Advecting normal vectors: A new method for calculating interface normals and curvatures when modeling two-phase flows

In simulating two-phase flows, interface normal vectors and curvatures are needed for modeling surface tension. In the traditional approach, these quantities are calculated from the spatial derivatives of a scalar function (e.g. the volume-of-fluid or the level set function) at any instant in time. The orders of accuracy of normals and curvatures calculated from these functions are studied. A new method for calculating these quantities is then presented, where the interface unit normals are advected along with whatever function represents the interface, and curvatures are calculated directly from these advected normals. To illustrate this new approach, the volume-of-fluid method is used to represent the interface and the advected normals are used for interface reconstruction. The accuracy and performance of the new method are demonstrated via test cases with prescribed velocity fields. The results are compared with those of traditional approaches.