Single-node second-order boundary schemes for the lattice Boltzmann method

Based on our recently developed Maxwell iteration for the lattice Boltzmann method, we propose a class of single-node boundary schemes for Dirichlet boundary conditions of the Navier–Stokes equations. The schemes all have second-order accuracy for both straight and curved boundaries. The accuracy and stability of two specific schemes are examined through several numerical experiments. The results validate the second-order accuracy and show that a boundary scheme with a convex combination of distribution functions has better stability.