Application of an Immersed Boundary Treatment in Simulation of Natural Convection Problems with Complex Geometry via the Lattice Boltzmann Method

In this study, a version of thermal immersed boundary-Lattice Boltzmann method (TIB-LBM) is used to simulate thermal flow problems within complex geometries. The present approach is a combination of the immersed boundary method (IBM) and the thermal lattice Boltzmann method (TLBM) under the double population approach. The method combines two different grid systems, an Eulerian grid for the flow domain and a Lagrangian grid for the boundary points immersed in the flow. In the present method, an unknown velocity correction is considered on the boundary points to impose the no-slip boundary condition. As a similar approach, an unknown internal energy correction on the boundary points is applied to satisfy the constant temperature boundary condition. The advantages of this approach are its second-order accuracy and straightforward calculation of the Nusselt number. The natural convection in an annulus with various outer cylinder shapes for different Rayleigh numbers have been simulated to demonstrate the capability and the accuracy of present approach. In terms of accuracy, the predicted results show an excellent agreement with those predicted by other experimental and numerical approaches.