AI 中文总结
本研究针对可压缩两相流的六、七方程非平衡模型，提出新型diffuse-interface方法，改进了相密度隐式捕获，经KEEP离散化后在高密度比测试中展现出长时间积分的准确性、稳定性与鲁棒性。
AI 中文摘要
本研究针对用于模拟可压缩两相流的六方程和七方程非平衡模型，提出了一种新型相场方法。这类公式化方案可获得单调的混合物声速，最大限度减少了界面传输过程中的人工波延迟。所提出的相场公式基于基准七方程模型构建，以散度形式添加了界面正则化项，同时保持了偏微分方程之间的一致性，且不会引入虚假源项。该公式支持保守的相和混合物熵输运方程，有助于构建离散保守格式。六方程公式是在瞬时速度平衡条件下得到的。为避免偏微分方程组的本征向量退化，对体积界面正则化通量进行了修改，以考虑有限量的共轭相，这改进了相密度的隐式捕获方式。可压缩两相流的稳定性依赖于界面平衡条件以及离散动能和熵的保持。对界面-对流项（IEC）的详细分析表明，所有量的对流项与界面正则化项之间的通量分裂一致性存在额外要求，同时分析了其对相内能通量分裂的影响。提出了一种KEEP离散化方法，并在一组高密度比测试案例中进行了评估，包括界面平流、声波诱导的气泡振荡、斜声波反射与透射以及两相Taylor-Green涡流动。结果表明，该方法在长时间积分中具有准确性、稳定性和鲁棒性，这是湍流流动和声学模拟所需的特性，因为该框架不依赖于添加数值耗散。
英文摘要
In this work, a novel phase-field method is proposed for the six- and seven-equation non-equilibrium models for simulating compressible two-phase flows. Such formulations allow for monotonic mixture speed of sound, minimizing artificial wave delay during transmission across an interface. The proposed phase field formulation is constructed from the baseline seven-equation model, and interface-regularization terms are added in divergence form, while maintaining consistency between the partial differential equations without introducing spurious source terms. It admits conservative phasic and mixture entropy transport equations, thus facilitating the construction of discrete conservative schemes. The six-equation formulation is obtained under instantaneous velocity equilibrium. To avoid eigenvector degeneracy of the system of PDEs, the volumetric interface regularization flux is modified to account for a finite amount of conjugate phase, which improves on how phasic density is captured implicitly. Stability of compressible two-phase flow rely on the preservation of the interface-equilibrium conditions, and the preservation of discrete kinetic energy and entropy. A detailed analysis of IEC demonstrates additional requirements on the consistency of flux splittings between the convective and interface-regularization terms for all quantities, as well as the effects on the phasic internal energy flux splittings. A KEEP discretization is proposed and evaluated over a suite of high-density ratio test cases, including interface advection, acoustic wave-induced bubble oscillation, oblique acoustic wave reflection and transmission, and two-phase Taylor-Green vortex flow. Results demonstrate accuracy, stability and robustness for very long time integrations, a desired feature for simulation of turbulent flows and acoustics, since the framework does not rely on the addition of numerical dissipation.
