Higher-order Galilean-invariant lattice Boltzmann model for microflows: Single-component gas

Abstract

We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation ͑without any cubic error͒. In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.

Rotational invariance in the three-dimensional lattice Boltzmann method is dependent on the choice of lattice

“…It is possible that for other systems or for similar systems with more complex flows than those investigated here, the 4th order isotropy displayed by D3Q27 may be insufficient. If this were the case, it would then be interesting to investigate if the recently reported higher order lattices [5] or the off lattice D3Q27 model [32] which displays 6th order isotropy would be more appropriate than the D3Q27 lattice. Further tests of the standard D3Q27 lattice to show whether or not its isotropy is sufficient, in flow systems beyond that investigated here, would therefore be beneficial, as it offers advantages such as reduced computational expense compared to the higher order model and simpler advection compared to the off lattice model.…”

Predicting the Knudsen paradox in long capillaries by decomposing the flow into ballistic and collision parts

“…The steady isothermal gas flow through long capillaries still remains an active research topic and a subject of many investigations [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, simple closed-form expressions for the reduced flow rate in long tubes in all flow regimes were deduced in [18] and [19] based on direct simulation Monte Carlo (DSMC) and kinetic simulations, respectively.…”

Fokker-Planck model of hydrodynamics

“…For this setup, Yudistiawan et al [22] had analytically solved a discrete velocity model solved by higher order LBM and …”