An iterative source correction based immersed boundary-lattice Boltzmann method for thermal flow simulations

Temperature jump at the boundary occurs when the conventional immersed boundary-lattice Boltzmann (IB-LB) method is applied to simulating the near boundary flows with heat transfer. To remedy this problem, an iterative correction is proposed to modify the heat source term in the IB-LB method. The source term in the LB equation is treated by Cheng's scheme, in which the heat source at the next timestep is taken as unknowns and iteratively corrected until the resulting boundary temperature matches its desired value. Typical verification cases, including the two-dimensional (2D) heat transfer between two horizontal plates, the natural convection between two concentric circular cylinders, and 2D sedimentation of a single particle with heat convection are simulated to analyze the accuracy of the method. It is shown that the boundary temperature jump can be effectively removed for a certain range of LB relaxation time τ, while the first-order spatial convergence of the IB method is still maintained. Also, a theoretical analysis is conducted based on the case of heat transfer between two plates. It is shown that the proposed method outperforms the widely-used direct source method in treating the Dirichlet boundary conditions when τ is smaller than 1.624. To further demonstrate its capability for resolving complicated fluid-structure interaction problems, a three-dimensional sedimentation of a single particle in a vertical channel is analyzed. We find that the thermal convection may fundamentally affect the way the particle interacts with the surrounding fluid.