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.

提出了一种简单的直接加热热浸边界网格Boltzmann方法，用于浮力驱动的具有复杂几何边界的不可压缩流，以模拟具有弯曲边界的自然对流。在新开发的方法中，将宏观方程中的Dirichlet和Neumann边界条件都推导为新型的介观离散热源。介观离散热源由简化的显式离散热源方案组成，该方案简化了计算复杂性，并引入到温度场的格子Boltzmann方程中，扩展了先前直接强迫IB-LBM的思想。在我们的模拟中，均考虑了等温边界条件（即Dirichlet边界条件）和恒定热通量边界条件（即Neumann边界条件）。通过模拟具有弯曲边界的二维和三维热流，证明了本方法的效率和准确性。数值结果表明，该方法的有效性和准确性与实验结果及其他数值结果吻合良好。本方法也已成功地应用于在垂直两侧都具有绝热壁的薄环带中自然对流的三维模拟。