Implicit-explicit finite-difference lattice Boltzmann method with viscid compressible model for gas oscillating patterns in a resonator

ifficulties for the conventional computational fluid dynamics and standard lattice Boltzmann method to study the gas oscillating patterns in a resonator are discussed. In light of the recent progresses in the lattice Boltzmann method world, we are now able to deal with the compressibility and non-linear shock wave effects in the resonator. The implicit-explicit finite-difference lattice Boltzmann method is used to investigate such problem. In particular, a lattice Boltzmann model for viscid compressible flows is introduced firstly. Then, the Boltzmann equation with Bhatnagar-Gross-Krook approximation is solved by a finite-difference method with the third-order implicit-explicit Runge-Kutta scheme for time discretization, and the fifth-order WENO scheme for space discretization. Numerical results obtained in this study agree quantitatively well with available experimental data and simulation results using conventional numerical methods. Moreover, with the implicit-explicit finite-difference lattice Boltzmann method, the computational convergence rate can be significantly improved compared with the previous finite-difference and standard lattice Boltzmann method. This work is carried out as the first effort to study phenomena in thermoacoustics engines with lattice Boltzmann method.