TY - JOUR
T1 - A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs
AU - Wu , Kailiang
AU - Xiu , Dongbin
AU - Zhong , Xinghui
JO - Communications in Computational Physics
VL - 2
SP - 423
EP - 447
PY - 2021
DA - 2021/05
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0167
UR - https://global-sci.org/intro/article_detail/cicp/19120.html
KW - Uncertainty quantification, ideal magnetohydrodynamics, generalized polynomial
chaos, stochastic Galerkin, symmetric hyperbolic, finite volume WENO method.
AB - <p style="text-align: justify;">In this paper, we investigate the ideal magnetohydrodynamic (MHD) equations with random inputs based on generalized polynomial chaos (gPC) stochastic
Galerkin approximation. A special treatment with symmetrization is carried out for
the gPC stochastic Galerkin method so that the resulting deterministic gPC Galerkin
system is provably symmetric hyperbolic in the spatially one-dimensional case. We
discretize the hyperbolic gPC Galerkin system with a high-order path-conservative finite volume weighted essentially non-oscillatory scheme in space and a third-order total variation diminishing Runge-Kutta method in time. The method is also extended to
two spatial dimensions via the operator splitting technique. Several numerical examples are provided to illustrate the accuracy and effectiveness of the numerical scheme.</p>