晶格波茲曼法（Lattice Boltzmann Method）是以微觀的角度來計算具有黏滯力的不可壓縮流場。本文主要除了使用常見的單一鬆弛時間晶格波茲曼法外，另外還包含有限差分下的晶格波茲曼法，以及配合沉浸邊界的晶格波茲曼法。
在晶格波茲曼法中，分別介紹開放、固體邊界和二階曲線邊界的處理方法。由於均勻格點無法靈活地運用在各種曲線邊界下，因此發展了在有限差分下的晶格波茲曼法。在此方法中，計算格點可以彈性使用各種適合於物體邊界的曲線不均勻格點。
沉浸邊界晶格波茲曼法，是組合並利用沉浸邊界法和晶格波茲曼法所擁有的特點。利用此沉浸邊界晶格波茲曼法，來探討流場中粒子受到周圍流場作用力後的運動行為，以及兩顆和多顆粒子在流場中對於流體與粒子以及粒子與粒子交互作用後的運動行為。

The Lattice Boltzmann Method（LBM）is a microscopic-based approach for solving the incompressible viscous flows. The numerical methods include the single relaxation time lattice Boltzmann method, the finite difference-based lattice Boltzmann method, and the immersed boundary-lattice Boltzmann method.
Three boundary conditions, open boundary, solid boundary and solid second-order curve boundary are applied in the LBM to handle the flow over a solid body. The finite difference-based lattice Boltzmann method using body-fitted curvilinear coordinates is invented to simulate the flows over complex configuration.
To study the fluid-particle interaction problems, The immersed boundary-lattice Boltzmann method is developed. The flow velocity field and particles are solved by adding a force density term into the lattice Boltzmann equation.

A.L.F. Lima E Silva, A. Silveira-Neto, J.J.R. Damasceno. Numerical simulation of two-dimensional flow over a circular cylinder using the immersed boundary method. J. Comput. Phys., 189, n.2, 351-370 (2004).
Behrend, Q., Solid-fluid boundaries in particle suspension simulation via the lattice boltzmann method, Phys. Rev. E., 52, 1164-1175 (1995).
Beyer RP, A computational model of the cochlea using the immersed boundary method, J. Comput. Phys., 98, 145–162 (1992).
Bouzidi, M., d’Humieres, D., Lallemand, P., Luo, L. -5, Lattice Boltzmann equation on a two-dimensional rectangular grid, J. Comp. Phys., 172, 704-7, 17 (2001).
Bouzidi, M., dFirdaouss, M., Lallemand, P., Momentum transfer of a lattice Boltzmann fluid with boundaries. Phys. Fluids, 13, 3452-3459 (2001).
Broadwell, J. E., Study of rarefied shear flow by the discrete velocity method, J. Fluid Mech., 19, 401-404 (1964).
Chen, H., Chen, S., Matthaeus, W. H., Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method, Phys. Rev. A,. 45, R5339-R5342 (1992).
Comubert, R., Dhumieres, D., Leverniore, D., A Knudsen layer theory for lattice gases, PhysicaD., 47, 291-297 (1991).
Dazhi Yu, Renwi Mei, Li-Shi Luo, Wei Shyy. Viscous flow computations with the method of lattice Boltzmann equation, Prog. Aerospace Sci., 39, 329-367 (2003).
Feng Z-G, Michaelides E.E., Hydrodynamic force on sheres in cylindrical and prismatic enclosures, Int. J. Multiphase Flow, 28, 479-496 (2002).
Feng Z-G, Michaelides E.E., Interparticle force and lift on a particle attached to a solid boundary in suspension flow, Phys. Fluids, 24, 49-60 (2002).
Feng Z-G, Michaelides E.E., The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems, J. Comput. Phys., 195, 602-628 (2004).
Filippova, O., Hanel, D. Grid refinement for lattice-BGK models, J. Comp. Phys., 147, 219-228 (1998).
Frisch, U., Hasslacher, B., Pomeau, Y., Lattice-Gas Automata for the Navier-Stokes Equations, Phys. Rev. Lett., 56, 1505-1508 (1986).
Glowinski R., Pan T.-W., Hesla T. I., Joseph D. D. and Periaux J., A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: Application to particulate flow, J. Comput. Phys., 169, 363-427 (2001).
Gmna, D.W., Lattice methods for modeling hydrodynamics, Ph.D. Dissertation, Colorado State University, (1993).
Hardy, J., de Pazzis, 0., Pomeau, Y., Molecular dynamics of a classical lattice gas: transport properties and time coffelation functions, Phys. Rev. A., 13, 1949-1961 (1976).
He, X., Luo, L.-S., A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, 55, R6333-R6336 (1997a).
He, X., Luo, L.-S., Theory of the lattice Boltzrnann equation: From Boltzmann equation to lattice Boltzmann equation, Phys. Rev. E, 56, 6811-6817 (1997b).
Higuera, F. J., Jimenez, J., Boltzmann approach to lattice gas simulations, Europhys. Lett., 9, 663-668 (1989).
Hofler K., Schwarzer S., Navier-Stokes simulation with constraint force: finite-difference method for particle-laden flow and complex geometries, Phys. Rev. E, 61, 7146-7160 (2000).
Hou S., Hou Q., Chen S., Doolen G., and Cogley AC, Simulation of cavity flow by the lattice Boltzmann method, J. Comput. Phys., 118, 329 (1995).
Hudong Chen, Shiyi Chen, and William H. Matthaeus, Recovery of the navier-stokes equations using a lttice-gas boltzmann method, Phys. Rev. A., 45, 5339-5342 (1992).
Ladd, A. J. C., Numerical simulation of particular suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation, J. Fluid Mech., 271, 285-309 (1994a).
Ladd, A. J. C., Numerical simulation of particular suspensions via a discretized Boltzmann equation. Part 2. Numerical results, J. Fluid Mech., 271, 311-339 (1994b).
McNamara, G., Alder, B. J., Analysis of the lattice Boltzmann treatment of hydrodynamics, Physica A, 194, 218-228 (1993).
McNamara, G., Zanetti, G., Use of the Boltzmann equation to simulate lattice-gas automata, Phys. Rev. Lett., 61, 2332-2335 (1988).
Mei, R., Luo, L.-S., Shyy, W., An accurate curved boundary treatment in the lattice Boltzmann method, J. Comp. Phys., 155, 307-330 (1999).
Peskin C.S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 220-252 (1977).
Qian, Y., d’Humieres, D., Lallemand, P., Recovery of Navier- Stokes equations using a lattice-gas Boltzmann method. Europhys. Lett., 17, 479- (1992).

Renwei Mei, Li-Shi Luo, and Wei Shyy. An accurate curved boundary treatment in the lattice Boltzmann method, J. Comput. Phys., 155, 307 (1999).
Renwei Mei , Wei Shyy, On the finite difference-based lattice Boltzmann method in curvilinear coordinates, J. Comput. Phys., 143, n.2, 426-448 (1998).
Skordos, P. A., Initial and boundary conditions for the lattice Boltzmann method, Phys. Rev. E., 48, 4823-4842 (1992).
Succi S., Lattice Boltzmann Equation: Failure or Success?, Physica A, 240, 221, (1997).
Wu J.-S. and Shao Y.-L., Simulation of Flow Past a Square Cylinder by Parallel Lattice Boltzmann Method Using Multi-Relaxation-Time Scheme , Journal of Mech., (2006).
Xiaoyi He , Gary Doolen, Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder, J. Comput. Phys., 134, 306-315 (1997).
Xiaoyi He, Gary D. Doolen, T. Clark. Comparison of the Lattice Boltzmann Method and the Artificial Compressibility Method for Navier-Stokes Equations, J. of Comput. Phys., 179, 439-451 (2002).

Ziegler D.P., Boundary conditions for lattice Boltzmann simulations, J. Stat. Phys., 71, 1171-1177 (1993).
Zou, Q., He, X., On pressure and velocity boundary conditions for the lattice Boltzrnann BGK model, Phys. Fluids, 9, 1591-1598 (1997).