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Distributed Lagrange multiplier/fictitious domain method in the framework of lattice Boltzmann method for fluid-structure interactions. (English) Zbl 1087.76543
Summary: A new implementation of the lattice Boltzmann method (LBM) for fluid-structure interactions is presented. The idea of the distributed-Lagrange-multiplier/fictitious-domain method (DLM/FD) is introduced in the framework of the lattice Boltzmann algorithm. This implementation employs a fixed mesh for the solution of the fluid problem and a Lagrangian formulation for the solid problem. The main advantage of the method is that the re-meshing procedure normally required in the ALE method is circumvented. Numerical examples are provided to verify the algorithm and illustrate the capacity of the method to deal with the fluid/elastic-solid interactions.

76M28 Particle methods and lattice-gas methods
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[1] Chen, S.; Doolen, G.D., Lattice Boltzmann method for fluid flows, Annu. rev. fluid mech., 30, 329, (1998) · Zbl 1398.76180
[2] Nourgaliev, R.R.; Dinh, T.N.; Theofanous, T.G.; Joseph, D., The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. multiphase flow, 29, 117, (2003) · Zbl 1136.76594
[3] Nie, X.; Doolen, G.D.; Chen, S.Y., Lattice Boltzmann simulation of fluid flows in MEMS, J. stat. phys., 107, 279, (2002) · Zbl 1007.82007
[4] Wagner, A.J.; Giraud, L.; Scott, C.E., Simulation of a cusped bubble rising in a viscoelastic fluid with a new numerical method, Comput. phys. commun., 129, 227, (2000) · Zbl 0987.76084
[5] Ispolatov, I.; Grant, M., Lattice Boltzmann method for viscoelastic fluids, Phys. rev. E, 65, 65704, (2002)
[6] Krafczyk, M.; Tölke, J.; Rank, E.; Schulz, M., Two-dimensional simulation of fluid-structure interaction using lattice-Boltzmann methods, Comput. struct., 79, 2031, (2001)
[7] Qi, D.; Aidun, C.K., A new method for analysis of the fluid interaction with a deformable membrane, J. stat. phys., 90, 145, (1998) · Zbl 0918.73050
[8] Ladd, A.J.C., Numerical simulation of particulate suspensions via a discretized Boltzmann equation, part 1. theoretical foundation, J. fluid mech., 271, 285, (1994) · Zbl 0815.76085
[9] Ladd, A.J.C.; Verberg, R., Lattice-Boltzmann simulations of particle-fluid suspensions, J. stat. phys., 104, 1191, (2001) · Zbl 1046.76037
[10] Feng, Z.-G.; Michaelides, E.E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. comput. phys., 195, 602, (2004) · Zbl 1115.76395
[11] Peskin, C.S., Numerical analysis of blood flow in the heart, J. comput. phys., 25, 220, (1977) · Zbl 0403.76100
[12] Donea, J.; Giuliani, S.; Halleux, J.P., An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Comput. meth. appl. mech. eng., 33, 689, (1982) · Zbl 0508.73063
[13] Glowinski, R.; Pan, T.; Périaux, J., A fictitious domain method for Dirichlet problems and applications, Comput. meth. appl. mech. eng., 111, 283, (1994) · Zbl 0845.73078
[14] Glowinski, R.; Pan, T.; Périaux, J., A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Comput. meth. appl. mech. eng., 112, 133, (1994) · Zbl 0845.76069
[15] Glowinski, R.; Pan, T.; Hesla, T.I.; Joseph, D.D., A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. multiphase flow, 25, 755, (1999) · Zbl 1137.76592
[16] Yu, Z.; Phan-Thien, N.; Fan, Y.; Tanner, R.I., Viscoelastic mobility problem of a system of particles, J. non-Newtonian fluid mech., 104, 87, (2002) · Zbl 1058.76592
[17] Baaijens, F.P.T., A fictitious domain/mortar element method for fluid-structure interaction, Int. J. numer. meth. fluids, 35, 743, (2001) · Zbl 0979.76044
[18] de Hart, J.; Peters, G.W.M.; Schreurs, P.J.G.; Baaijens, F.P.T., A three-dimensional computational analysis of fluid-structure interaction in the aortic valve, J. biomech., 36, 103, (2003)
[19] Z. Yu, A DLM/FD method for fluid/flexible-body interactions, J. Comput. Phys. (submitted) · Zbl 1177.76304
[20] Lee, T.; Lin, C., Pressure evolution lattice-Boltzmann-equation method for two-phase flow with phase change, Phys. rev. E, 67, 056703, (2003)
[21] Qian, Y.; d’Humières, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. lett., 17, 479, (1992) · Zbl 1116.76419
[22] Sussman, T.; Bathe, K.J., A finite element formulation for nonlinear incompressible elastic and inelastic analysis, Comput. struct., 26, 357, (1987) · Zbl 0609.73073
[23] Zienkiewicz, O.C.; Morgan, K., Finite elements and approximation, (1983), Wiley Chichester · Zbl 0582.65068
[24] Lai, M.C.; Peskin, C.S., An immersed boundary method with formal second order accuracy and reduced numerical viscosity, J. comput. phys., 160, 705, (2000) · Zbl 0954.76066
[25] Yu, D.; Mei, R.; Shyy, W., A multi-block lattice Boltzmann method for viscous fluid flows, Int. J. numer. meth. fluids, 39, 99, (2002) · Zbl 1036.76051
[26] Shu, C.; Chew, Y.T.; Niu, X.D., Least-squares-based lattice Boltzmann method: a meshless approach for simulation of flows with complex geometry, Phys. rev. E, 64, 045701, (2001)
[27] Tuann, S.Y.; Olson, M.D., Numerical studies of the flow around a circular cylinder by a finite element method, Comput. fluids, 6, 219, (1978) · Zbl 0394.76038
[28] Fornberg, B., A numerical study of steady viscous flow past a circular cylinder, J. fluid mech., 98, 819, (1980) · Zbl 0428.76032
[29] Gresho, P.M.; Chan, R.; Upson, C.; Lee, R., A modified finite element method for solving the time-dependent, incompressible Navier-Stokes equations: part 2: applications, Int. J. numer. methods fluids, 4, 619, (1984) · Zbl 0559.76031
[30] He, X.; Doolen, G., Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder, J. comput. phys., 134, 306, (1997) · Zbl 0886.76072
[31] Saiki, E.M.; Biringen, S., Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method, J. comput. phys., 123, 450, (1996) · Zbl 0848.76052
[32] Ding, H.; Shu, C.; Yeo, K.S.; Xu, D., Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method, Comput. methods appl. mech. eng., 193, 727, (2004) · Zbl 1068.76062
[33] Niu, X.D.; Chew, Y.T.; Shu, C., Simulation of flows around an impulsively started circular cylinder by Taylor series expansion- and least squares-based lattice Boltzmann method, J. comput. phys., 188, 176, (2003) · Zbl 1038.76033
[34] Chew, Y.T.; Shu, C.; Niu, X.D., Simulation of unsteady incompressible flows by using Taylor series expansion- and least square-based lattice Boltzmann method, Int. J. mod. phys. C, 13, 719, (2002) · Zbl 1086.82568
[35] Zhang, J.; Childress, S.; Libchaber, A.; Shelley, M., Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature, 408, 835, (2000)
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