Scalable implicit incompressible resistive MHD with stabilized FE and fullycoupled Newton–KrylovAMG
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 lengthscales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fullyimplicit 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 directtosteadystate solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fullycoupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the largescale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected orderofaccuracy 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:

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 Sandia National Lab. (SNLNM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 SAND201420573J
Journal ID: ISSN 00457825; PII: S0045782516300184
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 Computer Methods in Applied Mechanics and Engineering
 Additional Journal Information:
 Journal Volume: 304; Journal Issue: C; Journal ID: ISSN 00457825
 Publisher:
 Elsevier
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States); Sandia National Laboratories, Livermore, CA (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 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
 OSTI Identifier:
 1310309
 Alternate Identifier(s):
 OSTI ID: 1467499
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 fullycoupled Newton–KrylovAMG. United States: N. p.,
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 fullycoupled Newton–KrylovAMG. United States. doi: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.. 2016.
"Scalable implicit incompressible resistive MHD with stabilized FE and fullycoupled Newton–KrylovAMG". United States.
doi: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 fullycoupled Newton–KrylovAMG},
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 lengthscales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fullyimplicit 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 directtosteadystate solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fullycoupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the largescale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected orderofaccuracy 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 = {2016},
month = {2}
}