Lattice-Boltzmann method on quadtree-type grids for fluid-structure interaction. (English) Zbl 1323.76079

Bungartz, Hans-Joachim (ed.) et al., Fluid-structure interaction. Modelling, simulation, optimisation. Proceedings of the workshop, Hohenwart, Germany, October 2005. Berlin: Springer (ISBN 3-540-34595-7/pbk). Lecture Notes in Computational Science and Engineering 53, 270-293 (2006).
Summary: In this work a Lattice Boltzmann (LB) fluid flow solver based on unstructured quadtree/octree type Eulerian grids is coupled with a spectral Finite Element (p-FEM) structural mechanics solver based on a Lagrangian description to predict bidirectional fluid-structure interaction (FSI). The methods and algorithms are described in detail. Benchmark computations of a coupled transient problem of a 2D beam-like structure in a channel as defined by the DFG-Research Unit 493 are presented.
For the entire collection see [Zbl 1097.76002].


76M28 Particle methods and lattice-gas methods
74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: DOI


[1] P.L. Bhatnagar, E.P. Gross, M. Krook. \(A Model for Collision Processes in Gases\), Phys. Rev. 94, 511, (1954). · Zbl 0055.23609
[2] M. Bouzidi, M. Firdaouss, P. Lallemand. \(Momentum transfer of a Boltzmann- Lattice fluid with boundaries\), Physics of Fluids 13(11), 3452-3459, (2001). · Zbl 1184.76068
[3] M. Brenk, H.-J. Bungartz, M. Mehl, and T. Neckel. \(Fluid-Structure Interaction on Cartesian Grids: Flow Simulation and Coupling Environment\), In H.-J. Bungartz and M. Schäfer, editors, Fluid-Structure Interaction: Modelling, Simulation, Optimisation. Springer Verlag, (2006). · Zbl 1323.76047
[4] S. Chapman, T.G. Cowling. \(The mathematical theory of non-uniform gases\), Cambridge University Press, (1970). · Zbl 0063.00782
[5] J. Chung, G. Hulbert. \(A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation: The Generalized-\'a-Method\). J. of Applied Mechanics, vol. 60, pp. 1562-1566, (1993). · Zbl 0775.73337
[6] B. Crouse, E. Rank, M. Krafczyk, J. Tölke. \(A LB-based approach for adaptive flow simulations\), Int. J. of Modern Physics B 17, 109-112, (2002).
[7] B. Crouse. \(Lattice-Boltzmann Str\"omungssimulationen auf Baumdatenstrukturen\), PhD thesis (german), TU München, (2002).
[8] A. Düster, H. Bröker, H. Heidkamp, U. Heißerer, S. Kollmannsberger, R. Krause, A. Muthler, A. Niggl, V. Nübel, M. Rücker, D. Scholz. \(AdhoC\) 4 \(- User's Guide\). Lehrstuhl für Bauinformatik, TU München, (2004).
[9] O. Filippova, D. Hänel. \(Boundary-Fitting and Local Grid Re.nement for LBGK Models\), Int. J. Mod. Phys. C(8), 1271, (1998).
[10] U. Frisch, D. d’Humiéres, B. Hasslacher, P. Lallemand, Y. Pomeau, J.P. Rivet. \(Lattice gas hydrodynamics in two and three dimensions\), Complex Sys. 1, 649- 707, (1987). · Zbl 0662.76101
[11] S. Geller, M. Krafczyk, J. Tölke, S. Turek, J. Hron. \(Benchmark computations based on Lattice-Boltzmann, Finite Element and Finite Volume Methods for laminar Flows\), accepted for Comp.&Fluids, (2004). · Zbl 1177.76313
[12] I. Ginzburg, D. d’Humiéres. \(Multi-re.ection boundary conditions for Lattice- Boltzmann models\), Phys. Rev. E 68, 66614, (2003).
[13] X. He, L.-S. Luo. \(Lattice Boltzmann model for the incompressible Navier-Stokes equation\), Journal of Statistical Physics 88, 927-944, (1997). · Zbl 0939.82042
[14] X. He, L.-S. Luo. \(Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation\). Phys. Rev. E 56, 6811, (1997).
[15] D. d’Humiéres. \(in Rare.ed Gas Dynamics: Theory and Simulations\), Prog. Astronaut. Aeronaut. Vol. 159, edited by B. D. Shizgal and D. P. Weaver AIAA, Washington, D.C., (1992).
[16] D. d’Humiéres, I. Ginzburg, M. Krafczyk, P. Lallemand, L.-S. Luo. \(Multiplerelaxation- time lattice Boltzmann models in three-dimensions\), Philosophical Transections of Royal Society of London A 360(1792), 437-451, (2002). · Zbl 1001.76081
[17] M. Junk. \(A Finite Di.erence Interpretation of the Lattice Boltzmann Method\), Num. Meth. Part. Di. Equations Vol. 17, 383-402, (2001). · Zbl 0987.76082
[18] M. Junk, A. Klar, L.-S. Luo. \(Theory of the Lattice Boltzmann Method: Mathematical Analysis of the Lattice Boltzmann Equation\), preprint, (2004). · Zbl 1079.82013
[19] P. Lallemand, L.-S. Luo. \(Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability\), Physical Review E 61 6546-6562, (2000).
[20] P. Lallemand, L.-S. Luo. \(Lattice Boltzmann method for moving boundaries\), Journal of Computational Physics 184, 406-421, (2003). · Zbl 1062.76555
[21] R. Löhner, J.D. Baum, E.L. Mestreau, D. Sharov, Ch. Charman and D. Pelessone. \(Adaptive Embedded Unstructured Grid Methods\), AIAA-03-1116, (2003). · Zbl 1060.76574
[22] W. E. Lorensen and H. E. Cline. \(Marching Cubes: a high resolution 3D surface construction algorithm\), In Siggraph, volume 21, pages 163-169. ACM, (1987).
[23] L.-S. Luo. \(Consistent Initial Conditions for LBE Simulation\), preprint, (2006).
[24] J. Mackerle. \(Finite element linear and nonlinear, static and dynamic analysis of structural elements: a bibliography\), International Journal for Computer-Aided Engineering, 14 (4):347-440 (1997). · Zbl 0983.74500
[25] R. Mei, D. Yu, W. Shyy, L.-S. Luo. \(Force evaluation in the lattice Boltzmann method involving vurved geometry\), Phys. Rev. E 65, 041203, (2002).
[26] N.-Q. Nguyen, A.J.C. Ladd. \(Sedimentation of hard-sphere suspensions at low Reynolds number\) submitted to J. Fluid Mech. (2004).
[27] Y. H. Qian, D. d’Humiéres, P. Lallemand. \(Lattice BGK models for Navier- Stokes equation\), Europhys. Lett. 17 479-484, (1992). · Zbl 1116.76419
[28] M. Rheinländer. \(A Consistent Grid Coupling Method for Lattice-Boltzmann Schemes\), J. of Statistical Physics, Vol. 121, (2005). · Zbl 1107.82052
[29] P. le Tallec, J. Mouro. \(Fluid Structure Interaction with Large Structural Displacements\), Computer Methods in Applied Mechanics and Engineering, 190, 24-25, pp 3039-3068, (2001). · Zbl 1001.74040
[30] N. Thürey. \(A single-phase free-surface Lattice-Boltzmann Method\), diploma thesis, IMMD10, University of Erlangen-Nuremberg, (2003).
[31] J. Tölke, S. Freudiger, M. Krafczyk. \(An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations\), accepted for Comp.&Fluids, (2004). · Zbl 1177.76332
[32] S. Turek, J. Hron. \(Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow\), In H.-J. Bungartz and M. Schäfer, editors, Fluid-Structure Interaction: Modelling, Simulation, Optimisation. Springer Verlag, (2006). · Zbl 1323.76049
[33] D. Yu. \(Viscous Flow Computations with the Lattice Boltzmann equation method\), PhD thesis, Univ. of Florida, (2002).
[34] D. Yu, R. Mei, W. Shyy. \(A multi-block lattice Boltzmann method for viscous fluid flows\), Int. J. Numer. Methods Fluids 39(2), 99-120, (2002). · Zbl 1036.76051
[35] http://www.featflow.de/
[36] http://www-waterloo.ansys.com/cfx/
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.