Lattice Boltzmann method for conjugated heat and mass transfer with general interfacial conditions

Abstract

A general interfacial treatment for the transport process in multicomponent systems governed by the convection-diffusion equation, together with conjugated interfaces where continuity or discontinuity interfacial conditions with regard to the physical scalar and its flux exist, is developed using the lattice Boltzmann method (LBM) with a multiple-relaxation-time collision operator. Factors accounting for interfacial jumps at conjugated interfaces typically include the difference in solubility, porosity, and transport properties, and the interfacial transport resistance. Difficulties in satisfying the discontinuity conditions, where continuity conditions are inherent in the conventional LBM, are overcome based on a second-order accurate treatment for both Dirichlet and Neumann boundary conditions. As a result, the unknown populations at the interface are obtained with a combination of the existing postcollision populations and the defined interfacial jumps without finite-difference approximations, thereby enabling the interfacial requirements precisely. Since the present treatment considers local intersected link fractions of the interface, it can be applied for curved interfaces naturally. As for straight interfaces located at the midpoints of the nodes, the present treatment can be significantly simplified with only two current nodes required. Validation work on the present treatment are performed with four specific problems, including the steady and unsteady convection diffusion in a fluid-fluid channel, steady convection diffusion in a fluid-solid system, steady and unsteady pure conduction in a composite slab, and steady pure conduction in an annulus. Such an interfacial scheme is finally applied to the conjugated mass transfer in a heterogonous medium, highlighting its practicability in complex systems with complicated interfacial conditions. In addition, detailed error analysis on interior nodes, interfacial values, and interfacial fluxes shows that our model is second-order accurate in space for straight interfaces regardless of various interfacial conditions, indicating no artificial disturbance is introduced to the model. While for curved interface, only superlinear and first-order accuracies are obtained for the interior nodes and the interfacial values or fluxes, respectively. Discussions on the degradation of the accuracy are presented. Note that the present interfacial treatment is mainly focused on two-dimensional problems, extensions of the model to be three-dimensional are straightforward.