Lattice Boltzmann model for a class of convection–diffusion equations with variable coefficients

Brezis, 1998, Partial differential equations in the 20th century, Adv. Math., 135, 76, 10.1006/aima.1997.1713 Wazwaz, 2002 Cockburn, 1998, The lacal difcontinuous Galerkin method for time-dependent convection–diffusion systems, SIAM J. Numer. Anal., 35, 2440, 10.1137/S0036142997316712 Baligaa, 1980, A new finite-element formulation for convection–diffusion problems, Numer. Heat Transfer, 3, 393, 10.1080/01495728008961767 Gupta, 1984, A single cell high order scheme for the convection–diffusion equation with variable coefficients, Int. J. Numer. Methods Fluids, 4, 641, 10.1002/fld.1650040704 Kalita, 2002, A class of higher order compact schemes for the unsteady two-dimensional convectionCdiffusion equation with variable convection coefficients, Int. J. Numer. Methods Fluids, 38, 1111, 10.1002/fld.263 Angelini, 2013, A finite volume method on general meshes for a degenerate parabolic convection-reaction–diffusion equation, Numer. Math., 123, 219, 10.1007/s00211-012-0485-5 Benzi, 1992, The lattice Boltzmann equation: theory and applications, Phys. Rep., 222, 145, 10.1016/0370-1573(92)90090-M Zhang, 2011, Lattice Boltzmann method for microfluidics: models and applications, Microfluid. Nanofluid., 10, 1, 10.1007/s10404-010-0624-1 Inamuro, 2004, A lattice Boltzmann method for imcompressible two-phase flows with large density differences, J. Comput. Phys., 198, 628, 10.1016/j.jcp.2004.01.019 Swift, 1996, Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Phys. Rev. E, 54, 5041, 10.1103/PhysRevE.54.5041 Alexander, 1993, Lattice Boltzmann thermohydrodynamics, Phys. Rev. E, 47, R2249, 10.1103/PhysRevE.47.R2249 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 Dawson, 1993, Lattice Boltzmann computations for reaction–diffusion equations, J. Chem. Phys., 98, 1514, 10.1063/1.464316 Chopard, 2009, The lattice Boltzmann advection–diffusion model revisited, Eur. Phys. J. Spec. Top., 171, 245, 10.1140/epjst/e2009-01035-5 Shi, 2009, Lattice Boltzmann model for nonlinear convection–diffusion equations, Phys. Rev. E, 79, 016701, 10.1103/PhysRevE.79.016701 Ginzburg, 2005, Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation, Adv. Water Resour., 28, 1171, 10.1016/j.advwatres.2005.03.004 Chai, 2013, Lattice Boltzmann model for the convection–diffusion equation, Phys. Rev. E, 87, 063309, 10.1103/PhysRevE.87.063309 Xiang, 2012, Modified lattice Boltzmann scheme for nonlinear convection diffusion equations, Int. J. Nonlinear Sci. Numer. Simul., 17, 2415, 10.1016/j.cnsns.2011.09.036 Shi, 2009, Lattice Boltzmann model for high-order nonlinear partial differential equations, Phys. Comp., 10 Wu, 2012, A lattice Boltzmann model for the Fokker–Planck equation, Commun. Nonlinear Sci. Numer. Simul., 17, 2776, 10.1016/j.cnsns.2011.11.032 Guo, 2002, Non-equilibrium extrapolation method for velocity and pressure boundary conditionsin the lattice Boltzmann method, Chin. Phys., 11, 366, 10.1088/1009-1963/11/4/310