A volume-of-fluid interfacial flow solver with advected normals

We presented a new approach to calculating normal vectors to fluid interfaces in [JCP, 2007;226:774–97], by advecting unit normals along with an interface. In this paper, we introduce an implementation of the method in an interfacial flow solver. The advected normals are used to compute the interface curvature for calculating the surface tension force, and for reconstructing the interface in a volume-conserving volume-of-fluid (VOF) method. To improve the performance of the method in under-resolved regions of the flow, where normals vary sharply, a curvature-based criterion is used to detect and correct poorly defined normals. We present two-dimensional results of advection as well as actual flow problems and demonstrate that the new method is well suited for problems that involve large interface deformation and breakup (i.e. problems that involve substantial interface movement).