Interface Treatment for Conjugate Conditions in the Lattice Boltzmann Method for the Convection Diffusion Equation

Abstract

The lattice Boltzmann method (LBM) has emerged as an attractive numerical method for fluid flows and thermal and mass transport. For LBM modeling of transport between different phases or materials of distinct properties, effective treatment for the conjugate conditions at the interface is required. Recognizing the benefit of satisfying the conjugate conditions in each time step without iterative computations using LBM, various interface schemes have been proposed in the last decade. This chapter provides a review of those interface schemes, with a focus on the comparison of numerical accuracy and convergence orders. It is shown that in order to preserve the second-order accuracy in LBM, the local interface geometry must be considered; and the modified geometry-ignored interface schemes result in degraded convergence orders and/or much higher error magnitude. It is also verified that with appropriate interface schemes, interfacial transport with scalar and flux jumps can be effectively modeled.

Investigation of Temperature Distribution in a Slab Using Lattice Boltzmann Method

“…Heat transfer across different materials is a common occurrence in traditional sciences and engineering, such as in the cooling of turbine blades, heat exchangers, and electronic devices and the transfer of heat between solids and the fluids that surround them [1]. A configuration that is frequently observed in engineering components and systems is a solid slab that exists having its ends at different temperatures.…”