Improved non-equilibrium bounce-back boundary scheme for the incompressible lattice Boltzmann model

Abstract

In this paper, an improved non-equilibrium bounce-back (NEBB) boundary scheme is proposed for incompressible fluid flows. The boundary scheme is meticulously derived from the incompressible lattice Boltzmann (LB) model, a widely used variant of the LB model known for its simplicity and computational efficiency. Based on the NEBB concept, a comprehensive scheme for constructing velocity and pressure boundary conditions has been developed. The numerical LB solutions obtained using the new scheme are compared with the current boundary schemes in terms of analytical solutions. By analyzing the pressure difference driven Poiseuille flow, it can be found that the numerical solution simulated by the boundary scheme proposed by us can not only better match the analytical solution than the original NEBB boundary scheme, but also maintain the second-order numerical accuracy like the non-equilibrium extrapolation boundary scheme. Our model demonstrates superior numerical stability in simulating high-Reynolds-number lid-driven cavity flows and outperforms others in modeling unsteady cylinder flow simulations. In a few words, the proposed method achieves higher accuracy and improved stability for incompressible fluid flows compared to the traditional NEBB boundary scheme.

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