Discrete effects on boundary conditions of the lattice Boltzmann method for convection-diffusion equations with curved geometries

In this work, we are concerned with the discrete effects of curved boundary conditions in the lattice Boltzmann method (LBM) for convection-diffusion equations (CDEs). The mathematical derivations show that for previous boundary conditions only with the distance ratio, the relaxation time to eliminate the numerical slip at curved boundary geometries cannot remain constant. Motivated by a single-node boundary scheme which contains a free parameter besides the distance ratio, a strategy is then proposed within the framework of multiple-relaxation-time (MRT) model to achieve uniform relaxation times such that the numerical slip can be removed. It is also shown that the derived relation adapted with the halfway boundary scheme to eliminate the numerical slip fails for the case of curved boundaries. Some simulations are performed for the case of inclined and curved boundaries, and the numerical results are consistent with our theoretical analysis.

Automated summary

This work focuses on the discrete effects of curved boundary conditions in the lattice Boltzmann method for convection-diffusion equations. A new strategy is proposed to eliminate numerical slip, showing its effectiveness through mathematical derivations and simulations. The results support the proposed strategy's ability to achieve uniform relaxation times and remove numerical slip in cases of curved boundaries.