Institute of Applied Physics and Computational Mathematics, China
This presentation consists of three parts. In the first part we summarize the progress of Lattice Boltzmann (LB) modeling high speed fluids in our group in recent years. Main content includes the development of the Single-Relaxation-Time (SRT) model and the Multiple-Relaxation-Time (MRT) model. Compared with SRT, the MRT is a new framework from the view of physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The two kinds of models are complementary from the sides of convenience and applicability. The second and the third parts are for LB applications. The second part is for application in modeling hydrodynamic instabilities and the third is for modeling combustions phenomena. To show the merit of LB models over the traditional methods based on hydrodynamics, we show some results on the macroscopic effects of the systems due to deviating from thermodynamic equilibriums. For the hydrodynamic instability problem, we focus on the non-equilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed and consequently the Richtmyer-Meshkov(RM) instability occurs. For the combustion phenomena, we focus on the reaction zone to study the non-equilibrium effects. A method to qualitatively recover the actual distribution function from the results of discrete distribution function is illustrated. These results deepen our understanding of the mechanical and material interfaces from a more fundamental point of view, and provide valuable information to improve the physical modeling at a macroscopic level.