No. 2019.03
Hyperbolic stochastic Galerkin formulation for the p-system
S. Gerster, M. Herty, and A. Sikstel
Subject: Hyperbolic partial differential equations, uncertainty quantification, stochastic Galerkin method, Euler equations, Roe variable transform
Abstract
We analyze properties of stochastic hyperbolic systems using a Galerkin formulation, which reformulates the stochastic system as a deterministic one that describes the evolution of polynomial chaos modes. We investigate conditions such that the resulting systems are hyperbolic. We state the eigendecompositions in closed form. A Roe flux is presented and theoretical results are illustrated numerically.