The interface tends to behave as a circular shape under the effect of surface tension in the two-dimensional two-phase fluid flow. In this study, based on the coupled volume-of-fluid and level set (VOSET) method, an accurate circle-based interface reconstruction (CIR) algorithm for structured meshes is proposed, which features a straightforward implementation procedure. A portion of the standard circle is employed to approximate the curve interface, without the need for complex classification, coordinate transformation, and equation transformation. The radius of this circle is computed simply by the curvature and signed distance at the mixed cell center, and the center of this circle is determined using a straightforward dichotomy method under the mass conservation constraints. Results indicate that the coupled VOSET and CIR (VOSET-CIR) method maintains superior computational accuracy in the signed distance, interface curvature, and dynamic interface reconstruction compared to the coupled VOSET and piecewise linear interface calculation (VOSET-PLIC) method, with accuracy improvements ranging from 34% to 1490% across different test cases. Furthermore, the VOSET-CIR method outperforms the efficient least squares volume-of-fluid interface reconstruction (ELVIRA) and PLIC algorithms in reconstructing random circles and surpasses the quadratic spline based interface reconstruction (QUASI) algorithm in reconstructing random squares. In terms of computational efficiency, except for the initial PLIC algorithm, the time costs of the VOSET-CIR method are substantially lower than those of the ELVIRA and QUASI algorithms, as well as the VOSET-PLIC method.

中文翻译：

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一种基于流体体积与水平集耦合的圆界面重构算法

在二维两相流体流动中，在表面张力的作用下，界面趋于呈圆形。在本研究中，基于耦合流体体积和水平集（VOSET）方法，提出了一种用于结构化网格的精确的基于圆的界面重建（CIR）算法，该算法具有简单的实现过程。利用标准圆的一部分来逼近曲线界面，无需进行复杂的分类、坐标变换和方程变换。该圆的半径只需通过混合单元中心处的曲率和有符号距离即可计算，并且该圆的中心是在质量守恒约束下使用简单的二分法确定的。结果表明，与耦合 VOSET 和分段线性界面计算 (VOSET-PLIC) 方法相比，耦合 VOSET 和 CIR (VOSET-CIR) 方法在符号距离、界面曲率和动态界面重建方面保持了优异的计算精度，并且精度有所提高在不同的测试用例中，这一比例从 34% 到 1490% 不等。此外，VOSET-CIR方法在重建随机圆方面优于高效最小二乘流体体积界面重建（ELVIRA）和PLIC算法，在重建随机正方形方面优于基于二次样条的界面重建（QUASI）算法。从计算效率来看，除了最初的PLIC算法外，VOSET-CIR方法的时间成本大大低于ELVIRA和QUASI算法以及VOSET-PLIC方法。