Combining 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.
A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman–Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was first recovered to linearized macroscopic equations. Then, using the fractional-step calculation technique, the solution of these linearized equations was divided into two steps: a predictor step and corrector step. Next, the evolution of the perturbation distribution function was transformed into the evolution of the perturbation equilibrium distribution function using second-order interpolation approximation of the latter at other positions and times to represent the nonequilibrium part of the former; additionally, the calculation formulas of SLLBM were deduced. SLLBM inherits the advantages of the linearized lattice Boltzmann method (LLBM), calculating acoustic disturbance and the mean flow separately so that macroscopic variables of the mean flow do not affect the calculation of acoustic disturbance. At the same time, it has other advantages: the calculation process is simpler, and the cost of computing memory is reduced. In addition, to simulate the acoustic scattering problem caused by the acoustic waves encountering objects, the immersed boundary method (IBM) and SLLBM were further combined so that the method can simulate the influence of complex geometries. Several cases were used to validate the feasibility of SLLBM for simulation of acoustic wave propagation under the mean flow.
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