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.

A unified numerical model for simulating heat transfer in flows past porous bodies

“…Based on this, the flow quantities inside the porous media are quantified by the volume averaging theorem. [1][2][3] Recently, a set of unified governing equations 23 for mass and momentum conservation together with the interface conditions (shear stress-jump, normal stress continuity, and velocity continuity) are proposed in weakly compressible form through introducing a diffuse layer (with the buoyancy force considered)…”

“…This is determined by numerical validation for isothermal flows with the published benchmark results. 23 The transition profile of 𝛼 and its spatial gradient are shown in Figure 1.…”

“…For the velocity field, both 𝛽 1,2 are usually taken as 0 for simplicity. [6][7][8] Then Equations ( 3)-( 5) can be rewritten as a single equation 23 in the Cartesian coordinate system, ( 𝜕u n 𝜕n…”

“…Consequently, it may be rarely found in literature that LBM studies adopt the stress jump condition except for the work in Reference 14. To resolve the above challenges posed to the body‐fitted N–S solvers and LBM, a novel numerical method termed as the unified immersed boundary‐lattice Boltzmann flux solver (UIB‐LBFS) 23 is proposed recently. UIB‐LBFS incorporates lattice Boltzmann flux solver (LBFS) 24,25 and immersed boundary method (IBM) 26 as an integrated numerical method to simulate flows past porous objects.…”

“…In the predictor step of UIB‐LBFS, a diffuse layer 23 is introduced so that all the flow quantities including the porosity can be smoothly transitioned from one domain to the other. This step unifies the governing equations in both the porous and pure fluid domains since the whole computational domain is regarded as a resultant porous area with adjustable porosity.…”