Finite-difference-based lattice Boltzman method for inviscid compressible flows

A finite-difference-based Boltzmann model, employing the 2-D, 9-velocity sq uare (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 imcompressib le and compressible flow regimes. In the numerical treatment, to attain des irable accuracy, the total-variation-diminishing (TVD) scheme is adopted wi th either the minmod function or a second-order corrector as the flux limit er. The model can treat shock/expression waves as well as contact discontin uity. Both one-dimensional test cases are compared, and the results are com pared with the exact as well as the other reported numerical solutions, dem onstrating that there is consistency between macroscopic and kinetic comput ations for the compressible flow.