| Abstract: |
| Stochastic Galerkin methods offer an attractive intrusive framework for uncertainty quantification in hyperbolic conservation laws, but for nonlinear systems the projected stochastic Galerkin system may fail to preserve the hyperbolicity of the underlying equations. In this talk, we present a new framework for constructing hyperbolicity-preserving stochastic Galerkin methods for general systems of conservation laws with uncertain data. The central idea is to discretize the multiplication operator arising in the stochastic Galerkin formulation through an associative truncated polynomial product. Within this framework, we establish approximation properties, compare several choices of truncated products, and highlight the mechanisms by which the construction supports hyperbolicity preservation. We then present numerical results for the isothermal Euler equations and the compressible Euler equations with uncertain data, which demonstrate the robustness and effectiveness of the proposed approach. |
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