A simple direct heating thermal immersed boundary-lattice Boltzmann method for its application in incompressible flow

Abstract A simple direct heating thermal immersed boundary-lattice Boltzmann method for buoyancy-driven incompressible flow with complex geometry boundaries is developed to simulate natural convection with curved boundary. In the newly developed method, both Dirichlet and Neumann boundary conditions in macroscopic equation are deduced into a novel mesoscopic discrete heat source. The mesoscopic discrete heat source consists of simplified explicit discrete heat source scheme which reduces the computational complexities and is introduced into lattice Boltzmann equation for temperature field, which extends the idea of the previous direct forcing IB-LBM. Both isothermal boundary condition (i.e. Dirichlet boundary condition) and constant heat flux boundary condition (i.e. Neumann boundary condition) are considered in our simulations. The efficiency and accuracy of the present method are demonstrated by simulating both two dimensional and three dimensional thermal flow with curved boundaries. Numerical results indicate that the efficiency and accuracy of the present method are well consistent with experimental and the other numerical results. The present method has also been successfully applied to three dimensional simulations of natural convection in a thin annulus with adiabatic wall at both vertical sides.