The prototypical diffuse-interface model that describes multi-component flows is the Navier-Stokes Cahn-Hilliard model (NSCH). Over the last decades many NSCH models have appeared that claim to describe the same physical phenomena, yet are distinct from one another. In a recent article [M.F.P. ten Eikelder, K.G. van der Zee, I. Akkerman, and D. Schillinger, Math. Mod. Meth. Appl. S. 33, pp 175-221, 2023.] we have established a unified framework of virtually all NSCH models. The framework reveals that there is only a single consistent NSCH model that naturally emanates from the underlying mixture theory. In the current article we present, verify and validate this novel consistent NSCH model by means of numerical simulation. To this purpose we discretize a divergence-free velocity formulation of the NSCH model using divergence-conforming isogeometric spaces. We compare computations of our consistent model to results of existing models from literature. The predictive capability of the numerical methodology is demonstrated via three-dimensional computations of a rising bubble and the contraction of a liquid filament that compare well with experimental data.

翻译：典型的描述多组分流动的扩散界面模型为纳维-斯托克斯-卡恩-希利亚德模型（Navier-Stokes Cahn-Hilliard模型，简称NSCH模型）。近几十年来，虽声称描述相同物理现象，但彼此间存在差异的大量NSCH模型相继涌现。在近期文献[M.F.P. ten Eikelder, K.G. van der Zee, I. Akkerman, 和 D. Schillinger, Math. Mod. Meth. Appl. S. 33, pp 175-221, 2023.]中，我们建立了近乎涵盖所有NSCH模型的统一框架。该框架揭示，仅有一个一致性NSCH模型能够自然源自底层混合理论。本文通过数值模拟对该新型一致性NSCH模型进行验证与确认。为此，我们采用散度相容等几何空间对NSCH模型的无散度速度公式进行离散化，并将一致性模型的计算结果与文献中现有模型结果进行对比。通过三维气泡上升与液体细丝收缩的数值计算验证了该数值方法的预测能力，计算结果与实验数据吻合良好。