Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions

Abstract

The lattice Boltzmann method is developed to study gaseous slip flow in microchannels. An approach relating the Knudsen number with the relaxation time in the lattice Boltzmann evolution equation is proposed by using gas kinetic equation resulting from the Bhatnagar–Gross–Krook collision model. The slip velocity at the solid boundaries is obtained with kinetic theory boundary conditions. The two-dimensional micro-Couette flow, micro-Poiseuille flow, and micro-lid-driven cavity flow are simulated using the present model. It is found that the numerical results agree well with available analytical and benchmark solutions.

Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

“…Works into similar directions have been published at about the same time by Tang et al [3]. Sbragaglia and Succi presented a new formulation of kinetic boundary conditions for flows at finite Knudsen numbers in [20]; therefore, they proposed models based on slip, reflection and accomodation coefficients.…”

“…The first-order slip boundary condition and the MRT with viscosity adjustment were employed for the whole domain. The size of the duct system and the reaction chamber were chosen such that the Knudsen numbers within the channels and inside the chamber are 3 …”

“…Different methods have been proposed over the last years to extend existing continuum approaches to the finite Knudsen regime, i.e. to the slip and transition flow regime [2][3][4][5][6][7][8]. In this context, the Lattice Boltzmann method (LBM) has attracted particular attention, due to its kinetic origin and implementational simplicity.…”

Numerical Simulation and Experimental Validation for the Filtration Performance of Fibrous Air Filter Media with LB Method

“…The slip effects imposed at a solid-fluid interface were well captured by the current LB method. Two mesoscopic kinetic boundary conditions are widely used to realize the slip boundary conditions, i.e., the combination of bounce-back and specular reflection (BSR) scheme (Przekop and Gradoń, 2008;Guo et al, 2002;Succi, 2002;Tang et al, 2004;Sbragaglia and Succi, 2005) and the discrete Maxwellian (DM) scheme (Ansumali and Karlin, 2002;Niu et al, 2004;Tang et al, 2005;Zheng et al, 2012). Guo et al (2002) also pointed out that BSR and DM schemes are useful for different applications.…”

“…Recently, the Lattice Boltzmann equation (LBE), a discrete version of the continuous Boltzmann equation which can capture non-equilibrium gas flows, has been considered as a promising numerical approach for microscale gas flows (Tang et al, 2005;Kim et al, 2008;Przektop and Gradon, 2008;Agarwal et al, 2009;Chen et al, 2009;Wang et al, 2009;Neumann and Rohrmann, 2012;Cho et al, 2013;Bang and Yoon, 2014). The gas flow in the microscale channels has a big difference from the conventional situation.…”