A New Method for Calculating Interface Normal Vectors and Curvatures when Modelling Free-Surface Flows

In simulating free-surface flows, the interface normal vectors and curvature are needed for modelling surface tension e↵ects. We present a new method for accurately calculating these quantities. In this method, an entirely di↵erent approach is taken, compared to common methods where normals and curvature are obtained from the Volume-of-Fluid (VOF) or Level Set (LS) functions. In this fixed-grid method, the interface normals are advected along with the interface, although the methods of advecting normals and the interface are independent. In this work, the interface is tracked using the VOF method. The advected normals are used to reconstruct the interface at each timestep, and calculate the interface curvature at any point. The mathematical formulation for the advection of normals is derived from the evolution equation of the LS function, but the method is independent of the LS function. The implementation of the new method is straightforward, and its accuracy is demonstrated via two test cases: translation and rotation of a circle. The results show that this method is second-order accurate in calculating interface normals and curvature. Furthermore, the performance of the method has been examined in a flow field which includes shear.