Lattice Boltzmann model for compressible fluid on a square lattice

A two-level four-direction lattice Boltzmann model is formulated on a squar e lattice to simulate compressible flows with a high Mach number. The parti cle velocities are adaptive to the mean velocity and internal energy. There fore, the mean flow can have a high Mach number. Due to the simple form of the equilibrium distribution, the 4th order velocity tensors are not involv ed in the calculations. Unlike the standard lattice Boltzmann model, no spe cial treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-E nskog method from the BGK Boltzmann equation. The model can be easily exten ded to three-dimensional cubic lattices. Two-dimensional shock-wave propaga tion was simulated.