A novel lattice Boltzmann model for the Poisson equation

He, 2000, Lattice Boltzmann simulation of electrochemical systems, Comput. Phys. Commun., 129, 158, 10.1016/S0010-4655(00)00103-X Guo, 2005, A lattice Boltzmann algorithm for electro-osmotic flows in microfluidic devices, J. Chem. Phys., 122, 144907, 10.1063/1.1874813 Wang, 2006, Lattice Poisson–Boltzmann simulations of electro-osmotic flows in microchannels, J. Colloid. Interface Sci., 296, 729, 10.1016/j.jcis.2005.09.042 Chai, 2007, Simulation of electro-osmotic flow in microchannel with lattice Boltzmann method, Phys. Lett. A, 364, 183, 10.1016/j.physleta.2006.12.006 Siyyam, 2001, An accurate solution of the Poisson equation by the finite difference-Chebyshev-Tau method, Appl. Math. Mech., 22, 0935, 10.1007/BF02436392 Boschitsch, 2004, Hybrid boundary element and finite difference method for Solving the Nonlinear Poisson–Boltzmann equation, J. Comput. Chem., 25, 935, 10.1002/jcc.20000 Cai, 2006, A finite element method using singular functions for Poisson equations: mixed boundary conditions, Comput. Methods Appl. Mech. Engrg., 195, 2635, 10.1016/j.cma.2005.06.004 Kikuchi, 2007, Remarks on a posteriori error estimation for finite element solutions, J. Comput. Appl. Math., 199, 329, 10.1016/j.cam.2005.07.031 Liao, 1998, General boundary element method for Poisson equation with spatially varying conductivity, Eng. Anal. Bound. Elem., 21, 23, 10.1016/S0955-7997(97)00104-5 Benzi, 1992, The lattice Boltzmann equation: theory and applications, Phys. Rep., 222, 147, 10.1016/0370-1573(92)90090-M Chen, 1998, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 329, 10.1146/annurev.fluid.30.1.329 Chen, 2003, Extended Boltzmann kinetic equation for turbulent flows, Science, 301, 633, 10.1126/science.1085048 Frisch, 1986, Lattice-gas automata for the Navier–Stokes equation, Phys. Rev. Lett., 56, 1505, 10.1103/PhysRevLett.56.1505 He, 1997, A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, 55, R6333, 10.1103/PhysRevE.55.R6333 Shan, 1998, Discretization of the velocity space in the solution of Boltzmann equation, Phys. Rev. Lett., 80, 65, 10.1103/PhysRevLett.80.65 Guo, 1999, Fully Lagrangian and lattice Boltzmann methods for the advection–diffusion equation, J. Sci. Comput., 14, 291, 10.1023/A:1023273603637 Deng, 2005, A new lattice Bhatnagar–Gross–Krook model for convection–diffusion equation with a source term, Chin. Phys. Lett., 22, 267, 10.1088/0256-307X/22/2/001 Chen, 1995, Lattice methods and their applications to reacting systems, Comput. Chem. Engrg., 19, 617, 10.1016/0098-1354(94)00072-7 Zhang, 2004, A lattice Boltzmann model and simulation of KdV–Burgers equation, Commun. Theor. Phys., 42, 281, 10.1088/0253-6102/42/2/281 Ma, 2005, A new lattice Boltzmann model for KdV–Burgers equation, Chin. Phys. Lett., 29, 2313 Z. Chai, B. Shi, L. Zheng, A unified lattice Boltzmann model for some nonlinear partial differential equations, Chaos Solitons Fractals, in press, doi:10.1016/j.chaos.2006.07.023. Yan, 2000, A lattice Boltzmann equation for waves, J. Comput. Phys., 161, 61, 10.1006/jcph.2000.6486 Hirabayashi, 2001, The lattice BGK model for the Poisson equation, JSME Int. J. Ser. B, 44, 45, 10.1299/jsmeb.44.45 Guo, 2000, Lattice BGK model for incompressible Navier–Stokes equation, J. Comput. Phys., 165, 288, 10.1006/jcph.2000.6616 Dawson, 1993, Lattice Boltzmann Computations for reaction–diffusion equations, J. Chem. Phys., 98, 1514, 10.1063/1.464316 Averbuch, 1997, On a fast direct elliptic solver by a modified Fourier method, Numer. Algorithms, 15, 287, 10.1023/A:1019106223154 Guo, 2002, Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chin. Phys., 11, 366, 10.1088/1009-1963/11/4/310 Banda, 2006, A stability notion for lattice Boltzmann equations, SIAM J. Sci. Comput., 27, 2098, 10.1137/040606211