An Efficient, Partitioned Ensemble Algorithm for Simulating Ensembles of Evolutionary MHD Flows at Low Magnetic Reynolds Number


Studying the propagation of uncertainties in a nonlinear dynamical system usually involves generating a set of samples in the stochastic parameter space and then repeated simulations with different sampled parameters. The main difficulty faced in the process is the excessive computational cost. In this paper, we present an efficient, partitioned ensemble algorithm to determine multiple realizations of a reduced Magnetohydrodynamics (MHD) system, which models MHD flows at low magnetic Reynolds number. The algorithm decouples the fully coupled problem into two smaller subphysics problems, which reduces the size of the linear systems that to be solved and allows the use of optimized codes for each subphysics problem. Moreover, the resulting coefficient matrices are the same for all realizations at each time step, which allows faster computation of all realizations and significant savings in computational cost. We prove this algorithm is first order accurate and long time stable under a time step condition. Numerical examples are provided to verify the theoretical results and demonstrate the efficiency of the algorithm.


Mathematics and Statistics


Nan Jiang was partially supported by the US National Science Foundation grant DMS-1720001 and a University of Missouri Research Board grant. Michael Schneier was supported by the US Air Force Office of Scientific Research grant FA9550-15-1-0001 and US Department of Energy Office of Science grants DE-SC0009324 and DE-SC0010678.

Keywords and Phrases

Dynamical systems; Finite element method; Linear systems; Nonlinear dynamical systems; Reynolds number; Stochastic systems; Computational costs; Ensemble Algorithms; Magnetic Reynolds number; Partitioned methods; Propagation of uncertainties; Reduced magnetohydrodynamics; Stochastic parameters; Uncertainty quantifications; Magnetohydrodynamics; Ensemble algorithm; Finite element method; Low magnetic Reynolds number

International Standard Serial Number (ISSN)

0749-159X; 1098-2426

Document Type

Article - Journal

Document Version


File Type





© 2018 John Wiley & Sons, All rights reserved.

Publication Date

01 Nov 2018