A monolithic Lagrangian meshfree scheme for Fluid–Structure Interaction problems within the OTM framework

Jiang Fan1,2,3, Huming Liao1, Renjie Ke4, Erdem Kucukal4, Umut A. Gurkan4, Xiuli Shen1, Jian Lu5, Bo Li4
1School of Energy and Power Engineering, Beihang University, Beijing 100191, China
2Beijing Key Laboratory of Aero-Engine Structure and Strength, Beijing 100191, China
3Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100191, China
4Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, 44106, USA
5Guangdong Institute of Aeronautics and Astronautics Equipment & Technology, Zhuhai, Guangdong 519000, China

Tài liệu tham khảo

Hou, 2012, Numerical methods for fluid–structure interaction—a review, Commun. Comput. Phys., 12, 337, 10.4208/cicp.291210.290411s Felippa, 2001, Partitioned analysis of coupled mechanical systems, Comput. Methods Appl. Mech. Engrg., 190, 3247, 10.1016/S0045-7825(00)00391-1 Farhat, 2004 Gingold, 1977, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. R. Astron. Soc., 181, 375, 10.1093/mnras/181.3.375 Gingold, 1982, Kernel estimates as a basis for general particle methods in hydrodynamics, J. Comput. Phys., 46, 429, 10.1016/0021-9991(82)90025-0 Farhat, 2000, Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems, Comput. Methods Appl. Mech. Engrg., 182, 499, 10.1016/S0045-7825(99)00206-6 Jaiman, 2006, Conservative load transfer along curved fluid–solid interface with non-matching meshes, J. Comput. Phys., 218, 372, 10.1016/j.jcp.2006.02.016 Nobile, 2001, 203 Causin, 2005, Added-mass effect in the design of partitioned algorithms for fluid–structure problems, Comput. Methods Appl. Mech. Engrg., 194, 4506, 10.1016/j.cma.2004.12.005 Förster, 2007, Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows, Comput. Methods Appl. Mech. Engrg., 196, 1278, 10.1016/j.cma.2006.09.002 Degroote, 2008, Stability of a coupling technique for partitioned solvers in FSI applications, Comput. Struct., 86, 2224, 10.1016/j.compstruc.2008.05.005 Vierendeels, 2005, Analysis and stabilization of fluid–structure interaction algorithm for rigid-body motion, AIAA J., 43, 2549, 10.2514/1.3660 Osher, 1988, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12, 10.1016/0021-9991(88)90002-2 Hyman, 1984, Numerical methods for tracking interfaces, Physica D, 12, 396, 10.1016/0167-2789(84)90544-X Li, 2002, A moving frame of reference algorithm for fluid/structure interaction of rotating and translating bodies, Int. J. Numer. Meth. Fluid., 38, 187, 10.1002/fld.216 Kim, 2001, An immersed-boundary finite-volume method for simulations of flow in complex geometries, J. Comput. Phys., 171, 132, 10.1006/jcph.2001.6778 Yang, 2005, A strong coupling scheme for fluid–structure interaction problems in viscous incompressible flows Heil, 2004, An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems, Comput. Methods Appl. Mech. Engrg., 193, 1, 10.1016/j.cma.2003.09.006 Bathe, 2004, Finite element developments for general fluid flows with structural interactions, Internat. J. Numer. Methods Engrg., 60, 213, 10.1002/nme.959 Hron, 2006, A monolithic FEM/multigrid solver for an ALE formulation of fluid–structure interaction with applications in biomechanics, 146 Michler, 2004, A monolithic approach to fluid–structure interaction, Comput. & Fluids, 33, 839, 10.1016/j.compfluid.2003.06.006 Donea, 1982, An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid–structure interactions, Comput. Methods Appl. Mech. Engrg., 33, 689, 10.1016/0045-7825(82)90128-1 Donea, 2004, Arbitrary Lagrangian ulerian methods, 413 Hughes, 1981, Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Comput. Methods Appl. Mech. Engrg., 29, 329, 10.1016/0045-7825(81)90049-9 Donea, 2003 Idelsohn, 2009, Fluid–structure interaction problems with strong added-mass effect, Internat. J. Numer. Methods Engrg., 80, 1261, 10.1002/nme.2659 Rossi, 2010, Analysis of some partitioned algorithms for fluid–structure interaction, Eng. Comput., 27, 20, 10.1108/02644401011008513 Tezduyar, 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. Engrg., 94, 339, 10.1016/0045-7825(92)90059-S Tezduyar, 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. Engrg., 94, 353, 10.1016/0045-7825(92)90060-W Mittal, 1995, Parallel finite element simulation of 3D incompressible flows: Fluid–structure interactions, Int. J. Numer. Meth. Fluid., 21, 933, 10.1002/fld.1650211011 Tezduyar, 2006, Space–time finite element techniques for computation of fluid–structure interactions, Comput. Methods Appl. Mech. Engrg., 195, 2002, 10.1016/j.cma.2004.09.014 Tezduyar, 2007, Modelling of fluid–structure interactions with the space–time finite elements: solution techniques, Int. J. Numer. Meth. Fluid., 54, 855, 10.1002/fld.1430 Bazilevs, 2008, Isogeometric fluid–structure interaction: theory, algorithms, and computations, Comput. Mech., 43, 3, 10.1007/s00466-008-0315-x Idelsohn, 2008, 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, 10.1016/j.cma.2007.06.004 Oñate, 2004, The particle finite element method—an overview, Int. J. Comput. Meth., 1, 267, 10.1142/S0219876204000204 Idelsohn, 2006, Fluid–structure interaction using the particle finite element method, Comput. Methods Appl. Mech. Engrg., 195, 2100, 10.1016/j.cma.2005.02.026 Li, 2010, Optimal transportation meshfree approximation schemes for fluid and plastic flows, Internat. J. Numer. Methods Engrg., 83, 10.1002/nme.2869 Li, 2012, Verification and validation of the optimal transportation meshfree (otm) simulation of terminal ballistics, Int. J. Imp. Eng., 42, 25, 10.1016/j.ijimpeng.2011.11.003 C. Villani, Topics in Optimal Transportation, vol. 58, American Mathematical Soc., 2003. Arroyo, 2006, Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods, Internat. J. Numer. Methods Engrg., 65, 2167, 10.1002/nme.1534 Sulsky, 1994, A particle method for history-dependent materials, Comput. Methods Appl. Mech. Engrg., 118, 179, 10.1016/0045-7825(94)90112-0 Radovitzky, 1998, Lagrangian finite element analysis of Newtonian fluid flows, Internat. J. Numer. Methods Engrg., 43, 607, 10.1002/(SICI)1097-0207(19981030)43:4<607::AID-NME399>3.0.CO;2-N Radovitzky, 1999, Error estimation and adaptive meshing in strongly nonlinear dynamic problems, Comput. Methods Appl. Mech. Engrg., 172, 203, 10.1016/S0045-7825(98)00230-8 Macdonald, 1966, Some simple isothermal equations of state, Rev. Modern Phys., 38, 669, 10.1103/RevModPhys.38.669 Ortiz, 1999, The variational formulation of viscoplastic constitutive updates, Comput. Methods Appl. Mech. Engrg., 171, 419, 10.1016/S0045-7825(98)00219-9 Yang, 2006, A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids, J. Mech. Phys. Solids, 54, 401, 10.1016/j.jmps.2005.08.010 Benamou, 1999, A numerical method for the optimal time-continuous mass transport problem and related problems, Contemp. Math., 226, 1, 10.1090/conm/226/03232 Benamou, 2000, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numer. Math., 84, 375, 10.1007/s002110050002 McCann, 1997, A convexity principle for interacting gases, Adv. Math., 128, 153, 10.1006/aima.1997.1634 Martin, 2001, Blasius boundary layer solution with slip flow conditions, AIP Conf. Proc., 585, 518, 10.1063/1.1407604 Blasius, 1907 Pentecôte, 2003, Crashworthiness of helicopters on water: Test and simulation of a full-scale WG30 impacting on water, Int. J. Crashworth., 8, 559, 10.1533/ijcr.2003.0259 Anghileri, 2011, Rigid body water impact–experimental tests and numerical simulations using the sph method, Int. J. Imp. Eng., 38, 141, 10.1016/j.ijimpeng.2010.11.002 Shah, 2015, Water impact of rigid wedges in two-dimensional fluid flow, J. Appl. Fluid Mech., 8, 329, 10.18869/acadpub.jafm.67.221.22693 Chuang, 1966 Ganzenmuller, 2015, An hourglass control algorithm for Lagrangian smooth particle hydrodynamics, Comput. Methods Appl. Mech. Engrg., 286, 87, 10.1016/j.cma.2014.12.005 Weisenfels, 2018, Stabilization algorithm for the optimal transportation meshfree approximation scheme, Comput. Methods Appl. Mech. Engrg., 329, 421, 10.1016/j.cma.2017.09.031