Simulation of shock-wave propagation with finite volume lattice Boltzmann method

A new approach was recently proposed to construct equilibrium distribution functions (f(alpha)(eq)) of the lattice Boltzmann method for simulation of compressible flows. In this approach, the Maxwellian function is replaced by a simple function which satisfies all needed relations to recover compressible Euler equations. With Lagrangian interpolation polynomials, the simple function is discretized onto a fixed velocity pattern to construct f(alpha)(eq). In this paper, the finite volume method is combined with the new lattice Boltzmann models to simulate 1D and 2D shock-wave propagation. The numerical results agree well with available data in the literatures.