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A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations. (arXiv:1710.03587v1 [math.NA])
来源于:arXiv
Uncertainty Quantification through stochastic spectral methods is rising in
popularity. We derive a modification of the classical stochastic Galerkin
method, that ensures the hyperbolicity of the underlying hyperbolic system of
partial differential equations. The modification is done using a suitable
"slope" limiter, based on similar ideas in the context of kinetic moment
models. We apply the resulting modified stochastic Galerkin method to the
compressible Euler equations and the $M_1$ model of radiative transfer. Our
numerical results show that it can compete with other UQ methods like the
intrusive polynomial moment method while being computationally inexpensive and
easy to implement. 查看全文>>