In this article a coupled version of the improved divergence‐free‐condition compensated method will be proposed to simulate time‐varying geometries by direct forcing immersed boundary method. The proposed method can be seen as a quasi‐multi‐moment framework due to the fact that the momentum equations are discretized by both cell‐centered and cell‐face velocity. For simulating time‐varying geometries, a semi‐implicit iterative method is proposed for calculating the direct forcing terms. Treatments for suppressing spurious force oscillations, calculating drag/lift forces, and evaluating velocity and pressure for freshly cells will also be addressed. In order to show the applicability and accuracy, analytical as well as benchmark problems will be investigated by the present framework and compared with other numerical and experimental results.

中文翻译：

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开发改进的无散度补偿耦合框架，以解决随时间变化的几何形状的流动问题

在本文中，将提出一种改进版本的无散度条件补偿方法的耦合版本，以通过直接强制浸入边界方法来模拟时变几何。由于动量方程通过单元中心速度和单元表面速度离散化，因此该方法可以看作是准多矩框架。为了模拟时变几何，提出了一种半隐式迭代方法来计算直接强迫项。还将解决用于抑制杂散力振荡，计算阻力/升力以及评估新鲜单元的速度和压力的处理方法。为了显示适用性和准确性，本框架将研究分析问题和基准问题，并将其与其他数值和实验结果进行比较。