Temporary velocity correction-based immersed boundary–lattice Boltzmann method for incompressible flows in porous media at representative elementary volume scale

Abstract

The immersed boundary (IB)–lattice Boltzmann (LB) method is an effective strategy for complex boundary condition treatment. By adding an extra body force term in the LB equation properly, the specific velocity boundary condition can be enforced in this method. However, when it comes to incompressible flows through porous media at the representative elementary volume (REV) scale, the conventional IB–LB method fails because the velocity and the force term induced by porous media are coupled. In order to solve this problem, a temporary velocity is used to construct the IB-induced force term with the enforcement of the velocity boundary condition. The temporary velocity is decomposed into the intermediate temporary velocity and the corresponding correction. By this treatment, the temporary velocity correction is the linear function of the IB-induced force term. Furthermore, to obtain the force term accounting for the IB, the velocity boundary condition is transformed to the temporary velocity. Consequently, a temporary velocity correction-based IB–LB method is established for the incompressible flows at the REV scale. To avoid the error of explicitly calculating the IB-induced force term, the multi-direct-forcing scheme is employed in which iteration is carried out in terms of the specific boundary condition. The proposed IB–LB method for REV-scale incompressible flows is applied for the Couette flow in a porous annulus and lid driven flow in a square cavity filled with porous matrix. Numerical results show the computational accuracy of the developed IB–LB method.