New numerical techniques for some non-Newtonian fluid models and thin film heteroepitaxial growths
- Date: 01/10/2007
Young-Ju Lee (University of California, Los Angeles)
University of British Columbia
In this talk, we shall discuss the construction of discrete analogues
of continuous theories and their vital roles in two research areas,
fluid dynamics and material sciences.
For the simulation of rate-type non-Newtonian fluid flows, we present
new numerical discretization techniques obtained from the observation
that the constitutive equations can be recast into the well-known
symmetric matrix Riccati differential equations. Our discretization
schemes are then shown to preserve some important physical
characteristics that have been believed to be crucial for the numerical
stability of any discretization scheme. The confirmation of such a
belief shall be clearly demonstrated by providing the discrete analogue
of the energy estimate for the continuous models.
A discrete strain model is essential for understanding the strain
effects in the thin film heteroepitaxial growth (one atomic species
grows on a substrate of another material). New techniques are necessary
to impose certain artificial boundary condition for the solution of the
model, since the thickness of the substrate is considered to be
infinite compared to the film thickness. We develop the discrete
analogue of the conditions that ensure the existence of the exact
artificial boundary condition, whose validation leads to the reduction
of the computational domain siginificantly with no loss of accuracy.
Some illustrative but nontrivial applications of our methodologies shall be provided.
UBC Mathematics Department Colloquium Hosted by PIMS-UBC 2007