A lattice Boltzmann method with source term for acoustic problems

A lattice Boltzmann method with source term for acoustic problems is proposed in this paper. In the scheme, a term for the mass source, the force source, and the first spatial derivative of the force source are included in the lattice Boltzmann evolution equation to recover the macroscopic wave equation with source terms, which are corresponding to the monopole term, dipole term, and quadrupole term, respectively. Numerical experiments are carried out to test the performance of the proposed scheme. Cases 1-7 are simply examples in which the propagation of the acoustic monopole, dipole, quadrupole, and supercardioid point sources is simulated to validate the accuracy of the proposed scheme. Cases 8-12 are more complex acoustic problems to validate the generality of the proposed scheme. It is demonstrated by the numerical results that the present method is more general in theory and does not cause unphysical disturbances to the underlying flow near the location of the acoustic source compared to the so-called boundary-based method; and the source term form in the present method is simpler and independent on the discrete model of the lattice and, therefore, more convenient in implementation compared to the Viggen's work.