Lattice Boltzmann simulation of complex thermal flows via a simplified immersed boundary method

Abstract

A simplified immersed boundary (IB) lattice Boltzmann method (LBM) is developed in this study for simulating incompressible flows with heat transfer. The no-slip and constant temperature boundary conditions are both enforced by correcting the distribution functions. Similar to the previous distribution function correction (DFC)-IB method (S. Tao et al., 2021 [59]), the kinetic nature of LBM has been retained in the present scheme, which directly modifies the distribution functions other than models the interface as a source of IB force in the boundary treatment. However, this study presents two improvements. First, we reduce the number of distribution functions that need to be modified, and hence the computation load of the method can be reduced significantly. Furthermore, the correction term can be determined directly and explicitly, replacing the calculation of a local position-related adjustment parameter in the previous DFC-IB method. As a result, the computed velocity and temperature at the interface are consistent with their desired counterparts, and hence the Dirichlet boundary conditions can be accurately specified. The present simplified DFC IB method is validated in the simulations with both stationary and moving boundaries, including the flow past a hot cylinder, mixed convection in a square lid-driven cavity, and sedimentation of a particle in a long channel. The results demonstrate the accuracy and efficiency of the method.