This 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.

SPEAKERS
Andrzej Warzynski University of Leeds	Discontinuous-in-space explicit Runge-Kutta residual distribution schemes for time-dependent problems This talk will present explicit Runge-Kutta Residual Distribution (RD) schemes for hyperbolic conservation laws [1] 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.
Jae-Hun Jung, SUNY Buffalo	Uncertainty 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.
Lethuy Tran, University Of Utah	Th 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.
R.M Kirby, University of Utah	Smoothness-Increasing 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 details.