  In this mini-review we summarize the progress of Lattice Boltzmann(LB)
modeling and simulating compressible flows in our group in recent years. Main
contents include (i) Single-Relaxation-Time(SRT) LB model supplemented by
additional viscosity, (ii) Multiple-Relaxation-Time(MRT) LB model, and (iii) LB
study on hydrodynamic instabilities. The former two belong to improvements of
physical modeling and the third belongs to simulation or application. The
SRT-LB model supplemented by additional viscosity keeps the original framework
of Lattice Bhatnagar-Gross-Krook (LBGK). So, it is easier and more convenient
for previous SRT-LB users. The MRT-LB is a completely new framework for
physical modeling. It significantly extends the range of LB applications. The
cost is longer computational time. The developed SRT-LB and MRT-LB are
complementary from the sides of convenience and applicability.
