Adaptive generalized periodic boundary conditions for lattice Boltzmann simulations of pressure-driven flows through confined repetitive geometries

Abstract

An algorithm for an adaptive boundary condition for the simulation of fully developed, pressure driven flows using the lattice-Boltzmann method is introduced. The method simulates the effect of the solid walls confining a structure with dual periodicity, such as used in microfluidic devices. We combine a recently introduced boundary condition by Kim and Pitsch [Phys. Fluids 19, 108101 (2007)] for the treatment of pressure driven flows in periodic structures with a controller loop that adjusts a perpendicular pressure gradient to suppress any net momentum perpendicular to the outer walls. The method's accuracy in asymmetric geometries is tested against a periodic array structure that uses regularized zero-velocity boundary conditions as outer walls.