A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs (Communications in Computational Physics, 2021)
In this paper, we investigate the ideal magnetohydrodynamic (MHD) equations with random inputs based on generalized polynomial chaos (gPC) stochasticGalerkin approximation. A special treatment with symmetrization is carried out forthe gPC stochastic Galerkin method so that the resulting deterministic gPC Galerkinsystem is provably symmetric hyperbolic in the spatially one-dimensional case. Wediscretize 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 totwo spatial dimensions via the operator splitting technique. Several numerical examples are provided to illustrate the accuracy and effectiveness of the numerical scheme.
Keywords: Uncertainty quantification; ideal magnetohydrodynamics; generalized polynomial chaos; stochastic Galerkin; symmetric hyperbolic; finite volume WENO method.