Flow Simulations in a Sub-Micro Porous Medium by the Lattice Boltzmann and the Molecular Dynamics Methods

In order to devise and establish a cost-effective strategy to simulate flows in continuum to slip and transitional regimes, present study focuses on evaluating a lattice Boltzmann equation [Niu et al., Phys. Rev. E 76, 036711, 2007] formerly proposed by the present authors’ group. The main test flow case is a flow around a square cylinder situated in a sub-micro channel. Since a rather shorter streamwise domain size and a periodic streamwise boundary condition are imposed, the flow regime is regarded as a part of an infinite cylinder array set in a narrow channel which can be considered as a kind of micro-porous media. For the assessment of the lattice Boltzmann simulations, the molecular dynamics (MD) simulations using Leonard-Jones potential are also performed. In the MD simulations, novel boundary treatments are applied. The results of the square cylinder flow by both the simulations at Knudsen number Kn=0.08 show reasonable agreement and confirm the reliability of the present lattice Boltzmann method (LBM). The fact that the computational time of the present MD simulation to obtain the reliable statistics is 1800 times as much as that of the LBM clearly indicates the usability of the LBM for engineering applications even in the slip and transitional flow regimes.