A Multiscale Approach to Mesh-based Surface Tension Flows

1
A Multiscale Approach to Mesh-based Surface
Tension Flows
2
Tension
3
Navier-Stokes
4
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

5
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).
6
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.
7
Multiscale
8
Sub-grid Scale
Implicit Newmark time integration scheme
9
Grid Scale
10
Multiscale
11
Result