Lattice Boltzmann Method For Single Temperature Radiation Diffusion Equations With Jump Coefficients

The radiation diffusion equation is an important part of the radiation fluid mechanics equations describing the inertial confinement fusion(ICF).In the past three decades, the lattice Boltzmann method has become an efficient numerical simulation method in computational fluid dynamics. Therefore, it's a very meaningful work for the study of solving single temperature radiation diffusion(STRD) equation by the lattice Boltzmann method. At present, some corresponding works have been done for the STRD equation with smooth variable coefficient. However, this research is lack for the STRD equation with jump coefficients. So, it is a valuable work to design effective lattice Boltzmann method for the STRD equation with jump coefficients.The main research work of this paper are as follows:Firstly, a one-dimensional lattice Boltzmann model of STRD equation with smooth variable coefficient is derived by using the Chapman-Enskog multi scale expansion technique. Furthermore, using the conditions of temperature continuation and thermal flux continuation at the interface, we propose a one-dimensional lattice Boltzmann model for the STRD equation with jump coefficients. Meanwhile, the numerical results show that the present method has second order accuracy. Secondly,a two-dimensional lattice Boltzmann model of STRD equation with smooth variable coefficients is given. Here, similarly with one-dimensional model, a two-dimensional lattice Boltzmann model is given for the STRD with jumps coefficient. Also, the numerical results show that it has second order accuracy.