Finite-Difference-Based Lattice Boltzmann Method for Inviscid Compressible Flows

A finite-difference-based lattice Boltzmann model, employing the 2-D, 9-velocity square (D2Q9) lattice for the compressible Euler equations, is presented. The model is constructed by allowing the particles to possess both kinetic and thermal energies. Such a lattice structure can represent both incompressible and compressible flow regimes. In the numerical treatment, to attain desirable accuracy, the total-variation-diminishing (TVD) scheme is adopted with either the minmod function or a second-order corrector as the flux limiter. The model can treat shock/expansion waves as well as contact discontinuity. Both one- and two-dimensional test cases are computed, and the results are compared with the exact as well as other reported numerical solutions, demonstrating that there is consistency between macroscopic and kinetic computations for the compressible flow.