LAUSR

Summary We analytically and numerically investigate the boundary slip, including the velocity slip and the temperature jump, in immersed boundary-thermal lattice Boltzmann methods (IB-TLBMs) with the two-relaxation-time (TRT) collision operator. We derive the theoretical equation for the relaxation parameters considering the effect of the advection velocity on the temperature jump of the IB-TLBMs. The analytical and numerical solutions demonstrate that the proposed iterative correction methods without the computational cost of the sparse matrix solver reduce the boundary slip and boundary-value deviation as effectively as the implicit correction method for any relaxation time. Because the commonly used multi-direct forcing method does not consider the contributions of the body force to the momentum flux, it cannot completely eliminate the boundary slip due to the numerical instability for a long relaxation time. Both types of proposed iterative correction methods are more numerically stable than the implicit correction method. In simulations of flow past a circular cylinder and of natural convection, the present iterative correction methods yields adequate results without the errors of the velocity slip, the temperature jump and the boundary-value deviation for any relaxation time parameters and for any number of Lagrangian points per length. The combination of the present methods and the TRT collision operator is suitable for simulating fluid flow with thermal convection in the multi-block method in which the relaxation time increases in inverse proportion to the grid size. This article is protected by copyright. All rights reserved.