Natural gradient flow discretization of viscous thin<br/><br/>films on curved geometries

Monday, March 23, 2009 - 10:15am - 11:00am
EE/CS 3-180
Martin Rumpf (Rheinische Friedrich-Wilhelms-Universität Bonn)
The talk will focus on the numerical approximation of the
evolution of a thin viscous films on a curved geometry.
Here, the concept of natural time discretization for
gradient flows is revisited.
This is based on an explicit balance between the energy
decay and the corresponding
dissipation to be invested.
In case of thin films the dissipation is formulated in terms
of a transport field,
whereas the energy primarily depends on the film profile.
The velocity field and the film height
are coupled by the underlying transport equation. Hence, one
is naturally led to a PDE constraint optimization problem
and duality techniques from optimization are applied in the
minimization algorithm.
For the space discretization a discrete exterior calculus
approach is investigated.
The method can be generalized to the simulate thin coatings.
MSC Code: