Erratum: General bounce-back scheme for concentration boundary condition in the lattice-Boltzmann method [Phys. Rev. E85, 016701 (2012)

Abstract

We found a mistake in calculating the error shown in Fig. 7. In the paper, the relative global error is computed by Err(C) = ‖C−Cexact‖2 ‖Cexact‖2 , while in the measurement we did not compute the square-root after the summation of the squares. Consequently, based on the relative global error defined above, Fig. 7 should be replaced by the following Fig. 1; and simultaneously, the slope of the fitting line shown in Fig. 7 should be replaced with 1.03. The corrected results indicate that, in the test case of diffusion in an inclined channel, the halfway bounce-back scheme only has first-order accuracy in space.