A horizontal refined piecewise curve interface reconstruction (HOPCIR) algorithm for reconstructing the vapor-liquid interface

The vapor-liquid interface can be characterized as a circle or sphere affected by surface tension. However, linearization or planarization processing is commonly employed to simplify the reconstruction of the vapor-liquid interface within a grid cell, introducing errors in numerical simulations of two-phase flow. Therefore, this paper proposes a straightforward and accurate Horizontal Refined Piecewise Curve Interface Reconstruction (HOPCIR) algorithm to reconstruct the curve vapor-liquid interface for the two-dimensional structured grid. In this method, a standardized circle segment is employed to represent the vapor-liquid interface segment within each mixed grid cell, uniquely defined by its radius and center. The radius of this circle is determined by the curvature of the interface segment, and an iterative procedure is employed to calculate the circle's center using the known fluid volume fraction and initial interface obtained by linear reconstruction. Another integral aspect of the HOPCIR algorithm involves solving the reconstructed distance function to enhance the accuracy of curve reconstruction. Comparative analysis with the coupled volume-of-fluid and level set (VOSET) method demonstrates the superior performance of the HOPCIR algorithm in reconstructing vapor-liquid interfaces and solving the reconstructed distance function, interface curvature, surface tension, and fluid volume fraction.