A diffuse-interface lattice Boltzmann method for thermal particulate flows with Dirichlet boundary conditions

The lattice Boltzmann method has been widely used to study thermal particulate flows that are usually observed in both nature and engineering, while how to efficiently and accurately treat the fluid-solid boundary conditions is still an important and not well-resolved issue. In this paper, a diffuse-interface lattice Boltzmann method (DI-LBM) is developed for complex thermal particulate flows with Dirichlet boundary conditions. Unlike the previous works where the fluid-solid boundary is treated as a sharp interface, the fluid-solid boundary in the DI-LBM is implemented as a diffuse interface such that the physical variables and transport coefficients in the fluid and solid regions are varied smoothly. To depict the diffuse interface, a smooth function is introduced, and simultaneously, an additional source term is added in the evolution equation to reflect the effect of Dirichlet boundary condition imposed on the fluid-solid boundary. The present method is also tested by several classical problems, and the numerical results show that the DI-LBM is not only of second-order convergence rate in space, but also efficient in the study of complex thermal particulate flows.