Abstract
We consider the permeable bounce-back scheme in the lattice Boltzmann (LB) method for incompressible flows, in which a fraction of the distribution function is bounced back and the remainder travels to the neighboring lattice points. An asymptotic analysis of the scheme is carried out in order to show that the fractional coefficient, referred to as the transmission–reflection coefficient, relates the pressure drop to the flow velocity. The derived relation, which clarifies the role played by the transmission–reflection coefficient in the macroscopic description, is helpful in using the scheme to simulate flows involving a pressure drop or gradient. The scheme is compared with the existing methods in which the transmission–reflection coefficient is employed, and the difference is clarified. As an application of the permeable bounce-back scheme, we perform an LB simulation for flows through porous media described by the Brinkman model.
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