Filter-matrix lattice Boltzmann model for microchannel gas flows

Microchannel Gas Flow in the Multi-Flow Regime Based on the Lattice Boltzmann Method

In this work, a lattice Boltzmann method (LBM) for studying microchannel gas flow is developed in the multi-flow regime. In the LBM, by comparing previous studies' results on effective viscosity in multi-flow regimes, the values of the rarefaction factor applicable to multi-flow regions were determined, and the relationship between relaxation time and Kn number with the rarefaction factor is given. The Kn number is introduced into the second-order slip boundary condition together with the combined bounce-back/specular-reflection (CBBSR) scheme to capture the gas flow in the multi-flow regime. Sensitivity analysis of the dimensionless flow rate to adjustable parameters using the Taguchi method was carried out, and the values of adjustable parameters were determined based on the results of the sensitivity analysis. The results show that the dimensionless flow rate is more sensitive to j than h. Numerical simulations of Poiseuille flow and pulsating flow in a microchannel with second-order slip boundary conditions are carried out to validate the method. The results show that the velocity profile and dimensionless flow rate simulated by the present numerical simulation method in this work are found in the multi-flow regime, and the phenomenon of annular velocity profile in the microchannel is reflected in the phases.

Numerical Modelling of Microchannel Gas Flows in the Transition Flow Regime Using the Cascaded Lattice Boltzmann Method

In this article, a lattice Boltzmann (LB) method for studying microchannel gas flows is developed in the framework of the cascaded collision operator. In the cascaded lattice Boltzmann (CLB) method, the Bosanquet-type effective viscosity is employed to capture the rarefaction effects, and the combined bounce-back/specular-reflection scheme together with the modified second-order slip boundary condition is adopted so as to match the Bosanquet-type effective viscosity. Numerical simulations of microchannel gas flow with periodic and pressure boundary conditions in the transition flow regime are carried out to validate the CLB method. The predicted results agree well with the analytical, numerical, and experimental data reported in the literature.

Acoustic multipole sources for the regularized lattice Boltzmann method: Comparison with multiple-relaxation-time models in the inviscid limit

In this paper, a variant of the acoustic multipole source (AMS) method is proposed within the framework of the lattice Boltzmann method. A quadrupole term is directly included in the stress system (equilibrium momentum flux), and the dependency of the quadrupole source in the inviscid limit upon the fortuitous discretization error reported in the works of E. M. Viggen [Phys. Rev. E 87, 023306 (2013)PLEEE81539-375510.1103/PhysRevE.87.023306] is removed. The regularized lattice Boltzmann (RLB) method with this variant AMS method is presented for the 2D and 3D acoustic problems in the inviscid limit, and without loss of generality, the D3Q19 model is considered in this work. To assess the accuracy and the advantage of the RLB scheme with this AMS for acoustic point sources, the numerical investigations and comparisons with the multiple-relaxation-time (MRT) models and the analytical solutions are performed on the 2D and 3D acoustic multipole point sources in the inviscid limit, including monopoles, x dipoles, and xx quadrupoles. From the present results, the good precision of this AMS method is validated, and the RLB scheme exhibits some superconvergence properties for the monopole sources compared with the MRT models, and both the RLB and MRT models have the same accuracy for the simulations of acoustic dipole and quadrupole sources. To further validate the capability of the RLB scheme with AMS, another basic acoustic problem, the acoustic scattering from a solid cylinder presented at the Second Computational Aeroacoustics Workshop on Benchmark Problems, is numerically considered. The directivity pattern of the acoustic field is computed at r=7.5; the present results agree well with the exact solutions. Also, the effects of slip and no-slip wall treatments within the regularized boundary condition on this pure acoustic scattering problem are tested, and compared with the exact solution, the slip wall treatment can present a better result. All simulations demonstrate that the RLB scheme with the AMS method is capable of accurately simulating 2D and 3D acoustic generation, propagation, and scattering at zero viscosity.