This paper considers a modular grad-div stabilization method for approximating solutions of the time-dependent Boussinesq model of non-isothermal flows. The proposed method adds a minimally intrusive step to an existing Boussinesq code, with the key idea being that the penalization of the divergence errors, is only in the extra step (i.e. nothing is added to the original equations). The paper provides a full mathematical analysis by proving unconditional stability and optimal convergence of the methods considered. Numerical experiments confirm theoretical findings, and show that the algorithms have a similar positive effect as the usual grad-div stabilization.

中文翻译：

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不可压缩非等温流体流动的模块化梯度分度稳定

本文考虑了一种用于逼近非等温流动的瞬态 Boussinesq 模型的解的模块化梯度分度稳定方法。所提出的方法向现有的 Boussinesq 代码添加了一个最小侵入步骤，其关键思想是对发散误差的惩罚，只是在额外的步骤中（即没有添加到原始方程中）。该论文通过证明所考虑方法的无条件稳定性和最佳收敛性，提供了完整的数学分析。数值实验证实了理论发现，并表明该算法具有与通常的 grad-div 稳定类似的积极效果。