Quartic parameters for acoustic applications of lattice Boltzmann scheme

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 obtained in the case of D3Q27 lattice Boltzmann scheme. Various numerical tests support the coherence of this approach.