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:
-
- Department of Mathematics and Statistics Missouri University of Science and Technology Rolla Missouri 65409‐0020
- 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}
}
https://doi.org/10.1002/num.22281
Web of Science
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