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A new lattice Boltzmann scheme associated with flexible specific heat ratiois proposed. The new free degree is introduced via the internal energyassociated with the internal structure. The evolution equation of thedistribution function is reduced to two evolution equations. One is connectedto the density and velocity, the other is of the energy. A two-dimensionallattice Boltzmann model and a three-dimensional lattice Boltzmann model arederived via the Hermite expansion. The two lattice Boltzmann models are appliedto simulating the shock tube of one dimension. Good agreement between thenumerical results and the analytical solutions are obtained.

A new scheme based on the Hermite expansion to construct lattice Boltzmann models associated with arbitrary specific heat ratio