摘要Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background. It is demonstrated that the symmetry inherent in Navier--Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation (LBE), especially for shock calculation. Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.
Abstract：Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background. It is demonstrated that the symmetry inherent in Navier--Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation (LBE), especially for shock calculation. Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.
RAN Zheng. Note on Invariance of One-Dimensional Lattice-Boltzmann Equation[J]. 中国物理快报, 2007, 24(12): 3332-3335.
RAN Zheng. Note on Invariance of One-Dimensional Lattice-Boltzmann Equation. Chin. Phys. Lett., 2007, 24(12): 3332-3335.
[1] Frisch U, Hasslacher B and Pomeau Y 1986 Phys. Rev.Lett. 56 1505 [2] Benzi R, Succi S and Vergassola M 1992 Phys. Rep. 222 147 Ladd A J C 1994 J. Fluid Mech. 271 285 Qian Y H, Lebowitz J and Orszag S 1995 J. Sat. Phys. 81 1 Qian Y H, Succi S and Orszag S 1995 Ann. Rev. Comput. Phys. 3 195 Chen S and Doolen G D 1998 Ann. Rev. Fluid Mech. 30 329 [3] Shan X, Yu X and Chen H 2006 J. Fluid Mech. 550 413 [4] Chen H, Chen S and Matthaeus W H 1992 Phys. Rev. A 45 R5339 [5] Karlin I V, Gorban A N, Succi S and Boffi V 1998 Phys.Rev. Lett. 81 6 [6] Qian Y H, d'Humieres D and Lallemand P 1985 Advances inKinetic Theory and Continuum Mechanics ed Gatignol R and Soubbaramayer(Berlin: Springer) p 127 [7] Qian Y H, d'Humieres D and Lallemand P 1992 Europhys.Lett. 17 479 [8] Succi S, Karlin I V and Chen H 2002 Rev. Mod. Phys. 74 1203 [9] Qu K, Shu C and Chew Y T 2007 Phys. Rev. E 75 036706 [10] Olver P J 1986 Applications of Lie Group toDifferential Equations (New York: Springer) [11] Shokin Yu I 1983 The Method of DifferentialApproximation. (New York: Springer) [12] Dorodnitsyn V A 1991 J. Sov. Math. 55 1490 [13] Yanenko N N and Shokin Y I 1976 Am. Math. Soc.Transl. 104 259 [14] Ran Z 2005 Chin. Quart. Mechanics. 26 650 (in Chinese) [15] Ran Z 2007 SIAM J. Numer. Anal. (accepted)
2007, Vol. 24 
