A new interface tracking method: The polygonal area mapping method

We present a new method, the polygonal area mapping (PAM) method, for tracking a non-diffusive, immiscible material interface between two materials in two-dimensional incompressible flows. This method represents material areas explicitly as piecewise polygons, traces characteristic points on polygon boundaries along pathlines and calculates new material areas inside interface cells via polygon-clippings in a discrete manner. The new method has very little spatial numerical diffusion and tracks the interface singularities naturally and accurately. In addition to high accuracy, the PAM method can be directly used on either a structured rectangular mesh or an unstructured mesh without any modifications. The mass conservation is enforced by heuristic algorithms adjusting the volume of material polygons. The results from a set of widely used benchmark tests show that the PAM method is superior to existing volume-of-fluid (VOF) methods.