Diffuse interface-lattice Boltzmann modeling for heat and mass transfer with Neumann boundary condition in complex and evolving geometries

Abstract

In this research, a diffuse interface-lattice Boltzmann method is developed to model heat and mass transfer problems with Neumann boundary condition in complex and evolving geometries. In this model, the physical domain with curved and moving boundaries is extended to a larger and regular domain based on the concept of fictitious domain. The Neumann boundary condition is incorporated into the jump conditions of field variable at the inner interface. Then a unified convection-diffusion equation of field variable with two singular source terms is built. Using the smoothing technique, a diffuse interface equation is obtained. Moreover, an energy method is presented to derive the diffuse interface equation in a special case. We utilized a multiple-relaxation-time lattice Boltzmann scheme to numerically solve the diffuse interface equation. A simple example with analytical solutions validates the numerical accuracy of the present model. Finally, several thermal convection and mass transport problems are also simulated. The numerical results denotes the validity of the proposed diffuse interface model.