Numerical solution of hyperbolic-elliptic systems of conservation laws by multiresolution schemes
Event details
| Date | 23.06.2010 |
| Hour | 16:15 |
| Speaker | Dr. Stefan Berres |
| Location |
MAA112
|
| Category | Conferences - Seminars |
We consider the asymptotic solution behavior of hyperbolic-elliptic
systems of conservation laws when the initial data lie inside an
elliptic region and are chosen almost constant with an only slightly
perturbation in a small number of cells. For this setting and a
particular system, Frid and Liu [4] observed the appearance of a highly
oscillatory solution. We herein capture, and in part analyze, such
oscillations first for the system studied in [4], and then for a
hyperbolic-elliptic system that emerges from a model of sedimentation of
a bidisperse suspension [2].
Since the generic structure of solutions of initial value problems of
these mixed systems is not yet completely understood, the main goal of
this work is to give a contributition in understanding the essence of
the oscilatory phenomena. The novelty of our approach is that we employ
a WENO multiresolution method [3], which adaptively concentrates
computational effort associated with a given numerical scheme for
systems of conservation laws on areas of strong variation of the
solution. In our case, the method can be advantageously employed to
capture the oscillations due to the mixed-type nature of the system [1]
because of its capability to use very fine scales in concentrated
regions of the domain.
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- Ricardo Ruiz