A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations

摘要

Uncertainty Quantification through stochastic spectral methods is rising inpopularity. We derive a modification of the classical stochastic Galerkinmethod, that ensures the hyperbolicity of the underlying hyperbolic system ofpartial differential equations. The modification is done using a suitable"slope" limiter, based on similar ideas in the context of kinetic momentmodels. We apply the resulting modified stochastic Galerkin method to thecompressible Euler equations and the $M_1$ model of radiative transfer. Ournumerical results show that it can compete with other UQ methods like theintrusive polynomial moment method while being computationally inexpensive andeasy to implement.