Multiple-relaxation time lattice Boltzmann method for the finite Knudsen number region

A multiple-relaxation time lattice Boltzmann model discretized with second order trapezoid rule in a coherent framework is presented for the finite Knudsen number region. Combination of bounce back and specular reflection boundary condition is implemented at the walls, which gives tunable second order slip coefficient as it is shown by the analysis of the boundary condition. Plane channel flow is simulated in good agreement with the analytical derivation and predictions, which demonstrates the applicability of the present approach for microfluidic applications.