We present a novel interface-capturing scheme, THINC-scaling, to unify the VOF (volume of fluid) and the level set methods, which have been developed as two different approaches widely used in various applications. The key to success is to maintain a high-quality THINC reconstruction function using the level set field to accurately retrieve geometrical information and the VOF field to fulfill numerical conservativeness. The interface is well defined as a surface in form of a high-order polynomial, so-called the polynomial surface of interface (PSI). The THINC reconstruction function is then used to update the VOF field via a finite volume method, and the level set field via a semi-Lagrangian method. Seeing the VOF field and the level set field as two different aspects of the THINC reconstruction function, the THINC-scaling scheme preserves at the same time the advantages of both VOF and level set methods, i.e. the mass/volume conservation of the VOF method and the geometrical faithfulness of the level set method, through a straightforward solution procedure. The THINC-scaling scheme allows to represent an interface with high-order polynomials and has algorithmic simplicity which largely eases its implementation in unstructured grids. Two and three dimensional algorithms in both structured and unstructured grids have been developed and verified. The numerical results reveal that the THINC-scaling scheme, as an interface capturing method, is able to provide high-fidelity solution comparable to other most advanced methods, and more profoundly it can resolve sub-grid filament structures if the interface is represented by a polynomial higher than second order.

我们提出了一种新颖的界面捕获方案THINC缩放，以统一VOF（流体体积）和液位设置方法，这些方法已被开发为在各种应用中广泛使用的两种不同方法。成功的关键是使用水平集字段来准确检索几何信息，并使用VOF字段来满足数值保守性，从而保持高质量的THINC重建功能。界面被很好地定义为高阶多项式形式的表面，即所谓的界面多项式表面（PSI）。然后使用THINC重建函数通过有限体积方法更新VOF字段，并通过半拉格朗日方法更新水平集字段。将VOF字段和水平集字段视为THINC重建功能的两个不同方面，THINC缩放方案通过简单的求解过程，同时保留了VOF和水平集方法的优点，即VOF方法的质量/体积守恒和水平集方法的几何真实性。THINC缩放方案允许用高阶多项式表示一个接口，并且算法简单，这极大地简化了其在非结构化网格中的实现。已经开发和验证了结构化和非结构化网格中的二维和三维算法。数值结果表明，THINC缩放方案作为一种接口捕获方法，能够提供可与其他最先进方法相媲美的高保真解决方案，