kang, M., A PDE-based fast local level set method, J. Comput. Phys., 155, 410-438 (1999)
[8] Idelsohn, S. R.; Oñate, E.; Pin, F. D., The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Internat. J. Numer. Methods Engrg., 61, 964-989 (2004)
[9] Franci, A.; Cremonesi, M., On the effect of standard PFEM remeshing on volume conservation in free-surface fluid flow problems, Comput. Part. Mech., 4, 331-343 (2017)
[10] Liu, G. R.; Gu, Y. T., An Introduction to Meshfree Methods and their Programming (2005), Springer
[11] Violeau, D.; Rogers, B. D., Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future, J. Hydraul. Res., 254, 1-26 (2016)
[12] Li, S. F.; Liu, W. K., Meshfree and particle methods and their applications, Appl. Mech. Rev., 55, 1-34 (2002)
[13] 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)
[14] Koshizuka, S.; Oka, Y., Moving-particle semi-implicit method for fragmentation of incompressible fluid, Nucl. Sci. Eng., 123, 421-434 (1996)
[15] Koshizuka, S., A particle method for incompressible viscous flow with fluid fragmentation, Comput. Fluid Dyn. J., 4, 29-46 (1995)
[16] Vacondio, R.; Rogers, B. D.; Stansby, P. K.; Mignosa, P.; Feldman, J., Variable resolution for SPH: A dynamic particle coalescing and splitting scheme, Comput. Methods Appl. Mech. Engrg., 256, 132-148 (2013)
[17] Hu, X. Y.; Adams, N. A., A constant-density approach for incompressible multi-phase SPH, J. Comput. Phys., 228, 2082-2091 (2009)
[18] Wang, P. P.; Zhang, A. M.; Ming, F. R.; Sun, P. N.; Cheng, H., A novel non-reflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics, J. Fluid Mech., 860, 81-114 (2019)
[19] Vuyst, T. D.; Vignjevic, R.; Campbell, J. C., Coupling between meshless and finite element methods, Int. J. Impact Eng., 31, 1054-1064 (2005)
[20] Fourey, G.; Oger, G.; Touzé, D.; Alessandrini, B., Violent fluid – structure interaction simulations using a coupled SPH/fem method, (IOP Conference Series: Materials Science and Engineering (2010), IOP Publishing), 012041
[21] Hu, D.; Long, T.; Xiao, Y.; Han, X.; Gu, Y., Fluid – structure interaction analysis by coupled FE-SPH model based on a novel searching algorithm, Comput. Methods Appl. Mech. Engrg., 276, 266-286 (2014)
[22] Groenenboom, P. H.L.; Cartwright, B. K., Hydrodynamics and fluid – structure interaction by coupled SPH-FE method, J. Hydraul. Res., 48, 61-73 (2009)
[23] Attaway, S. W.; Heinstein, M. W.; Swegle, J. W., Coupling of smooth particle hydrodynamics with the finite element method, Nucl. Eng. Des., 150, 199-205 (1994)
[24] Yang, Q.; Jones, V.; Mccue, L., Free-surface flow interactions with deformable structures using an SPH-FEM model, Ocean Eng., 55, 136-147 (2012)
[25] Long, T.; Hu, D.; Wan, D.; Zhuang, C.; Yang, G., An arbitrary boundary with ghost particles incorporated in coupled FEM-SPH model for FSI problems, J. Comput. Phys., 350, 166-183 (2017)
[26] Ogino, M.; Iwama, T.; Asai, M., Development of a partitioned coupling analysis system for fluid – structure interactions using an in-house ISPH code and the adventure system, Int. J. Comput. Methods, Article 1843009 pp. (2018)
[27] Chen, J. S.; Wu, C. T.; Yoon, S.; You, Y., A stabilized conforming nodal integration for Galerkin mesh-free methods, Int. J. Numer. Methods Eng., 50, 2001, 435-466 (2010)
[28] Liu, G. R.; Dai, K. Y.; Nguyen, T. T., A smoothed finite element method for mechanics problems, Comput. Mech., 39, 859-877 (2007)
[29] Liu, G. R.; Nguyen, T. T.; Dai, K. Y.; Lam, K. Y., Theoretical aspects of the smoothed finite element method (SFEM), Internat. J. Numer. Methods Engrg., 71, 902-930 (2007)
[30] Phung-Van, P.; Nguyen-Thoi, T.; Luong-Van, H.; Thai-Hoang, C.; Nguyen-Xuan, H., A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise deformation theory for dynamic response of composite plates resting on viscoelastic foundation, Comput. Methods Appl. Mech. Engrg., 272, 138-159 (2014)
[31] Liu, G. R.; Nguyen-Thoi, T.; Lam, K. Y., An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids, J. Sound Vib., 320, 1100-1130 (2009)
[32] Nguyen-Xuan, H.; Liu, G. R.; Bordas, S.; Natarajan, S.; Rabczuk, T., An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order, Comput. Methods Appl. Mech. Engrg., 253, 252-273 (2013)
[33] Nguyen-Thoi, T.; Liu, G. R.; Lam, K. Y.; Zhang, G. Y., A face-based smoothed finite element method (fs-fem) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements, Internat. J. Numer. Methods Engrg., 78, 324-353 (2009)
[34] Liu, M. B.; Xie, W. P.; Liu, G. R., Modeling incompressible flows using a finite particle method, Appl. Math. Model., 29, 1252-1270 (2005)
[35] Liu, M. B.; Liu, G. R., Smoothed particle hydrodynamics (SPH): an overview and recent developments, Arch. Comput. Methods Eng., 17, 25-76 (2010)
[36] Asprone, D.; Auricchio, F.; Reali, A., Novel finite particle formulations based on projection methodologies, Internat. J. Numer. Methods Fluids, 65, 1376-1388 (2011)
[37] Asprone, D.; Auricchio, F.; Montanino, A.; Reali, A., A modified finite particle method: Multi-dimensional elasto-statics and dynamics, Int. J. Numer. Methods Eng., 99, 2014, 1-25 (2010)
[38] Huang, C.; Zhang, D. H.; Si, Y. L.; Shi, Y. X.; Lin, Y. G., Coupled finite particle method for simulations of wave and structure interaction, Coastal Eng., 140, 147-160 (2018)
[39] Zhang, Z. L.; Liu, M. B., A decoupled finite particle method for modeling incompressible flows with free surfaces, Appl. Math. Model., 60, 606-633 (2018)
[40] Zhang, Z. L.; Walayat, K.; Chang, J. Z.; Liu, M. B., Meshfree modeling of a fluid-particle two-phase flow with an improved SPH method, Internat. J. Numer. Methods Engrg., 116, 530-569 (2018)
[41] Long, T.; Huang, C.; Zhang, Z. L.; Hu, D.; Liu, M. B., A Lagrangian finite element method with adaptive element-particle conversion ability for incompressible flows with free surfaces, Appl. Math. Model (2019), submitted for publication
[42] Zhang, Z. Q.; Liu, G. R., Solution bound and nearly exact solution to nonlinear solid mechanics problems based on the smoothed FEM concept, Eng. Anal. Bound. Elem., 42, 99-114 (2014)
[43] Marrone, S.; Colagrossi, A.; Mascio, A. D.; Touzé, D. L., Prediction of energy losses in water impacts using incompressible and weakly compressible models, J. Fluids Struct., 54, 802-822 (2015)
[44] Sun, P.; Colagrossi, A.; Marrone, S.; Zhang, A. M., The \(\delta\) plus-SPH model: Simple procedures for a further improvement of the SPH scheme, Comput. Methods Appl. Mech. Engrg., 315, 25-49 (2017)
[45] Shao, S.; Ji, C.; Graham, D. I.; Reeve, D. E.; James, P. W.; Chadwick, A. J., Simulation of wave overtopping by an incompressible SPH model, Coastal Eng., 53, 723-735 (2006)
[46] Khayyer, A.; Gotoh, H.; Falahaty, H.; Shimizu, Y., An enhanced ISPH-SPH coupled method for simulation of incompressible fluid-elastic structure interactions, Comput. Phys. Comm., 232, 139-164 (2018)
[47] Shadloo, M. S.; Zainali, A.; Sadek, S. H.; Yildiz, M., Improved incompressible smoothed particle hydrodynamics method for simulating flow around bluff bodies, Comput. Methods Appl. Mech. Engrg., 200, 1008-1020 (2011)
[48] Monaghan, J. J., Smoothed particle hydrodynamics and its diverse applications, Annu. Rev. Fluid Mech., 44, 323-346 (2012)
[49] Zhang, Z. L.; Walayat, K.; Huang, C.; Chang, J. Z.; Liu, M. B., A finite particle method with particle shifting technique for modeling particulate flows with thermal convection, Int. J. Heat Mass Transfer, 128, 1245-1262 (2019)
[50] Anderson, J. D., Computational Fluid Dynamics: The Basics with Applications (2002), McGraw Hill: McGraw Hill New York
[51] Xiao, Y.; Han, X.; Hu, D. A., A coupling algorithm of finite element method and smoothed particle hydrodynamics for impact computations, Comput. Mater. Con., 584, 1-26 (2011)
[52] Antoci, C.; Gallati, M.; Sibilla, S., Numerical simulation of fluid – structure interfaction by SPH, Comput. Struct., 85, 879-890 (2007)
[53] Hwang, S. C.; Khayyer, A.; Gotoh, H.; Park, J. C., Development of a fully Lagrangian MPS-based coupled method for simulation of fluid – structure interaction problems, J. Fluids Struct., 50, 497-511 (2014)
[54] Rafiee, A.; Thiagarajan, K. P., An SPH projection method for simulating fluid-hypoelastic structure interaction, Comput. Methods Appl. Mech. Engrg., 198, 2785-2795 (2009)
[55] Morris, J. P.; Fox, P. J.; Zhu, Y., Modeling low reynolds number incompressible flows using SPH, J. Comput. Phys., 136, 214-226 (1997)
[56] Ghia, U.; Ghia, K. N.; Shin, C. T., High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48, 387-411 (1982)
[57] Fourey, G.; Hermange, C.; Letouzé, D.; Oger, G., An efficient FSI coupling strategy between smoothed particle hydrodynamics and finite element methods, Comput. Phys. Comm., 217, 66-81 (2017)
[58] Li, Z.; Leduc, J.; Nunez-Ramirez, J.; Combescure, A.; Marongiu, J. C., A non-intrusive partitioned approach to couple smoothed particle hydrodynamics and finite element methods for transient fluid – structure interaction problems with large interface motion, Comput. Mech., 55, 697-718 (2015)
[59] Scolan, Y. M., Hydroelastic behaviour of a conical shell impacting on a quiescent-free surface of an incompressible liquid, J. Sound Vib., 277, 163-203 (2004)
[60] Zeng, W.; Liu, G. R., Smoothed finite element methods (S-FEM): an overview and recent developments, Arch. Comput. Methods Eng., 25, 1-39 (2016)
[61] He, Z. C.; Liu, G. R.; Zhong, Z. H.; Wu, S. C.; Zhang, G. Y., An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems, Comput. Methods Appl. Mech. Engrg., 199, 20-33 (2009)
[62] 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)
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.