477 IGPM477.pdf        March 2018
TITLE Hyperbolic Stochastic Galerkin Formulation for the p-System
AUTHORS Stephan Gerster, Michael Herty, Aleksey Sikstel
ABSTRACT We analyze properties of stochastic hyperbolic systems with a Galerkin formulation, which reformulates the stochastic system as a deterministic one that describes the evolution of polynomial chaos modes. We guarantee that the resulting systems remain hyperbolic and discuss the representation of positive physical quantities. Furthermore, we state eigendecompositions in closed form and present numerical results based on an adaptive discontinuous Galerkin method.
KEYWORDS Hyperbolic Partial Differential Equations, Uncertainty Quantification, Stochastic Galerkin Method, Euler Equations, Roe Variable Transformation