A pressure‐based method is developed to solve the unified conservation laws for incompressible and compressible fluids. A polytropic law is used to model the compressibility of a gas and decouple the energy equation. The pressure field is calculated by solving a single‐pressure Poisson equation for the entire flow domain. The effects of the compressibility of the gas are reflected in the source term of the Poisson equation. The continuities of pressure and normal velocity across a material interface are achieved without any additional treatment along the interface. To validate the developed method, the oscillation of a water column in a closed tube due to the compression and expansion of air in the tube is simulated. The computed time history of the pressure at the end wall of the tube is in good agreement with other computational results. The free drop of a water column in a closed tank is simulated. The time history of the pressure at the center of the bottom of the tank shows good agreement with other reported results. The developed code is applied to simulate the air cushion effect of entrapped air in a dam break flow. The computed result is in good agreement with other experimental and computational results until the air is entrapped. As the entrapped air pocket undergoes rapid pulsation, the pressure field of water around the air pocket oscillates synchronously.

中文翻译：

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使用基于压力的统一方程方法模拟不可压缩自由表面流中截留空气的可压缩性

开发了一种基于压力的方法来解决不可压缩和可压缩流体的统一守恒律。使用多变定律对气体的可压缩性进行建模，并将能量方程解耦。通过求解整个流域的单压力泊松方程来计算压力场。气体可压缩性的影响反映在泊松方程的源项中。沿材料界面实现压力和法向速度的连续性，而无需沿界面进行任何其他处理。为了验证开发的方法，模拟了封闭管中水柱由于管中空气的压缩和膨胀而产生的振荡。管端壁处压力的计算时间历史与其他计算结果非常吻合。模拟了密闭罐中水柱的自由下落。储罐底部中心压力的时间历程与其他报告的结果显示出良好的一致性。开发的代码适用于模拟截流中截留的空气的气垫效果。计算结果与其他实验和计算结果非常吻合，直到空气被夹带。当夹带的气穴经历快速脉动时，气穴周围水的压力场会同步振荡。计算结果与其他实验和计算结果非常吻合，直到空气被夹带。当夹带的气穴经历快速脉动时，气穴周围水的压力场会同步振荡。计算结果与其他实验和计算结果非常吻合，直到空气被夹带。当夹带的气穴经历快速脉动时，气穴周围水的压力场会同步振荡。