Application of half-way approach to discrete unified gas kinetic scheme for simulating pore-scale porous media flows

Abstract

Simulation of pore-scale porous media flows is generally considered to be a non-trivial task due to the complicacy of geometry structures involved. In the recent decades, the mesoscopic scheme of lattice Boltzmann equation (LBE), combined with the inherent half-way (HW) bounce-back boundary method has been proved to efficiently handle those complex flows. More recently, a new mesoscopic method called discrete unified gas kinetic scheme (DUGKS) is proposed in the literature, which is partially derived from the LBE. In view of that, the HW-type boundary approach is introduced to the DUGSK in this study, which is accomplished within the framework of the ghost-cell (GC) method. The HWGC-DUGKS is then developed for extending the application of DUGKS to the complex flows in the porous media. The simulations of the cylindrical Couette flow, flow through a square array of cylinders and flow in the random porous media are performed to validate the present HWGC-DUGKS. The results demonstrate the accuracy and feasibility of the method for pore-scale porous media flows, and the non-uniform mesh and rarefied effect can be conveniently incorporated into the method.