Lattice Boltzmann Method For Diffusion Equation With Discontinuous Coefficients

Diffusion equation with discontinuous coefficients is widely involved in engineer-ing field,so numerical solution of the equation is extremely useful and meaningful.In the past three decades, the lattice Boltzmann method has become an important numerical method in computational fluid dynamics. In this paper, the lattice Boltz-mann method for the diffusion equation with discontinuous coefficients is studied,which is a valuable work. The main content and innovations of the paper are given as following: Firstly, an one-dimensional lattice Boltzmann model of diffusion equar tion with smooth coefficients is derived by using the Chapman-Enskog multi-scale expansion technique; Furthermore,using the conditions of solution continuation and flux continuation at the interface, we propose an one-dimensional lattice Boltz-mann model for the diffusion equation with discontinuous coefficients; The present method can well be used to solve the diffusion equation with strongly discontin-uous coefficients including piecewise constant coefficients and variable coefficients,and the numerical results show that the present method has second order accu-racy; Secondly, a two-dimensional lattice Boltzmann model of diffusion equation with smooth coefficients is derived, which is similar to the one-dimensional model.However, based on this model, it is difficult to give a lattice Boltzmann method for the two-dimensional diffusion equation with discontinuous coefficients; For this,a simplified lattice Boltzmann model is proposed. The lattice Boltzmann method based on this model is two order accuracy. Furthermore, using the conditions of solution continuation and flux continuation at the interface, the lattice Boltzmann method is proposed for the two-dimensional diffusion equation with discontinuous coefficients, and the numerical results show that it has second order accuracy.