  Using the Taylor expansion method, we show that it is possible to improve the
lattice Boltzmann method for acoustic applications. We derive a formal
expansion of the eigenvalues of the discrete approximation and fit the
parameters of the scheme to enforce fourth order accuracy. The corresponding
discrete equations are solved with the help of symbolic manipulation. The
solutions are explicited in the case of D3Q27 lattice Boltzmann scheme. Various
numerical tests support the coherence of this approach.
