THINC scaling method that bridges VOF and level set schemes
THINC scaling method that bridges VOF and level set schemes
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DOI：
10.1016/j.jcp.2021.110323
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Ronit Kumar;Lidong Cheng;Y. Xiong;B. Xie;R. Abgrall;F. Xiao
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作者：
Ronit Kumar;Lidong Cheng;Y. Xiong;B. Xie;R. Abgrall;F. Xiao
我们提出了一种新的界面捕获方案，THINC-scaling，以统一VOF（流体体积）和水平集方法，这两种方法已经发展成为广泛应用于各种应用的两种不同方法。成功的关键是利用水平集域精确检索几何信息，利用VOF域实现数值保守性，从而保持高质量的THINC重构函数。界面被很好地定义为一个高阶多项式形式的曲面，即所谓的多项式界面曲面（PSI）。然后利用THINC重构函数用有限体积法更新VOF场，用半拉格朗日法更新水平集场。将VOF场和水平集场视为THINC重构函数的两个不同方面，THINC标度方案通过简单的求解过程，同时保留了VOF方法和水平集方法的优点，即VOF方法的质量/体积守恒性和水平集方法的几何忠实性。thinc缩放方案允许用高阶多项式表示接口，并且具有算法简单性，这在很大程度上简化了其在非结构化网格中的实现。已经开发并验证了结构化和非结构化网格的二维和三维算法。数值结果表明，作为一种界面捕获方法，THINC-scaling方案能够提供与其他最先进的方法相媲美的高保真度解，并且当界面用高于二阶的多项式表示时，它可以更深入地解析亚网格细丝结构。
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.