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Title: An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number

Abstract

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.

Authors:
ORCiD logo [1];  [2]
  1. Department of Mathematics and Statistics Missouri University of Science and Technology Rolla Missouri 65409‐0020
  2. Department of Scientific Computing Florida State University Tallahassee Florida 32306‐4120
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1472199
Grant/Contract Number:  
DE‐SC0009324; DE‐SC0010678
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Numerical Methods for Partial Differential Equations
Additional Journal Information:
Journal Name: Numerical Methods for Partial Differential Equations Journal Volume: 34 Journal Issue: 6; Journal ID: ISSN 0749-159X
Publisher:
Wiley Blackwell (John Wiley & Sons)
Country of Publication:
United States
Language:
English

Citation Formats

Jiang, Nan, and Schneier, Michael. An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number. United States: N. p., 2018. Web. doi:10.1002/num.22281.
Jiang, Nan, & Schneier, Michael. An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number. United States. https://doi.org/10.1002/num.22281
Jiang, Nan, and Schneier, Michael. Sun . "An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number". United States. https://doi.org/10.1002/num.22281.
@article{osti_1472199,
title = {An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number},
author = {Jiang, Nan and Schneier, Michael},
abstractNote = {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.},
doi = {10.1002/num.22281},
journal = {Numerical Methods for Partial Differential Equations},
number = 6,
volume = 34,
place = {United States},
year = {Sun May 20 00:00:00 EDT 2018},
month = {Sun May 20 00:00:00 EDT 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1002/num.22281

Citation Metrics:
Cited by: 14 works
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