A unified immersed boundary-lattice Boltzmann flux solver (UIB-LBFS) for simulation of flows past porous bodies

Abstract

A novel numerical method named the unified immersed boundary-lattice Boltzmann flux solver (UIB-LBFS) for simulating incompressible flows past homogeneous porous bodies is proposed in this paper. A diffuse layer through which the porosity is smoothly changed is introduced. As a consequence, the governing equations in the porous domain and the pure-fluid domain can be unified. The solutions to each domain can be smoothly transitioned from one to the other through the diffuse layer around the domain interface. A fractional-step technique is employed to split the computational procedure into the predictor step and the corrector step, respectively. In the predictor step, an intermediate flow field is first predicted without considering the domain interface by the unified lattice Boltzmann flux solver. Then, the physical conditions at the fluid-porous interface are implemented through the immersed boundary method to correct the flow field in the corrector step. All the flow quantities are evaluated at the cell centers, while the viscous and the inviscid numerical fluxes are locally reconstructed at each cell interface simultaneously. Numerical validations are carried out, and excellent agreements between the present and published results are achieved. The accuracy and the reliability of the UIB-LBFS are thus proven.