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A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs

A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs
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Year:    2021

Author:    Kailiang Wu, Dongbin Xiu, Xinghui Zhong

Communications in Computational Physics, Vol. 30 (2021), Iss. 2 : pp. 423–447

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0167

Communications in Computational Physics, Vol. 30 (2021), Iss. 2 : pp. 423–447

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Uncertainty quantification ideal magnetohydrodynamics generalized polynomial chaos stochastic Galerkin symmetric hyperbolic finite volume WENO method.

Author Details

Kailiang Wu

Dongbin Xiu

Xinghui Zhong

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