Acoustic multipole source–simplified lattice Boltzmann method for simulating acoustic propagation problems

Abstract

AbstractCombining the advantages of the acoustic multipole source (AMS) method and the simplified lattice Boltzmann method (SLBM), a method called AMS–SLBM is proposed for simulating the propagation of acoustic multipole sources in fluids. A particle source term is introduced to the right‐hand side of the lattice Boltzmann equation using the AMS method, and the macroscopic equations with source terms are derived via the Chapman–Enskog expansion analysis. Employing the fractional step technique, the solving process of the macroscopic equations can be divided into three steps: the predictor, corrector, and supplement steps. In the predictor and corrector steps, macroscopic equations without source terms are solved by SLBM, and in the supplement step, the time advancement of the source terms is solved using the finite difference method. AMS–SLBM uses SLBM to simulate the propagation of sound waves by directly evolving the macroscopic variables, which evades the evolution and storage of the distribution function, and the computational process is simpler and memory can be reduced compared to the standard LBM. Moreover, since the acoustic source term is introduced to the right‐hand side of the lattice Boltzmann equation by the AMS method, AMS–SLBM avoids the disadvantage that the traditional forced equilibrium distribution function method will interfere and cover the original flow field during the calculations. Several cases including the propagation of a plane wave, a Gaussian pulse and acoustic monopole, dipole, and quadrupole sources are simulated to validate the robustness and accuracy of the present method. The results show that AMS–SLBM can well simulate acoustic multipole sources propagation, and it affords second‐order accuracy.