[1]
|
Frisch, U., Hasslacher, B. and Pomeau, Y. (1986) Lattice Gas Automata for the Navier-Stokes Equations. Physical Review Letters, 56, 1505-1508. https://doi.org/10.1103/PhysRevLett.56.1505
|
[2]
|
Chen, S.Y. and Doolen, G.D. (1998) Lattice Boltzmann Method for Fluid Flows. Annual Review of Fluid Mechanics, 30, 329-364.
|
[3]
|
Succi, S. (2001) The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, New York.
|
[4]
|
Benzi, R., Succi, S. and Vergassola, M. (1992) The Lattice Boltzmann Equations: Theory and Applications. Physics Reports, 222, 147-197.
|
[5]
|
Ladd, A. (1994) Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation. Part II. Journal of Fluid Mechanics, 271, 311-339. https://doi.org/10.1017/S0022112094001783
|
[6]
|
Chen, S.Y., Chen, H.D., Martíınez, D. and Matthaeus, W. (1991) Lattice Boltzmann Model for Simulation of Magneto-Hydrodynamics. Physical Review Letters, 67, 3776-3779. https://doi.org/10.1103/PhysRevLett.67.3776
|
[7]
|
Gunstensen, A.K. (1992) Lattice-Boltzmann Studies of Multiphase Flow through Porous Media. MIT, Boston.
|
[8]
|
Chen, S.Y., Dawson, S.P., Doolen, G., Jenecky, D. and Lawniczak, A. (1995) Lattice Methods for Chemically Reacting Systems. Computers & Chemical Engineering, 19, 617-646.
|
[9]
|
Yan, G.W. (2000) A Lattice Boltzmann Equation for Waves. Journal of Computational Physics, 161, 61-69.
https://doi.org/10.1006/jcph.2000.6486
|
[10]
|
Yan, G.W. and Zhang, J.Y. (2009) A Higher-Order Moment Method of the Lattice Boltzmann Model for the Korteweg-de Vries Equation. Mathematics and Computers in Simulation, 79, 1554-1565.
|
[11]
|
Velivelli, A.C. and Bryden, K.M. (2006) Parallel Performance and Accuracy of Lattice Boltzmann and Traditional Finite Difference Methods for Solving the Unsteady Two Dimensional Burger’s Equation. Physica A, 362, 139-145.
|
[12]
|
Zhang, J.Y. and Yan, G.W. (2008) Lattice Boltzmann Methods for One and Two-Dimensional Burger’s Equation. Physica A, 387, 4771-4786.
|
[13]
|
Succi, S. (1993) Lattice Boltzmann Equation for Quantum Mechanics. Physica D, 69, 327-332.
|
[14]
|
Palpacelli, S. and Succi, S. (2007) Numerical Validation of the Quantum Lattice Boltzmann Scheme in Two and Three Dimension. Physical Review E, 75, Article ID: 066704. https://doi.org/10.1103/PhysRevE.75.066704
|
[15]
|
Zhong, L.H., Feng, S.D., Dong, P. and Gao, S.T. (2006) Lattice Boltzmann Schemes for the Nonlinear Schrodinger Equation. Physical Review E, 74, Article ID: 036704. https://doi.org/10.1103/PhysRevE.74.036704
|
[16]
|
Chai, Z.H. and Shi, B.C. (2007) A Novel Lattice Boltzmann Model for the Poisson Equation. Applied Mathematical Modelling, 32, 2050-2058.
|
[17]
|
Wang, M.R., Wang, J.K. and Chen, S.Y. (2007) Roughness and Cavitations Effect on Electro-Osmotic Flows in Rough Microchannels Using the Lattice Poisson-Boltzmann Methods. Journal of Computational Physics, 226, 836-851.
|
[18]
|
King, J.T. (1984) Introduction to Numerical Computation. McGraw-Hill Inc., New York.
|
[19]
|
Chapman, S. and Cowling, T.G. (1970) The Mathematical Theory of Non-Uniform Gas. Cambridge University Press, Cambridge.
|
[20]
|
Yan, G.W. and Yuan, L. (2000) Lattice Boltzmann Solver of Rössler Equation. Communications in Nonlinear Science & Numerical Simulation, 5, 64-68.
|