A Multiscale Approach to Mesh-based Surface Tension Flows

Tension

Navier-Stokes surface tension coefficient, curvature normal of the liquid interface

Problems Many cells are required to resolve the shape of a single droplet (?) Surface tension forces impose a strict time step restriction on the solver

How to solve? surface tension forces integrated over the length of a time step can be related to the distance of the liquid surface to another version of the surface advected by a volume preserving mean curvature flow (VCF).

What is VCL? a family of surfaces evolves under mean curvature flow if the velocity of which a point on the surface moves is given by the mean curvature of the surface. In another word, mean curvature flow can describe the transformation of surface under pure tension force.

Multiscale

Sub-grid Scale Implicit Newmark time integration scheme

Grid Scale

Multiscale

Result