Error assessment of lattice Boltzmann equation method for variable viscosity flows

Abstract

In lattice Boltzmann simulations, variable viscosity can complicate the truncation error analysis and create additional interaction between the truncation error and the boundary condition error. In order to address this issue, two boundary conditions for the lattice Boltzmann equation (LBE) simulations are used, including an exact, but narrowly applicable scheme previously proposed by Noble et al. ( Phys. Fluids 1995; 7 (1):203–209) and the popular bounce-back-on-link scheme. Using a 2-D laminar channel flow with a specified variable viscosity as a test case, it is shown that the boundary treatment error does not have a significant interaction with the truncation error associated with variable viscosity. The truncation error behaviour of the LBE for flows with variable viscosity is further investigated through a comparison between the LBE solution and the Navier–Stokes solution, showing that in the presence of strong variable viscosity the truncation error behaviour of the LBE solution is consistent with that of the Navier–Stokes solution, indicating that the LBE model closely matches the Navier–Stokes model for fluid flows with large viscosity variation. Copyright © 2006 John Wiley & Sons, Ltd.