Abstract： A two-level four-direction lattice Boltzmann model is formulated on a square lattice to simulate compressible flows with a high Mach number. The particle velocities are adaptive to the mean velocity and internal energy. Therefore, 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 involved in the calculations. Unlike the standard lattice Boltzmann model, no special treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-Enskog method from the BGK Boltzmann equation. The model can be easily extended to three-dimensional cubic lattices. Two-dimensional shock-wave propagation was simulated.
SUN Cheng-Hai. Lattice Boltzmann Model for Compressible Fluid on a Square Lattice[J]. 中国物理快报, 2000, 17(10): 743-745.
SUN Cheng-Hai. Lattice Boltzmann Model for Compressible Fluid on a Square Lattice. Chin. Phys. Lett., 2000, 17(10): 743-745.
2000, Vol. 17 
