title: Boundary condition at a two-phase interface in the lattice Boltzmann method for the convection-diffusion equation.
abstract: A boundary scheme in the lattice Boltzmann method (LBM) for the convection-diffusion equation, which correctly realizes the internal boundary condition at the interface between two phases with different transport properties, is presented. The difficulty in satisfying the continuity of flux at the interface in a transient analysis, which is inherent in the conventional LBM, is overcome by modifying the collision operator and the streaming process of the LBM. An asymptotic analysis of the scheme is carried out in order to clarify the role played by the adjustable parameters involved in the scheme. As a result, the internal boundary condition is shown to be satisfied with second-order accuracy with respect to the lattice interval, if we assign appropriate values to the adjustable parameters. In addition, two specific problems are numerically analyzed, and comparison with the analytical solutions of the problems numerically validates the proposed scheme.
authors.affiliation: Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan and Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8245, Japan.
authors.forename: Hiroaki
authors.initials: H
authors.lastname: Yoshida
authors.affiliation: Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan.
authors.forename: Takayuki
authors.initials: T
authors.lastname: Kobayashi
authors.affiliation: Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan.
authors.forename: Hidemitsu
authors.initials: H
authors.lastname: Hayashi
authors.affiliation: Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan and Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8245, Japan.
authors.forename: Tomoyuki
authors.initials: T
authors.lastname: Kinjo
authors.affiliation: Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan and Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8245, Japan.
authors.forename: Hitoshi
authors.initials: H
authors.lastname: Washizu
authors.affiliation: Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan.
authors.forename: Kenji
authors.initials: K
authors.lastname: Fukuzawa
mesh_terms: D000465:Algorithms; D018481:Convection; D004058:Diffusion; D008962:Models, Theoretical