A comparative study of immersed-boundary and interpolated bounce-back methods in LBE

Progress in Computational Fluid Dynamics

Volumn 8, Issue 1-4, 2008, Pages 156-167

  Peng, Yan ^a   Luo, Li Shi ^a  

^a OLD DOMINION UNIVERSITY   (United States)

Author keywords

Immersed boundary method; Interpolated bounce back; Lattice Boltzmann equation; LBE

Indexed keywords

BOLTZMANN EQUATION; BOUNDARY CONDITIONS; CIRCULAR CYLINDERS; COMPUTATIONAL EFFICIENCY; REYNOLDS NUMBER; TURBULENT FLOW;

COMPARATIVE STUDIES; COMPUTATIONAL COSTS; IMMERSED BOUNDARY METHODS; INTERPOLATED BOUNCE-BACK; LATTICE BOLTZMANN EQUATIONS; NO-SLIP BOUNDARY CONDITIONS; NUMERICAL ACCURACY; SECOND-ORDER RATES;

NUMERICAL METHODS;

EID: 56349098815     PISSN: 14684349     EISSN: None     Source Type: Journal    
DOI: 10.1504/PCFD.2008.018086     Document Type: Article

References (43)

1. Bouzidi, M., Firdaouss, M. and Lallemand, P. (2001) 'Momentum transfer of a Boltzmann-lattice fluid with boundaries', Phys. Fluids, Vol. 13, No. 11, pp.3452-3459.
2. Chen, H., Chen, S. and Matthaeus, H.W. (1992) 'Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method', Phys. Rev. A, Vol. 45, No. 8, pp.R5339-R5342.
3. Chen, S., Martinez, D. and Mei, R. (1996) 'On boundary conditions in lattice Boltzmann method', Phys. Fluids, Vol. 8, No. 9, pp.2527-2536.
4. Crouse, B., Rank, E., Krafczyk, M. and Tölke, J. (2003) 'A LB based approach for adaptive flow simulations', Int. J. Mod. Phys. C, Vol. 17, Nos. 1-2, pp.109-112.
5. d'Humières, D. (1992) 'Generalized lattice-Boltzmann equations', in Shizgal, B.D. and Weave, D.P. (Eds.): Rarefied Gas Dynamics: Theory and Simulations, Vol. 159 of Prog. Astronaut. Aeronaut., AIAA, Washington DC, pp.450-458.
6. d'Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P. and Luo, L-S. (2002) 'Multiple-relaxation-time lattice Boltzmann models in three-dimensions', Philos. Trans. R. Soc. Lond. A, Vol. 360, No. 1792, pp.437-451.
7. Feng, Z. and Michaelides, E. (2004) 'The immersed boundarylattice Boltzmann method for solving fluid-particles interaction problems', J. Comput. Phys., Vol. 195, No. 2, pp.602-628.
8. Feng, Z. and Michaelides, E. (2005) 'Proteus: A direct forcing method in the simulations of particulate flows', J. Comput. Phys., Vol. 202, No. 1, pp.20-51.
9. Filippova, O. and Hänel, D. (1998) 'Grid refinement for lattice-BGK models', J. Comput. Phys., Vol. 147, No. 1, pp.219-228.
10. Ginzburg, I. (2005a) 'Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation', Adv. Water Res., Vol. 28, No. 11, pp.1171-1195.
11. Ginzburg, I. (2005b) 'Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic-dispersion equations', Adv. Water Res., Vol. 28, No. 11, pp.1196-1216.
12. Ginzburg, I. (2006) 'Variably saturated flow with the anisotropic lattice Boltzmann methods', Comput. Fluids, Vol. 35, Nos. 8-9, pp.831-848.
13. Ginzburg, I. (2007) 'Lattice Boltzmann modeling with discontinuous collision components: Hydrodynamic and advection-diffusion equations', J. Stat. Phys., Vol. 126, No. 1, pp.157-206.
14. Ginzbourg, I. and Adler, P. (1994) 'Boundary flow condition analysis for the three-dimensional lattice Boltzmann method', J. Phys. II, Vol. 4, No. 2, pp.191-214.
15. Ginzburg, I. and d'Humières, D. (1996) 'Local second-order boundary methods for lattice Boltzmann models', J. Stat. Phys., Vol. 84, Nos. 5-6, pp.927-971.
16. Ginzburg, I. and d'Humières, D. (2003) 'Multireflection boundary conditions for lattice Boltzmann models', Phys. Rev. E, Vol. 68, No. 6, p.066614.
17. He, X. and Luo, L-S. (1997) 'A priori derivation of the lattice Boltzmann equation', Phys. Rev. E, Vol. 55, No. 6, pp.R6333-R6336.
18. He, X., Luo, L-S. and Dembo, M. (1996) 'Some progress in lattice Boltzmann method: Part I. Nonuniform mesh grids', J. Comput. Phys. Vol. 129, No. 2, pp.357-363.
19. He, X., Luo, L-S. and Dembo, M. (1997) 'Some progress in lattice Boltzmann method: Enhancement of Reynolds number in simulations', Physica A, Vol. 239, Nos. 1-3, pp.276-285.
20. Junk, M., Klar, A. and Luo, L-S. (2005) 'Asymptotic analysis of the lattice Boltzmann equation', J. Comput. Phys., Vol. 210, No. 2, pp.676-704.
21. Kim, J., Kim, D. and Choi, H. (2001) 'An immersed-boundary finite-volume method for simulations of flow in complex geometries', J. Comput. Phys., Vol. 171, No. 1, pp.132-150.
22. Ladd, A.J.C. (1994a) 'Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation', J. Fluid Mech., Vol. 271, pp.285-309.
23. Ladd, A.J.C. (1994b) 'Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results', J. Fluid Mech., Vol. 271, pp.311-339.
24. Ladd, A.J.C. and Verberg, R. (2001) 'Lattice Boltzmann simulations of particle-fluid suspensions', J. Stat. Phys., Vol. 104, Nos. 5-6, pp.1191-1251.
25. Lai, M.C. and Peskin, C.S. (2000) 'An immersed boundary method with formal second-order accuracy and reduced numerical viscosity', J. Comput. Phys., Vol. 160, No. 2, pp.705-719.
26. Lallemand, P. and Luo, L-S. (2000) 'Theory of the lattice Boltzmann method: Dispersion, isotropy, Galilean invariance and stability', Phys. Rev. E, Vol. 61, No. 3, pp.6546-6562.
27. Lallemand, P. and Luo, L-S. (2003) 'Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions', Phys. Rev. E, Vol. 63, No. 3, p.036706.
28. Lallemand, P., Luo, L-S. and Peng, Y. (2007) 'A lattice Boltzmann front-tracking method for interface dynamics with surface tension in two-dimensions', J. Comput. Phys., Vol. 226, No. 2, pp.1367-1384.
29. Li, Z. and Ito, K. (2006) The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains, SIAM, Philadelphia.
30. Mei, R., Luo, L-S., Lallemand, P. and d'Humières, D. (2006) 'Consistent initial conditions for lattice Boltzmann simulations', Comput. Fluids, Vol. 35, Nos. 8-9, pp.855-862.
31. Mittal, R. and Iaccarino, G. (2005) 'Immersed boundary methods', Annu. Rev. Fluid Mech., Vol. 37, pp.239-261.
32. Pan, C., Luo, L-S. and Miller, C.T. (2006) 'An evaluation of lattice Boltzmann schemes for porous medium flow simulation', Comput. Fluids Vol. 35, No. 8, pp.898-909.
33. Peskin, C.S. (1977) 'Numerical analysis of blood flow in the heart', Phys. Fluids, Vol. 13, No. 3, pp.3452-3459.
34. Peskin, C.S. (2002) 'The immersed boundary method', Acta Numer., Vol. 11, pp.479-517.
35. Qi, D. and Luo, L-S. (2002) 'Transitions in rotations of a nonspherical particle in a three-dimensional moderate Reynolds number Couette flow', Phys. Fluids, Vol. 14, No. 12, pp.4440-4443.
36. Qi, D. and Luo, L-S. (2003) 'Rotational and orientational behaviour of a three-dimensional spheroidal particles in Couette flow', J. Fluid Mech., Vol. 477, pp.201-213.
37. Qi, D., Luo, L-S., Aravamuthan, R. and Strieder, W. (2002) 'Lateral migration and orientation of elliptical particles in poiseuille flows', J. Stat. Phys., Vol. 107, Nos. 1-2, pp.102-120.
38. Qian, Y.H., d'Humières, D. and Lallemand, P. (1992) 'Lattice BGK models for Navier-Stokes equation', Europhys. Lett., Vol. 17, No. 6, pp.479-484.
39. Schäfer, M. and Turek, S. (1996) 'Benchmark computations of laminar flow around a cylinder', in Hirschel, E.H. (Ed.): Notes in Numerical Fluid Mechanics: Flow Simulations with High Performance Computers II, Vieweg, Braunschweig, Germany, pp.547-566.
40. Skordos, P.A. (1993) 'Initial and boundary conditions for the lattice Boltzmann method', Phys. Rev. E, Vol. 48, No. 6, pp.4823-4842.
41. Tölke, J., Freudiger, S. and Krafczyk, M. (2006) 'An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations', Comput. Fluids, Vol. 35, Nos. 8-9, pp.820-830.
42. Tyagi, M. and Acharya, S. (2005) 'Large eddy simulation of turbulent flows in complex and moving rigid geometries using the immersed boundary method', Int. J. Numer. Meth. Fluids, Vol. 48, No. 7, pp.691-722.
43. Yu, D., Mei, R., Luo, L-S. and Shyy, W. (2003) 'Viscous flow computations with the method of lattice Boltzmann equation', Prog. Aerospace Sci., Vol. 39, No. 5, pp.329-367.