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

Difficulties for the conventional computational fluid dynamics and the standard lattice Boltzmann method (LBM) to study the gas oscillating patterns in a resonator have been discussed. In light of the recent progresses in the LBM world, we are now able to deal with the compressibility and non-linear shock wave effects in the resonator. A lattice Boltzmann model for viscid compressible flows is introduced firstly. Then, the Boltzmann equation with the Bhatnagar-Gross-Krook approximation is solved by the finite-difference method with a third-order implicit-explicit (IMEX) Runge-Kutta scheme for time discretization, and a fifth-order weighted essentially non-oscillatory (WENO) scheme for space discretization. Numerical results obtained in this study agree quantitatively with both experimental data available and those using conventional numerical methods. Moreover, with the IMEX finite-difference LBM (FDLBM), the computational convergence rate can be significantly improved compared with the previous FDLBM and standard LBM. This study can also be applied for simulating some more complex phenomena in a thermoacoustics engine.