A Multiscale Approach to Mesh-based Surface Tension Flows

摘要

We present an approach to simulate flows driven by surface tensionrnbased on triangle meshes. Our method consists of two simulationrnlayers: the first layer is an Eulerian method for simulatingrnsurface tension forces that is free from typical strict time steprnconstraints. The second simulation layer is a Lagrangian finite elementrnmethod that simulates sub-grid scale wave details on the fluidrnsurface. The surface wave simulation employs an unconditionallyrnstable, symplectic time integration method that allows for a highpropagation speed due to strong surface tension. Our approach canrnnaturally separate the grid- and sub-grid scales based on a volumepreservingrnmean curvature flow. As our model for the sub-grid dynamicsrnenforces a local conservation of mass, it leads to realisticrnpinch off and merging effects. In addition to this method for simulatingrndynamic surface tension effects, we also present an efficientrnnon-oscillatory approximation for capturing damped surface tensionrnbehavior. These approaches allow us to efficiently simulaterncomplex phenomena associated with strong surface tension, such asrnRayleigh-Plateau instabilities and crown splashes, in a short amountrnof time.