in Methods for Hyperbolic Equations, I
Martin Berzins, University of Utah
Lilia Krivodonova, University of Waterloo
Minisyposium, the first of two, will address recent advances in the
solution of hyperbolic equations. Topics included will be include methods
such as Discontinuous Galerkin methods as well as new finite volume
schemes and substantial impriovemnets of existing schemes to preserve
positivity or to better postprocess the existing high-order solutions.
University of Leeds
explicit Runge-Kutta residual distribution schemes for time-dependent
This talk will present explicit Runge-Kutta Residual Distribution
(RD) schemes for hyperbolic conservation laws  in conjunction
with discontinuous-in-space data representation. This extends previous
work on the discontinuous residual distribution schemes for steady
problems . It also extends work of Abgrall and Shu in the sense
that it reformulates the Runge-Kutta Discontinuous Galerkin (DG)
method in the framework of Runge-Kutta Residual Distribution schemes.Numerical
results for two-dimensional hyperbolic conservation laws on structured
and unstructured triangular meshes will also be presented.
quantification and detailed study of numerical methods for the perturbed
sine-Gordon equation with impulsive forcing
We consider the sine-Gordon equation with a point-like impurity
and investigate the kink interactions with the singular impurity.
First we provide the detailed study of numerical convergence for
various numerical methods including the spectral collocation and
Galerkin methods and finite difference methods with different approximations
of the singular forcing term. We show that some of numerical methods
yield wrong kink dynamics and should be avoided. Then we consider
the kink interaction when uncertainties are involved in the system.
We use the generalized polynomial chaos method and provide some
preliminary results. This is a joint work with Gino Biondini, Danhua
Wang, and Debananda Chakraborty.
University Of Utah
Improved Productuion ICE Method for High Speed Flows
The Implicit Continuous-fluid Eulerian (ICE) method is a successful
and widely used semi-implicit flow finite-volume solver.The IMproved
Production ICE (IMPICE) method for the one-dimensional Euler equations
was introduced by Tran and Berzins with aim to remove the discrepancies
and unphysical oscillations in the numerical solutions of the Production
ICE method. The IMPICE method is now generalized to the multi-dimensional
cases. The obtained numerical solutions to several chosen test cases
for two-dimensional and three-dimensional system of Euler equations
using the multi-dimensional IMPICE method are presented.
University of Utah
Accuracy-Conserving (SIAC) Filtering: Practical Consideration When
Apllied to Visualization
The discontinuous Galerkin (DG) method continues to maintain heightened
levels of interest within the simulation community because of the
discretization flexibility it provides. This flexibility generates
a plethora of dificulties when one attempts to post-process DG fields
for analysis and evaluation of scientific results. Smoothness- increasing
accuracy-conserving (SIAC) filtering enhances the smoothness of
the field by elimi- nating the discontinuity between elements. We
will apply SIAC filtering to DG fields for the purposes of visualization.
Included in the topics to be discussed will be comparisons between
exact and approximate quadrature algorithms, extensions of SIAC
filtering to triangular meshes and implementation and parallelization