A piecewise circular interface construction (PCIC) method is described, where height functions based curvature estimates are directly utilised for accurate interface reconstruction under the framework of volume of fluid method. The present work is an attempt to develop a robust and accurate higher order interface reconstruction algorithm that is capable of accurate simulation of surface tension dominated flows. The proposed hybrid method (H-PCIC) is thus able to take advantage of merits of both PCIC and HF methods, achieving at least second order convergence with respect to both interface reconstruction and curvature computation. This is in addition to the significantly superior quality of the reconstructed interface with respect to PLIC methods. This seamless blending of the HF and PCIC quantities is enabled by c0-correction procedures applied to base PLIC and initial PCIC steps. More recent variants of the height function method with variable stencil size are used for calculation of radius of curvature. The capability of this proposed method towards simulation of flow problems within a well-balanced two-phase solver is established with help of multiple complex two-phase flow problems. This validation exercise also demonstrates the capability of PCIC class of methods towards solutions of two-phase flows with intricate physics.

中文翻译：

---

使用高度函数的分段圆形界面构造

描述了分段圆形界面构造（PCIC）方法，其中直接利用基于曲率估计的高度函数在流体体积方法的框架下进行精确的界面重建。目前的工作是尝试开发一种稳健且准确的高阶界面重建算法，该算法能够准确模拟表面张力主导的流动。因此，所提出的混合方法（H-PCIC）能够利用 PCIC 和 HF 方法的优点，在界面重构和曲率计算方面至少实现二阶收敛。除此之外，相对于 PLIC 方法，重建界面的质量显着提高。HF 和 PCIC 量的这种无缝混合是通过应用于基本 PLIC 和初始 PCIC 步骤的 c0 校正程序实现的。具有可变模板尺寸的高度函数方法的最新变体用于计算曲率半径。借助多个复杂的两相流问题，建立了该方法在平衡良好的两相求解器中模拟流动问题的能力。该验证练习还展示了 PCIC 类方法解决具有复杂物理场的两相流的能力。