A simple and efficient curved boundary scheme of the lattice Boltzmann method for Robin boundary conditions of convection–diffusion equations

This paper is concerned with boundary schemes of the lattice Boltzmann method for Robin conditions convection–diffusion equations on curved boundaries. For such conditions, all existing suffer from possibility that denominator in scheme may become zero, which will lead to numerical instability. To avoid this possibility, we propose a by approximating gradient along outgoing discrete velocity at given condition and interior point next boundary. With approximated boundary, classical bounce back Neumann-type employed obtain unknown distribution function point. The obtained has first-order accuracy boundaries its advantages are: (1) simple form so it can be easily implemented; (2) avoids (3) single-node, i.e., only involves information present Numerical examples demonstrate designed good stability our complex