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A new scheme for the finite difference lattice Boltzmann method is proposed, in which negative viscosity term is introduced to reduce the viscosity and the calculation time can be remarkably reduced for high Reynolds number flows. A model with additional internal degree of freedom is also presented for diatomic gases such as air, in which an additional distribution function is introduced. Direct simulations of aero-acoustics by using the proposed model and scheme are presented. Speed of sound is correctly recovered. As typical examples, the Aeolian tone emitted by a circular cylinder is successfully simulated even very low Mach number flow. Full three-dimensional sound emission is also given.