A new scheme for source term in LBGK model for convection-diffusion equation

A new scheme for source term in the lattice BGK (LBGK) model for convection-diffusion equation is proposed. Unlike the models proposed previously, the present scheme only requires the source term in order of the Knudsen number by adding a differential operator of the source term to the evolution equation. The scheme can be applied to reaction-diffusion systems directly. Numerical results are found to be in excellent agreement with the analytical solutions. It is also found that the numerical accuracy of the present scheme is generally much better than that of the existing models.

[1]  施保昌,et al.  Lattice Bhatnagar—Gross—Krook Simulations of Turbulent Natural Convection in a Cavity , 2002 .

[2]  Wang Neng-Chao,et al.  Lattice Bhatnagar-Gross-Krook Simulations of Turbulent Natural Convection in a Cavity , 2002 .

[3]  Sauro Succi,et al.  Recent Advances in Lattice Boltzmann Computing , 1995 .

[4]  John W. Crawford,et al.  A lattice BGK model for advection and anisotropic dispersion equation , 2002 .

[5]  Peter M. A. Sloot,et al.  Lattice dependence of reaction-diffusion in lattice Boltzmann modeling , 2000 .

[6]  Yue-Hong Qian,et al.  Simulating thermohydrodynamics with lattice BGK models , 1993 .

[7]  闫广武.  A lattice Boltzmann equation for waves , 2000 .

[8]  R. Sman,et al.  Convection-Diffusion Lattice Boltzmann Scheme for Irregular Lattices , 2000 .

[9]  P. Lallemand,et al.  Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Shiyi Chen,et al.  Lattice Boltzmann computations for reaction‐diffusion equations , 1993 .

[11]  Zhaoli Guo,et al.  Lattice Boltzmann model for incompressible flows through porous media. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  I. Ginzburg.  Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation , 2005 .

[13]  He Zhenmin,et al.  EMC effect on p-A high energy collisions , 1991 .

[14]  Byron Goldstein,et al.  Lattice Boltzmann Simulation of Diffusion-Convection Systems with Surface Chemical Reaction , 2000 .

[15]  Z. L. Guo,et al.  Fully Lagrangian and Lattice Boltzmann Methods for the Advection-Diffusion Equation , 1999, J. Sci. Comput..

[16]  Sauro Succi,et al.  A multi-relaxation lattice kinetic method for passive scalar diffusion , 2005 .

[17]  郑楚光,et al.  Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method , 2005 .

[18]  Zhong Yijun,et al.  Lattice Boltzmann Method for Diffusion-Reaction-Transport Processes in Heterogeneous Porous Media , 2004 .

[19]  A. Ladd,et al.  Lattice-Boltzmann Simulations of Particle-Fluid Suspensions , 2001 .

[20]  Chenghai Sun,et al.  Lattice-Boltzmann models for high speed flows , 1998 .

[21]  B. Shi,et al.  Discrete lattice effects on the forcing term in the lattice Boltzmann method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Shiyi Chen,et al.  Lattice Boltzmann method for three-dimensional moving particles in a Newtonian fluid , 2004 .

[23]  B. Shi,et al.  Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method , 2002 .