Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG
Abstract
Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method, and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling ofmore »
- Authors:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1310309
- Alternate Identifier(s):
- OSTI ID: 1467499
- Report Number(s):
- SAND-2014-20573J
Journal ID: ISSN 0045-7825; PII: S0045782516300184
- Grant/Contract Number:
- AC04-94AL85000; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 304; Journal Issue: C; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; stabilized FE; variational multiscale methods; resistive magnetohydrodynamics; implicit methods; Newton–Krylov; algebraic multigrid methods
Citation Formats
Shadid, J. N., Pawlowski, R. P., Cyr, E. C., Tuminaro, R. S., Chacon, L., and Weber, P. D. Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG. United States: N. p., 2016.
Web. doi:10.1016/j.cma.2016.01.019.
Shadid, J. N., Pawlowski, R. P., Cyr, E. C., Tuminaro, R. S., Chacon, L., & Weber, P. D. Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG. United States. https://doi.org/10.1016/j.cma.2016.01.019
Shadid, J. N., Pawlowski, R. P., Cyr, E. C., Tuminaro, R. S., Chacon, L., and Weber, P. D. Wed .
"Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG". United States. https://doi.org/10.1016/j.cma.2016.01.019. https://www.osti.gov/servlets/purl/1310309.
@article{osti_1310309,
title = {Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG},
author = {Shadid, J. N. and Pawlowski, R. P. and Cyr, E. C. and Tuminaro, R. S. and Chacon, L. and Weber, P. D.},
abstractNote = {Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method, and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.},
doi = {10.1016/j.cma.2016.01.019},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 304,
place = {United States},
year = {Wed Feb 10 00:00:00 EST 2016},
month = {Wed Feb 10 00:00:00 EST 2016}
}
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