×

zbMATH — the first resource for mathematics

A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows. (English) Zbl 1181.76111
Summary: A momentum exchange-based immersed boundary-lattice Boltzmann method is presented in this Letter for simulating incompressible viscous flows. This method combines the good features of the lattice Boltzmann method (LBM) and the immersed boundary method (IBM) by using two unrelated computational meshes, an Eulerian mesh for the flow domain and a Lagrangian mesh for the solid boundaries in the flow. In this method, the non-slip boundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation (LBE). Unlike the conventional IBM using the penalty method with a user-defined parameter or the direct forcing scheme based on the Navier-Stokes (NS) equations, the forcing term is simply calculated by the momentum exchange of the boundary particle density distribution functions, which are interpolated by the Lagrangian polynomials from the underlying Eulerian mesh. Numerical examples show that the present method can provide very accurate numerical results.

MSC:
76M28 Particle methods and lattice-gas methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] McNamara, G.R.; Zanetti, G., Phys. rev. lett., 61, 2332, (1988)
[2] Qian, Y.H.; d’Humières, D.; Lallemand, P., Europhys. lett., 17, 479, (1992)
[3] Chen, S.; Chen, H.; Martinez, D.; Matthaeus, W.H., Phys. rev. lett., 67, 3776, (1991)
[4] Chen, S.; Dawson, S.P.; Doolen, G.D.; Janecky, D.R.; Lawniczak, A., Comput. chem. eng., 19, 617, (1995)
[5] Chen, S.; Doolen, G.D., Annu. rev. fluid mech., 30, 329, (1998)
[6] Succi, S., The lattice Boltzmann equation for fluid dynamics and beyond, (2001), Oxford Univ. Press New York · Zbl 0990.76001
[7] Yu, H.; Luo, L.-S.; Girimaji, S.S., J. comput. eng. sci., 3, 73, (2002)
[8] He, X.; Zou, Q.; Luo, L.-S.; Dembo, M., J. stat. phys., 87, 115, (1997)
[9] Cornubert, R.; d’Humières, D.; Levermore, D., Physica D, 47, 241, (1991)
[10] Filippova, O.; Hänel, D., J. comput. phys., 147, 219, (1998)
[11] Mei, R.; Luo, L.-S.; Shyy, W., J. comput. phys., 155, 307, (1999)
[12] Bouzidi, M.; Firdaouss, M.; Lallemand, P., Phys. fluids, 13, 3452, (2001)
[13] Ladd, A.J.C., J. fluid mech., 271, 285, (1994)
[14] He, X.; Doolen, G.D., Phys. rev. E, 56, 434, (1997)
[15] He, X.; Doolen, G.D., J. comput. phys., 134, 306, (1997)
[16] Shu, C.; Chew, Y.T.; Niu, X.D., Phys. rev. E, 64, 045701, (2001)
[17] Shu, C.; Niu, X.D.; Chew, Y.T., Phys. rev. E, 65, 036708, (2002)
[18] Niu, X.D.; Chew, Y.T.; Shu, C., J. comput. phys., 188, 176, (2003)
[19] Peskin, C.S., J. comput. phys., 25, 220, (1977)
[20] Glowinski, R.; Pan, T.-W.; Hesla, T.I.; Joseph, D.D.; Periaux, J., J. comput. phys., 169, 363, (2001)
[21] Höfler, K.; Schwarzer, S., Phys. rev. E, 61, 7146, (2000)
[22] Patankar, N.A.; Singh, P.; Joseph, D.D.; Glowinski, R.; Pan, T.-W., Int. J. multiphase flow, 26, 1509, (2000)
[23] Feng, Z.G.; Michaelides, E.E., J. comput. phys., 195, 602, (2004)
[24] Feng, Z.G.; Michaelides, E.E., J. comput. phys., 202, 20, (2005)
[25] d’Humières, D., Generalized lattice Boltzmann equations, (), 450
[26] Aidun, C.K.; Lu, Y., J. stat. phys., 81, 49, (1995)
[27] Inamuro, T.; Maeba, K.; Ogino, F., Int. J. multiphase flow, 26, 1981, (2000) · Zbl 1137.76620
[28] Dennis, S.C.R.; Chang, G.Z., J. fluid mech., 42, 471, (1980)
[29] Fornberg, B., J. fluid mech., 98, 819, (1980)
[30] Feng, J.; Hu, H.H.; Joseph, D.D., J. fluid mech., 277, 271, (1994) · Zbl 0876.76040
[31] Lallemand, P.; Luo, L.-S., Phys. rev. E, 61, 6546, (2000)
[32] Ginzburg, I.; Adler, P.M., J. phys. II, 4, 191, (1994)
[33] Guo, Z.; Zheng, C.; Shi, B., Phys. rev. E, 65, 046308, (2002)
[34] Ladd, A.J.C.; Verberg, R., J. stat. phys., 104, 1191, (2001)
[35] Lallemand, P.; Luo, L.-S., Phys. rev. E, 68, 3, 036706, (2003)
[36] Peskin, C.S., Acta numer., 11, 479, (2002)
[37] Luo, L.S., Phys. rev. lett., 81, 1618, (1998)
[38] Luo, L.S., Phys. rev. E, 62, 4982, (2000)
[39] Ladd, A.J.C.; Frenkel, D., Phys. fluids A, 2, 1921, (1990)
[40] Fortes, A.; Joseph, D.D.; Lundgren, T.S., J. fluid mech., 177, 467, (1987)
[41] N.A. Patankar, A formulation for fast computations of rigid particulate flows, Annual Research Briefs-2001, Center for Turbulent Research, Stanford University, 2001
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.