International Journal of Heat and Mass Transfer 000 (2020) 119694 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt Accuracy of interface schemes for conjugate heat and mass transfer in the lattice Boltzmann method David Korba, Nanqiao Wang, Like Li ∗ Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS 39762, USA a r t i c l e i n f o Article history: Received 22 November 2019 Revised 20 March 2020 Accepted 23 March 2020 Available online xxx a b s t r a c t 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 nu- merical accuracy and convergence orders. The various interface schemes examined include the geometry- considered interpolation-based treatment that constructs second-order accurate corrections to the dis- tribution 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 consid- eration 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 or- ders – 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 ob- served for the numerical solutions obtained from using these modified schemes without considering the interface geometry. © 2020 Elsevier Ltd. All rights reserved. 1. Introduction Conjugate conditions at the interface of different phases or ma- terials of distinct properties are encountered in almost all practi- cal science and engineering applications involving heat and mass transfer, such as cooling of turbine blades and electronic devices, insulation for pipes, heat exchangers and thermochemical reactors, and thermal and mass transport in porous media and particulate systems, to name a few [1–11]. The basic and most well-known conjugate conditions include the continuity of both the tempera- ture (concentration) and the heat (mass) flux at the interface [12– 15]. Other conjugate conditions, such as with temperature (con- centration) jumps and flux discontinuities [16–18], the Henry’s law relationship [19], and the Kapitza resistance in heat transfer [20], are also noticed. Theoretical analysis for conjugate heat and mass transfer is limited as analytical solutions are only available to sim- ple transport problems with regular geometry. Experimental mea- ∗ Corresponding author. E-mail address: likeli@me.msstate.edu (L. Li). surement of interfacial values is often a challenge as the interfaces are usually inaccessible to probing devices in most cases. Substan- tial research effort, as a result, has been devoted to numerical sim- ulation of conjugate heat and mass transfer problems with effec- tive interface treatment. The common approach in dealing with conjugate conditions is to treat them as boundary conditions for the adjacent domains, and the heat and mass transfer in each domain can be solved separately using typical numerical methods for the convection- diffusion equations (CDE). Since the conjugate conditions are implicit (i.e., with given relationships between the scalar and its fluxes in the adjacent domains rather than the explicit interfacial values, see Eqs. (6), (7)) and with both Dirichlet and Neumann type conditions, a popular approach for their implementation is applying iterative schemes, e.g., a predictor-corrector based Dirich- let condition is imposed for one domain and with that a Neumann condition can be constructed for the other; and the conjugate conditions at the interface can be satisfied after multiple itera- tions. Extrapolation is usually required in these iterative schemes to obtain the interfacial temperature (concentration) and fluxes. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119694 0017-9310/© 2020 Elsevier Ltd. All rights reserved.