Accuracy of interface schemes for conjugate heat and mass transfer in the lattice Boltzmann method

Abstract

The lattice Boltzmann method (LBM) is attractive for conjugate heat and mass transfer modeling due to its capability to satisfy the interfacial conjugate conditions without nested iterations. This paper presents a comparison of the popular interface schemes proposed in the literature with the focus on their numerical accuracy and convergence orders. The various interface schemes examined include the geometry-considered interpolation-based treatment that constructs second-order accurate corrections to the distribution functions across the interface by treating the interface as a shared boundary for the adjacent domains, as well as representative modified schemes that bypass the local geometry and topology consideration by either reformulating the macroscopic governing energy equation with additional source terms, or proposing modified microscopic equilibrium distribution functions in the lattice Boltzmann model. It is recognized that for the interface schemes based on governing equation reformulation, approximation of the discontinuous heat capacitance gradient at the interface is required to account for the interfacial heat flux continuity. Through analysis and numerical tests including both straight and curved interfaces, it is shown that in order to preserve the second-order accuracy in the LBM, the local interface geometry must be considered; and the modified geometry-ignored interface schemes result in degraded convergence orders – at most first order for general cases and only zeroth order is achieved for the schemes requiring discontinuous heat capacitance gradient approximation. In addition, much higher error magnitude is observed for the numerical solutions obtained from using these modified schemes without considering the interface geometry.