Boundary recognition; Free-surface flow; Mass conservation; Mesh adaptation; Particle finite element method (PFEM); α-Shape-criterion; Computational Mechanics; Numerical Analysis
Résumé :
[en] The particle finite element method (PFEM) is a Lagrangian method that avoids large mesh distortion through automatic remeshing when the computational grid becomes too distorted. The method is well adapted for flows with deforming interfaces and moving boundaries. However, the α-shape technique used to identify these boundaries presupposes a mesh of approximately uniform size. Moreover, the α-shape criterion is purely geometric and, thus, leads to violations of mass conservation at boundaries. We propose a new algorithm for mesh refinement and adaptation in two dimensions to improve the ratio accuracy to computational cost of the PFEM. A local target mesh size is prescribed according to geometric and/or physics-based criteria, and particles are added or removed to approximately enforce this target mesh size. Additionally, the new boundary recognition algorithm relies on the tagging of boundary nodes and a local α-shape criterion that depends on the target mesh size. The method allows thereby reducing mass conservation errors at free surfaces and improving the local accuracy through mesh refinement and simultaneously offers a new boundary tracking algorithm. The new algorithm is tested on four two-dimensional validation cases. The first two cases, i.e., the lid-driven cavity flow at Reynolds number 400 and the flow around a static cylinder at Reynolds numbers below 200, do not feature a free surface and mainly illustrate the mesh refinement capability. The last two test cases consist in the sloshing problem in a reservoir subjected to forced oscillations and the fall of a 2D liquid drop into a tank filled with the same viscous fluid. These last two cases demonstrate the more accurate representation of the free surface and a corresponding reduction of the error in mass conservation.
Disciplines :
Ingénierie aérospatiale
Auteur, co-auteur :
Falla, Romain ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Bobach, Billy-Joe ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Boman, Romain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique
Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Terrapon, Vincent ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Modélisation et contrôle des écoulements turbulents
Langue du document :
Anglais
Titre :
Mesh adaption for two-dimensional bounded and free-surface flows with the particle finite element method
Date de publication/diffusion :
2023
Titre du périodique :
Computational Particle Mechanics
ISSN :
2196-4378
eISSN :
2196-4386
Maison d'édition :
Springer Science and Business Media Deutschland GmbH
The financial support of the Belgian Fund for Scientific Research under research project WOLFLOW (F.R.S.-FNRS, PDR T.0021.18) is gratefully acknowledged.
Acrivos A, Leal LG, Snowden DD, Pan F (1968) Further experiments on steady separated flows past bluff objects. J Fluid Mech 34(1):25–48. 10.1017/S0022112068001758 DOI: 10.1017/S0022112068001758
Bathe K, Zhang H (2009) A mesh adaptivity procedure for CFD and fluid-structure interactions. Comput Struct 87(11–12):604–617. 10.1016/j.compstruc.2009.01.017 DOI: 10.1016/j.compstruc.2009.01.017
Berger M, Colella P (1989) Local adaptive mesh refinement for shock hydrodynamics. J Comput Phys 82:64–84. 10.1016/0021-9991(89)90035-1 DOI: 10.1016/0021-9991(89)90035-1
Bernadini F, Bajaj CL (1997) Sampling and reconstructing manifolds using alpha-shapes. Technical report. 97-013, Department of computer science technical reports
Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. ESAIM Math Model Numer Anal Modél Math Anal Numér 8(R2):129–151
Bristeau M, Glowinski R, Periaux J (1987) Numerical methods for the Navier–Stokes equations. Applications to the simulation of compressible and incompressible viscous flows. Comput Phys Rep 6:73–187 DOI: 10.1016/0167-7977(87)90011-6
Carbonell J, Rodríguez J, Oñate E (2020) Modelling 3D metal cutting problems with the particle finite element method. Comput Mech 66:603–624. 10.1007/s00466-020-01867-5 DOI: 10.1007/s00466-020-01867-5
Cerquaglia M, Deliége G, Boman R, Papeleux L, Ponthot J (2017) The particle finite element method for the numerical simulation of bird strike. Int J Impact Eng 109:1–13. 10.1016/j.ijimpeng.2017.05.014 DOI: 10.1016/j.ijimpeng.2017.05.014
Cerquaglia M, Deliége G, Boman R, Terrapon V, Ponthot J (2017) Free-slip boundary conditions for simulating free-surface incompressible flows through the particle finite element method. Int J Numer Methods Eng 110(10):921–946. 10.1002/nme.5439 DOI: 10.1002/nme.5439
Cerquaglia M, Thomas D, Boman R, Terrapon V, Ponthot J (2019) A fully partitioned Lagrangian framework for FSI problems characterized by free surfaces, large solid deformations and displacements, and strong added-mass effects. Comput Methods Appl Mech Eng 348:409–442. 10.1016/j.cma.2019.01.021 DOI: 10.1016/j.cma.2019.01.021
Cerquaglia ML (2019) Development of a fully-partitioned PFEM-FEM approach for fluid-structure interaction problems characterized by free surfaces, large solid deformations, and strong added-mass effects. Ph.D. thesis, University of Liege
Cerquaglia ML, Deliége G, Boman R, Ponthot JP (2017) Preliminary assessment of the possibilities of the particle finite element method in the numerical simulation of bird impact on aeronautical structures, pp 101–108. 10.1016/j.proeng.2016.12.043
Coutanceau M, Bouard R (1977) Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. Part 1. Steady flow. J Fluid Mech 79(2):231–256. 10.1017/S0022112077000135 DOI: 10.1017/S0022112077000135
Cremonesi M, Ferri F, Perego U (2016) A Lagrangian PFEM approach to the numerical simulation of 3D large scale landslides impinging in water reservoirs. In: ECCOMAS congress 2016: VII European congress on computational methods in applied sciences and engineering. 10.7712/100016.1840.7927
Cremonesi M, Franci A, Idelsohn S (2020) A state of the art review of the particle finite element method (PFEM). Arch Comput Methods Eng 27:1709–1735. 10.1007/s11831-020-09468-4 DOI: 10.1007/s11831-020-09468-4
Cremonesi M, Frangi A, Perego U (2010) A Lagrangian finite element approach for the analysis of fluid-structure interaction problems. Int J Numer Methods Eng 184(5):610–630. 10.1002/nme.2911 DOI: 10.1002/nme.2911
Dannenhofer F, Baron J (1985) Grid adaptation for the 2D Euler equations. 10.2514/6.1985-484
De Sterck H, Manteuffel T, McCormick S, Nolting J, Ruge J, Tang L (2008) Efficiency-based h- and hp-refinement strategies for finite element methods. Numer Linear Algebra Appl 00:1–25. 10.1002/nla.567 DOI: 10.1002/nla.567
Delaunay B (1934) Sur la sphère vide, à la mémoire de Georges Voronoï. Bulletin de l’Académie des sciences de l’URSS. Classe des sciences mathématiques et naturelles 6:793–800
Delorme L, Colagrossi A, Souto-Iglesias A et al (2009) A set of canonical problems in sloshing, part 1: pressure field in forced roll-comparison between experimental results and SPH. Ocean Eng 36(2):168–178. 10.1016/j.oceaneng.2008.09.014 DOI: 10.1016/j.oceaneng.2008.09.014
Douglas NA, Arup M, Luc P (2000) On global and local mesh refinements by a generalized conforming bisection algorithm. SIAM J Sci Comput 22(2):431–448. 10.1137/S1064827597323373 DOI: 10.1137/S1064827597323373
Duval M, Lozinskic A, Passieuxb J, Salaunb M (2018) Residual error based adaptive mesh refinement with the non-intrusive patch algorithm. Comput Methods Appl Mech Eng 329:118–143. 10.1016/j.cma.2017.09.032 DOI: 10.1016/j.cma.2017.09.032
Dávalos C, Cante J, Hernández J, Oliver J (2015) On the numerical modeling of granular material flows via the particle finite element method (PFEM). Int J Solids Struct 71:99–125. 10.1016/j.ijsolstr.2015.06.013 DOI: 10.1016/j.ijsolstr.2015.06.013
Eberhard B (1991) An adaptive finite-element strategy for the three-dimensional time-dependent Navier–Stokes equations. J Comput Appl Math 36:3–28. 10.1016/0377-0427(91)90224-8 DOI: 10.1016/0377-0427(91)90224-8
Edelsbrunner H, Kirkpatrick DG, Seidel R (1983) On the shape of a set of points in the plane. IEEE Trans Inf Theory 29(4):551–559. 10.1109/TIT.1983.1056714 DOI: 10.1109/TIT.1983.1056714
Edelsbrunner H, Mücke EP (1994) Three-dimensional alpha shapes. ACM Trans Graph 13(1):43–72. 10.1145/147130.147153 DOI: 10.1145/147130.147153
Edelsbrunner H, Shah N (1996) Incremental topological flipping works for regular triangulations. Algorithmica 15:223–241. 10.1007/BF01975867 DOI: 10.1007/BF01975867
Franci A, Cremonesi M (2017) On the effect of standard PFEM remeshing on volume conservation in free-surface fluid flow problems. Comput Particle Mech 4(3):331–343. 10.1007/s40571-016-0124-5 DOI: 10.1007/s40571-016-0124-5
Franci A, Zhang X (2018) 3D numerical simulation of free-surface Bingham fluids interacting with structures using the PFEM. J Nonnewton Fluid Mech 259:1–15. 10.1016/j.jnnfm.2018.05.001 DOI: 10.1016/j.jnnfm.2018.05.001
Friedel H, Grauer R, Marliani C (1997) Adaptive mesh refinement for singular current sheets in incompressible magnetohydrodynamic flows. J Comput Phys 134(1):190–198. 10.1006/jcph.1997.5683 DOI: 10.1006/jcph.1997.5683
Ghia U, Ghia K, Shin CT (1982) High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method. J Comput Phys 48:387–411. 10.1016/0021-9991(82)90058-4 DOI: 10.1016/0021-9991(82)90058-4
Grove AS, Shair FH, Peterson E (1964) An experimental investigation of the steady separated flow past a circular cylinder. J Fluid Mech 19(1):60–80. 10.1017/S0022112064000544 DOI: 10.1017/S0022112064000544
Hannukainen A, Korotov S, Křížek M (2010) On global and local mesh refinements by a generalized conforming bisection algorithm. J Comput Appl Math 235(2):419–436. 10.1016/j.cam.2010.05.046 DOI: 10.1016/j.cam.2010.05.046
Henderson RD (1994) Adaptive spectral element methods, parallel algorithms and simulations. Ph.D. thesis, Princeton University
Henderson RD (1995) Details of the drag curve near the onset of vortex shedding. Phys Fluids 7(9):2102–2104. 10.1063/1.868459 DOI: 10.1063/1.868459
Henderson RD (1997) Non-linear dynamics and pattern formation in turbulent wake transition. J Fluid Mech 352:65–112. 10.1017/S0022112097007465 DOI: 10.1017/S0022112097007465
Hou S, Zou Q, Chen S, Doolen G, Cogley A (1995) Simulation of cavity flow by the lattice Boltzmann method. J Comput Phys 118:329–347. 10.1006/jcph.1995.1103 DOI: 10.1006/jcph.1995.1103
Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Computer Methods Appl Mech 54(3):85–99. 10.1016/0045-7825(86)90025-3 DOI: 10.1016/0045-7825(86)90025-3
John B, Marsha B, Jeff S, Welcome M (1994) Three-dimensional adaptive mesh refinement for hyperbolic conservation laws. SIAM J Sci Comput 15:127–138. 10.1137/0915008 DOI: 10.1137/0915008
Keller HB, Takami H (1966) Numerical studies of viscous flow about cylinders, p 115
Lee DT, Schachter BJ (1980) Two algorithms for constructing a Delaunay triangulation. Int J Comput Inf Sci 9(3):219–242. 10.1007/BF00977785 DOI: 10.1007/BF00977785
Lohner R, Morgan K (1986) Improved adaptive refinement strategies for finite element aerodynamic computations. 10.2514/6.1986-499
Meduri S, Cremonesi M, Perego U (2018) An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free-surface fluid flow simulations. Int J Numer Meth Eng 117(4):430–452. 10.1002/nme.5962 DOI: 10.1002/nme.5962
Monforte L, Carbonell J, Arroyo M, Gens A (2017) Performance of mixed formulations for the particle finite element method in soil mechanics problems. Comput Particle Mech 4(3):269–284. 10.1007/s40571-016-0145-0 DOI: 10.1007/s40571-016-0145-0
Norberg C (2001) Flow around a circular cylinder: aspects of fluctuating lift. J Fluids Struct 15:459–469. 10.1006/jfls.2000.0367 DOI: 10.1006/jfls.2000.0367
Oñate E, Celigueta M, Idelsohn SR (2006) Modeling bed erosion in free surface flows by the particle finite element method. Acta Geotech 1(4):237–252. 10.1142/S0219876204000204 DOI: 10.1142/S0219876204000204
Oñate E, Idelsohn SR (2004) The particle finite element method—an overview. Int J Comput Methods 1(2):267–307. 10.1142/S0219876204000204 DOI: 10.1142/S0219876204000204
Park S, Lee S, Kim J (2005) A surface reconstruction algorithm using weighted alpha shapes. In: Fuzzy systems and knowledge discovery, second international conference, FSKD, pp 1141–1150. 10.1007/11539506_143
Rajan VT (1994) Optimality of the Delaunay triangulation in Rd. Discrete Comput Geom 12:189–202. 10.1007/BF02574375 DOI: 10.1007/BF02574375
Rodríguez J, Carbonell J, Cante J (2017) Continuous chip formation in metal cutting processes using the particle finite element method (PFEM). Int J Solids Struct 120:81–102. 10.1016/j.ijsolstr.2017.04.030 DOI: 10.1016/j.ijsolstr.2017.04.030
Sani RL, Gresho PM, Lee RL, Griffiths DF (1981) The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier–Stokes equations: part 1. Int J Numer Methods Fluids 1(1):171–204. 10.1002/fld.1650010104 DOI: 10.1002/fld.1650010104
Sen S, Mittal S, Biswas G (2009) Steady separated flow past a circular cylinder at low Reynolds numbers. J Fluid Mech 620:89–119. 10.1017/S0022112008004904 DOI: 10.1017/S0022112008004904
Sheard G, Hourigan K, Thompson M (2005) Computations of the drag coefficients for low-Reynolds-number flow past rings. J Fluid Mech 526:257–275. 10.1017/S0022112004002836 DOI: 10.1017/S0022112004002836
Souto-Iglesias A, Bulian G, Botia-Vera E (2015) A set of canonical problems in sloshing. Part 2: influence of tank width on impact pressure statistics in regular forced angular motion. Ocean Eng 38(16):1823–1830. 10.1016/j.oceaneng.2011.09.008 DOI: 10.1016/j.oceaneng.2011.09.008
Sun WK, Zhang LW, Liew KM (2022) Adaptive particle refinement strategies in smoothed particle hydrodynamics. Comput Methods Appl Mech Eng. 10.1016/j.cma.2021.114276 DOI: 10.1016/j.cma.2021.114276
Taneda S (1956) Experimental investigation of the wake behind cylinders and plates at low Reynolds number. J Phys Soc Jpn 11(3):302–307. 10.1143/JPSJ.11.302 DOI: 10.1143/JPSJ.11.302
Tezduyar S, Mittal S, Ray E, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity pressure elements. Comput Methods Appl Mech Eng 95(2):221–242. 10.1016/0045-7825(92)90141-6 DOI: 10.1016/0045-7825(92)90141-6
Tournois J, Srinivasan R, Alliez P (2009) Perturbing slivers in 3d Delaunay meshes, pp 157–173. 10.1007/978-3-642-04319-2_10
Vacondio R, Altomare C, De Leffe M et al (2020) Grand challenges for smoothed particle hydrodynamics numerical schemes. Comput Particle Mech 8:575–588. 10.1007/s40571-020-00354-1 DOI: 10.1007/s40571-020-00354-1
Vanella M, Rabenold P, Balaras E (2010) A direct-forcing embedded-boundary method with adaptive mesh refinement for fluid-structure interaction problems. J Comput Phys 229(18):6427–6449. 10.1016/j.jcp.2010.05.003 DOI: 10.1016/j.jcp.2010.05.003
Vanka S (1986) Block-implicit multigrid solution of Navier–Stokes equations in primitive variables. J Comput Phys 65:138–158. 10.1016/0021-9991(86)90008-2 DOI: 10.1016/0021-9991(86)90008-2
Wieselberger Cv (1921) Neuere Feststellungen über die Gestze des Flussigkeits - und Luftwiderstands. Phys Z 22(11):321–328
Williamson CHK (1996) Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech 28(1):477–539. 10.1146/annurev.fluid.28.1.477 DOI: 10.1146/annurev.fluid.28.1.477
Yang X, Kong SC (2019) Adaptive resolution for multiphase smoothed particle hydrodynamics. Comput Phys Commun 239:112–125. 10.1016/j.cpc.2019.01.002 DOI: 10.1016/j.cpc.2019.01.002
Zhang HQ, Uwe F, Noack BR et al (1995) On the transition of the cylinder wake. Phys Fluids 7(4):779–794. 10.1063/1.868601
Zhang X, Krabbenhoft K, Sheng D, Li W (2015) Numerical simulation of a flow-like landslide using the particle finite element method. Comput Mech 55(1):167–177. 10.1007/s00466-014-1088-z
