Linear discrete velocity model-based lattice Boltzmann flux solver for simulating acoustic propagation in fluids

A linear lattice velocity model is developed, and a corresponding lattice Boltzmann flux solver (LBFS) is constructed based on it. This solver calculates the fluxes of the linearized Euler equations (LEEs), which are discretized by the finite volume method (FVM), and can simulate acoustic propagation in fluids. First, the expressions for the distribution function and the lattice velocity of the linear discrete velocity model are constructed using the moment relations in linear form. Second, based on Chapman-Enskog analysis and moment relations, the mesoscopic flux expression can be constructed by comparing the linear lattice Boltzmann equation and LEEs. Finally, the developed scheme is used to calculate the LEE flux term. The developed linear lattice velocity model-based LBFS has the following advantages: (i) It extends the lattice Boltzmann model-based flux solver from solving the macroscopic equations of fluid dynamics to solving linear equations; (ii) it also inherits the advantages of the Boltzmann model-type flux solver. The variables at the interface are calculated from the local solution of the lattice Boltzmann equation, making it more physical. In addition, least-squares-based finite differences and Gaussian integration are used for the FVM to discretize the LEE, making it a high-precision algorithm. Thus, the developed algorithm can accurately capture acoustic propagation in fluids and acoustic scattering in complex geometries. Several numerical cases for propagating acoustics in fluids are simulated to validate the accuracy and robustness of the present algorithm, and an accuracy test shows it approaches fourth-order accuracy.