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.
N. Jiang and M. Schneier, "An Efficient, Partitioned Ensemble Algorithm for Simulating Ensembles of Evolutionary MHD Flows at Low Magnetic Reynolds Number," Numerical Methods for Partial Differential Equations, vol. 34, no. 6, pp. 2129 - 2152, John Wiley & Sons, Nov 2018.
The definitive version is available at https://doi.org/10.1002/num.22281
Mathematics and Statistics
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)
Article - Journal
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01 Nov 2018