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A coupled lattice Boltzmann-finite element approach for two-dimensional fluid-structure interaction. (English) Zbl 1290.76120

Summary: A systematic approach to couple the lattice Boltzmann and the finite element methods is presented for fluid-structure interaction problems. In particular, elastic structures and weakly compressible viscous fluids are considered. Three partitioned coupling strategies are proposed and the accuracy and convergence properties of the resultant algorithms are numerically investigated together with their computational efficiency. The corotational formulation is adopted to account for structure large displacements. The Time Discontinuous Galerkin method is used as time integration scheme for structure dynamics. The advantages over standard Newmark time integration schemes are discussed. In the lattice Boltzmann solver, an accurate curved boundary condition is implemented in order to properly define the structure position. In addition, moving boundaries are treated by an effective refill procedure.

MSC:

76M28 Particle methods and lattice-gas methods
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76N15 Gas dynamics (general theory)
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[1] van Brummelen, E. H., Partitioned iterative solution methods for fluid-structure interaction, Int J Numer Meth Fluids, 65, 3-27 (2011) · Zbl 1427.74049
[2] Succi, S., The Lattice Boltzmann equation for fluid dynamics and beyond (2001), Clarendon · Zbl 0990.76001
[3] Benzi, R.; Succi, S.; Vergassola, M., The Lattice Boltzmann equation: theory and applications, Phys Rep, 222, 145-197 (1992)
[4] Chen, H.; Chen, S.; Matthaeus, W. H., Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method, Phys Rev Lett, 45, R5339-R5342 (1992)
[5] Chen, S.; Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu Rev Fluid Mech, 30, 329-364 (1998) · Zbl 1398.76180
[6] Qian, Y.; D’Humières, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys Lett, 17, 479-484 (1992) · Zbl 1116.76419
[7] Boghosian, B.; Yepez, J.; Coveney, P.; Wagner, A., Entropic Lattice Boltzmann methods, Proc Roy Soc A: Math Phys Eng Sci, 457, 717-766 (2001) · Zbl 0984.76069
[8] Filippova, O.; Hänel, D., Lattice Boltzmann simulation of gas-particle flow in filters, Comput Fluids, 26, 697-712 (1997) · Zbl 0902.76077
[9] Mei, R.; Luo, L.; Shyy, W., An accurate curved boundary treatment in the Lattice Boltzmann method, J Comput Phys, 155, 307-330 (1999) · Zbl 0960.82028
[10] Falcucci, G.; Aureli, M.; Ubertini, S.; Porfiri, M., Transverse harmonic oscillations of laminae in viscous fluids: a lattice Boltzmann study, Philos Trans Roy Soc - Ser A, 369, 2456-2466 (2011) · Zbl 1223.76072
[11] De Rosis, A.; Falcucci, G.; Ubertini, S.; Ubertini, F., Lattice Boltzmann analysis of fluid-structure interaction with moving boundaries, Commun Comput Phys, 13, 823-834 (2012) · Zbl 1373.76234
[12] Felippa, C.; Haugen, B., A unified formulation of small-strain corotational finite elements: I. Theory, Comput Methods Appl Mech Eng, 194, 2285-2335 (2005) · Zbl 1093.74055
[13] Mancuso, M.; Ubertini, F., A methodology for the generation of low-cost higher-order methods for linear dynamics, Int J Numer Method Eng, 56, 1883-1912 (2003) · Zbl 1031.65082
[14] Mancuso, M.; Ubertini, F., An efficient time discontinuous Galerkin procedure for non-linear structural dynamics, Comput Method Appl Mech Eng, 195, 6391-6406 (2006) · Zbl 1122.74024
[15] Kollmannsberger, S.; Geller, S.; Duster, A.; Tolke, J.; Sorger, C.; Krafczyk, M., Fixed-grid fluid-structure interaction in two dimensions based on a partitioned lattice Boltzmann and \(p\)-fem approach, Int J Numer Meth Eng, 79, 817-845 (2009) · Zbl 1171.74340
[16] Lee, J. S.; Shin, J. H.; Lee, S. H., Fluid-structure interaction of a flapping flexible plate in quiescent fluid, Comput Fluids, 57, 124-137 (2012) · Zbl 1365.74069
[17] Inamuro, T., Lattice Boltzmann methods for moving boundary flows, Fluid Dynam Res, 44, 024001 (2012) · Zbl 1319.76039
[18] Mei, R.; Yu, D.; Shyy, W.; Luo, L., Force evaluation in the lattice Boltzmann method involving curved geometry, Phys Rev Lett E, 65, 041203 (2002)
[19] Breuer, M., Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume, Int J Heat Fluid Flow, 21, 186-196 (2000)
[20] Piperno, S.; Farhat, C., Partitioned procedures for the transient solution of coupled aeroelastic problems - part II: energy transfer analysis and three-dimensional applications, Comput Meth Appl Mech Eng, 190, 3147-3170 (2001) · Zbl 1015.74009
[21] Farhat, C.; Vanderzee, K.; Geuzaine, P., Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Comput Meth Appl Mech Eng, 195, 1973-2001 (2006) · Zbl 1178.76259
[22] Degroote, J.; Bruggeman, P.; Haelterman, R.; Vierendeels, J., Stability of a coupling technique for partitioned solvers in FSI applications, Comput Struct, 86, 2224-2234 (2008)
[23] Causin, P.; Gerbeau, J. F.; Nobile, F., Added-mass effect in the design of partitioned algorithms for fluid-structure problems, Comput Meth Appl Mech Eng, 194, 4506-4527 (2005) · Zbl 1101.74027
[24] van Brummelen, E. H., Added mass effects of compressible and incompressible flows in fluid-structure interaction, J Appl Mech, 76, 021206 (2009)
[25] Bhatnagar, P.; Gross, E.; Krook, M., A model for collisional processes in gases: small amplitude processes in charged and neutral one-component system, Phys Rev Lett, 94, 515-523 (1954) · Zbl 0055.23609
[26] Ladd, A., Numerical simulation of particulate suspensions via a discretized Boltzmann equation, part 1. Theoretical foundation, J Fluid Mech, 271, 285-310 (1994) · Zbl 0815.76085
[27] Ladd, A., Numerical simulation of particular suspensions via discretized Boltzmann equation, part 2. Numerical results, J Fluid Mech, 271, 311-339 (1994)
[28] Mancuso, M.; Ubertini, F., An efficient integration procedure for linear dynamics based on a time discontinuous Galerkin formulation, Comput Mech, 32, 154-168 (2003) · Zbl 1038.74558
[29] Mancuso, M.; Ubertini, F., The Nørsett time integration methodology for finite element transient analysis, Comput Meth Appl Mech Eng, 191, 3297-3327 (2002) · Zbl 1010.65036
[30] Govoni, L.; Mancuso, M.; Ubertini, F., Hierarchical higher-order dissipative methods for transient analysis, Int J Numer Meth Eng, 67, 1730-1767 (2006) · Zbl 1113.74025
[31] de Miranda, S.; Mancuso, M.; Ubertini, F., Time discontinuous Galerkin methods with energy decaying correction for non-linear elastodynamics, Int J Numer Meth Eng, 83, 323-346 (2010) · Zbl 1193.74050
[32] Walhorn, E.; Hübner, B.; Dinkler, D., Space-time finite elements for fluid-structure interaction, Proc Appl Math Mech, 1, 81-82 (2002) · Zbl 1419.74122
[33] Gratsch, T.; Bathe, K., Goal-oriented error estimation in the analysis of fluid flows with structural interactions, Comput Meth Appl Mech Eng, 195, 5673-5684 (2006) · Zbl 1122.76055
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