Elliptic Interface Reconstruction for Two-Phase Flow Problems Using the Volume of Fluid Method

An interface reconstruction algorithm for the Volume of Fluid (VOF) method is required for two-phase flow problems for advection of phase interface. The primary method for interface reconstruction has been through piecewise linear interface calculation (PLIC) reconstruction. However, while PLIC reconstruction is highly accurate at representing small curvature interfaces by approximating planes across multiple grid cells, accuracy problems arise when the size of the mesh is too coarse to accurately approximate a large curvature without resorting to refining the mesh. An elliptic interface reconstructing algorithm is explored for two-phase flow problems in 2D to determine the viability of a higher-order interface reconstruction algorithm. This requires first developing an area overlap function between an arbitrary triangle and ellipse, which is then extended to calculate the area fraction field of an ellipse within a mesh. Then, the "reverse" problem of elliptic interface reconstruction given an area fraction field is examined. A study is conducted to determine the presence of any local minimums when varying the ellipse parameters. In the future, a multi-dimensional root-finding solver using Newton's Method will be developed to properly reconstruct the elliptic interface given the area fraction field.