A High-precision calculation method for interface normal and curvature on an unstructured grid

Ito, Kei; Kunugi, Tomoaki*; Ohno, Shuji  ; Kamide, Hideki ; Ohshima, Hiroyuki

In the volume-of-fluid algorithm, the calculations of the interface normal and curvature are crucially important for accurately simulating interfacial flows. In this paper, the authors develop a height function method that works appropriately on an unstructured grid. In the process, the definition of the height function is discussed, and the high-precision calculation method of the interface normal is developed to meet the necessary condition for a second-order method. The curvature calculation method is also discussed and the approximated quadric curve of an interface is employed to calculate the curvature. Following a basic verification, the developed height function method is shown to successfully provide superior calculation accuracy and highly reduced computational cost compared with conventional calculation methods in terms of the interface normal and curvature.