An explicit MPS/FEM coupling algorithm for three-dimensional fluid-structure interaction analysis

Abstract Currently, accurate simulations of fluid structure interaction (FSI) problems still remain a challenging task in the academic community. The purpose of this work is to develop a three-dimensional (3D) coupling algorithm to achieve the end, where the explicit moving particle simulation method (MPS) and the finite element method (FEM) are respectively employed to account for fluid flows and structural deformation. The developed coupling algorithm inherits the advantages of the aforementioned methods, while also addressing their shortcomings. We start by extending a newly proposed ghost cell boundary (GCB) model, which has proved to be an effective method to deal with the wall boundary of complicated shapes, to three dimensions. For the problems of interest, the finite elements for structural discretization serve as ghost cells for interaction force calculation, thereby providing an easy and natural way for the construction of ghost cells. The interactions between fluids and structures are dealt with using an integral version of the MPS model, and the resultant interaction forces calculated at integration points of a cell are distributed to finite element nodes for the update of nodal kinematics in the context of an explicit time integration scheme. The effectiveness and accuracy of the 3D GCB model are validated via two numerical examples, i.e., the dam break test and the water flow in a rotating gear test. Afterwards, the developed coupling algorithm is applied to two common FSI problems, i.e., the dam break tests with respective an elastic obstacle and an elastic gate. The good agreements between our simulation results and the existing data in literature demonstrate the accuracy and capacity of the developed coupling algorithm in solving FSI problems.

[1]  David Le Touzé,et al.  An efficient FSI coupling strategy between Smoothed Particle Hydrodynamics and Finite Element methods , 2017, Comput. Phys. Commun..

[2]  K. Szewc,et al.  Analysis of the incompressibility constraint in the smoothed particle hydrodynamics method , 2011, 1110.5752.

[3]  P. Tallec,et al.  Fluid structure interaction with large structural displacements , 2001 .

[4]  Koulis Pericleous,et al.  Dynamic fluid–structure interaction using finite volume unstructured mesh procedures , 2002 .

[5]  U. Perego,et al.  An explicit Lagrangian approach for 3D simulation of fluid-structure-interaction problems , 2018 .

[6]  D. Wan,et al.  Numerical simulation of the solitary wave interacting with an elastic structure using MPS-FEM coupled method , 2017 .

[7]  E. Oñate,et al.  Possibilities of the particle finite element method for fluid–soil–structure interaction problems , 2011 .

[8]  Bernd Simeon,et al.  A finite volume method on NURBS geometries and its application in isogeometric fluid-structure interaction , 2012, Math. Comput. Simul..

[9]  M. Souli,et al.  ALE formulation for fluid–structure interaction problems , 2000 .

[10]  Jianren Fan,et al.  Numerical simulation of two-phase non-Newtonian blood flow with fluid-structure interaction in aortic dissection , 2019, Computer methods in biomechanics and biomedical engineering.

[11]  Tiangang Zhang,et al.  Enhancement of stabilization of MPS to arbitrary geometries with a generic wall boundary condition , 2019, Computers & Fluids.

[12]  S. Koshizuka.  A particle method for incompressible viscous flow with fluid fragmentation , 1995 .

[13]  C. Antoci,et al.  Numerical simulation of fluid-structure interaction by SPH , 2007 .

[14]  Eugenio Oñate,et al.  Unified Lagrangian formulation for elastic solids and incompressible fluids: Application to fluid–structure interaction problems via the PFEM , 2008 .

[15]  Paul W. Cleary,et al.  Three‐dimensional wave impact on a rigid structure using smoothed particle hydrodynamics , 2012 .

[16]  A. Zhang,et al.  Study of a complex fluid-structure dam-breaking benchmark problem using a multi-phase SPH method with APR , 2019, Engineering Analysis with Boundary Elements.

[17]  Xiangyu Hu,et al.  SPH modeling of fluid-structure interaction , 2018 .

[18]  Zhijun Shen,et al.  Surface treatment technique of MPS method for free surface flows , 2019, Engineering Analysis with Boundary Elements.

[19]  S. Yoshimura,et al.  Explicitly represented polygon wall boundary model for the explicit MPS method , 2015, CPM 2015.

[20]  Victor Oancea,et al.  A partitioned fully explicit Lagrangian finite element method for highly nonlinear fluid‐structure interaction problems , 2018 .

[21]  R. Mittal,et al.  Interface tracking finite volume method for complex solid-fluid interactions on fixed meshes , 2001 .

[22]  Tiangang Zhang,et al.  Improvement of pressure distribution to arbitrary geometry with boundary condition represented by polygons in particle method , 2017 .

[23]  Bertrand Alessandrini,et al.  Violent Fluid-Structure Interaction simulations using a coupled SPH/FEM method , 2010 .

[24]  Joe J. Monaghan,et al.  SPH particle boundary forces for arbitrary boundaries , 2009, Comput. Phys. Commun..

[25]  Shinobu Yoshimura,et al.  A novel ghost cell boundary model for the explicit moving particle simulation method in two dimensions , 2020 .

[26]  R. Courant,et al.  On the Partial Difference Equations, of Mathematical Physics , 2015 .

[27]  Kohei Murotani,et al.  MPS–FEM PARTITIONED COUPLING APPROACH FOR FLUID–STRUCTURE INTERACTION WITH FREE SURFACE FLOW , 2014 .

[28]  Changhong Hu,et al.  A coupled FDM–FEM method for free surface flow interaction with thin elastic plate , 2013 .

[29]  P. Groenenboom,et al.  Hydrodynamics and fluid-structure interaction by coupled SPH-FE method , 2010 .

[30]  A. Korobenko,et al.  FSI Simulation of two back-to-back wind turbines in atmospheric boundary layer flow , 2017 .

[31]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[32]  Murat Özbulut,et al.  A numerical investigation into the correction algorithms for SPH method in modeling violent free surface flows , 2014 .

[33]  Bin Chen,et al.  An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models , 2018, International Journal for Numerical Methods in Engineering.

[34]  S. Koshizuka,et al.  Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid , 1996 .

[35]  Hitoshi Gotoh,et al.  Development of a fully Lagrangian MPS-based coupled method for simulation of fluid-structure interaction problems , 2014 .

[36]  C. Farhat,et al.  Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems , 2000 .

[37]  Wenyang Duan,et al.  Two-dimensional numerical simulation of an elastic wedge water entry by a coupled FDM-FEM method , 2013 .

[38]  Gang Yang,et al.  An arbitrary boundary with ghost particles incorporated in coupled FEM-SPH model for FSI problems , 2017, J. Comput. Phys..

[39]  E. Oñate,et al.  Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM , 2008 .

[40]  Hitoshi Gotoh,et al.  An enhanced ISPH-SPH coupled method for simulation of incompressible fluid-elastic structure interactions , 2018, Comput. Phys. Commun..

[41]  Shinobu Yoshimura,et al.  Parallel analysis system for free-surface flow using MPS method with explicitly represented polygon wall boundary model , 2020, Computational Particle Mechanics.

[42]  Moubin Liu,et al.  A novel coupling approach of smoothed finite element method with SPH for thermal fluid structure interaction problems , 2020 .

[43]  Decheng Wan,et al.  MPS-FEM coupled method for sloshing flows in an elastic tank , 2017 .

[44]  Mengyan Zang,et al.  A three-dimensional computational framework for impact fracture analysis of automotive laminated glass , 2015 .

[45]  C. K. Thornhill,et al.  Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , 1952, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[46]  Leigh McCue,et al.  Free-surface flow interactions with deformable structures using an SPH–FEM model , 2012 .

[47]  David J. Benson,et al.  A single surface contact algorithm for the post-buckling analysis of shell structures , 1990 .

[48]  Eugenio Oñate,et al.  The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves , 2004 .

[49]  Seiichi Koshizuka,et al.  Numerical Simulation of Three-Dimensional Free-Surface Flows with Explicit Moving Particle Simulation Method , 2011 .

[50]  Yong Zhao,et al.  A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid-structure interaction , 2007, J. Comput. Phys..

[51]  Zhi-qian Zhang,et al.  Coupling of SPH with smoothed point interpolation method for violent fluid-structure interaction problems , 2019, Engineering Analysis with Boundary Elements.

[52]  Yee-Chung Jin,et al.  A weakly compressible MPS method for modeling of open‐boundary free‐surface flow , 2009 .

[53]  J. Halleux,et al.  An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions , 1982 .

[54]  D. Wan,et al.  Numerical study of the wave-induced slamming force on the elastic plate based on MPS-FEM coupled method , 2018 .

[55]  Gui-Rong Liu,et al.  The Finite Element Method , 2007 .