In this paper, we consider and analyze the stability of three implicit/explicit (IMEX) schemes for the time-dependent natural convection problem, these considered numerical schemes contain the first order backward Euler scheme, second order Crank-Nicolson IMEX scheme and BDF2-AB2 combination. All numerical schemes deal with the linear terms implicitly and the nonlinear terms explicitly. Then the original nonlinear problem is split into two linearized subproblems with constant coefficient matrixes, which reduces the computational complexity and saves a lot of storage. The biggest feature of this paper is to establish the unconditional stability of three IMEX schemes for incompressible flows, which improves and supplements the published theoretical findings. Finally, some numerical examples are provided to show the performances of the considered numerical schemes.

在本文中，我们考虑并分析了三种隐式/显式 (IMEX) 方案对时间相关的自然对流问题的稳定性，这些考虑的数值方案包括一阶后向 Euler 方案、二阶 Crank-Nicolson IMEX 方案和 BDF2- AB2 组合。所有数值方案都隐含地处理线性项和显式处理非线性项。然后将原来的非线性问题拆分成两个具有常系数矩阵的线性化子问题，降低了计算复杂度，节省了大量存储空间。本文最大的特点是建立了三个不可压缩流动IMEX格式的无条件稳定性，对已发表的理论结果进行了改进和补充。最后，