不可压缩非等温流体流动的模梯度-梯度稳定化
Modular grad-div stabilization for the incompressible non-isothermal fluid flows
摘要：
本文考虑了一种用于非等温流动的时变Boussinesq模型近似解的模块梯度-div稳定化方法。所提出的方法在现有Boussinesq码上增加了一个最小侵入步骤，其关键思想是发散误差的惩罚仅在额外的步骤中（即没有添加到原始方程中）。本文通过证明所考虑的方法的无条件稳定性和最优收敛性，提供了一个完整的数学分析。数值实验证实了理论研究结果，并表明该算法具有类似的积极效果，通常的梯度-div稳定。
英文摘要：
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.
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