Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz

Handle URI:
http://hdl.handle.net/10754/562235
Title:
Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz
Authors:
Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of . r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the . x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated. © 2012 Elsevier Inc.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Extreme Computing Research Center
Publisher:
Elsevier
Journal:
Journal of Computational Physics
Issue Date:
Jul-2012
DOI:
10.1016/j.jcp.2012.05.009
Type:
Article
ISSN:
00219991
Sponsors:
This work was supported by the Department of Applied Physics and Applied Mathematics of Columbia University (under Contract No. DE-FC02-06ER54863), the Center for Simulation of RF Wave Interactions with Magnetohydrodynamics, which is funded by the U.S. Department of Energy, Office of Science, and the King Abdullah University of Science and Technology (KAUST). The computational sources were provided by the National Energy Research Scientific Computing Center (NERSC) (under Contract No. DE-AC02-05CH11231). Their support is gratefully acknowledged.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorYuan, Xuefeien
dc.contributor.authorJardin, Stephen C.en
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2015-08-03T09:57:25Zen
dc.date.available2015-08-03T09:57:25Zen
dc.date.issued2012-07en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2012.05.009en
dc.identifier.urihttp://hdl.handle.net/10754/562235en
dc.description.abstractNumerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of . r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the . x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated. © 2012 Elsevier Inc.en
dc.description.sponsorshipThis work was supported by the Department of Applied Physics and Applied Mathematics of Columbia University (under Contract No. DE-FC02-06ER54863), the Center for Simulation of RF Wave Interactions with Magnetohydrodynamics, which is funded by the U.S. Department of Energy, Office of Science, and the King Abdullah University of Science and Technology (KAUST). The computational sources were provided by the National Energy Research Scientific Computing Center (NERSC) (under Contract No. DE-AC02-05CH11231). Their support is gratefully acknowledged.en
dc.publisherElsevieren
dc.subjectDynamically adaptive griden
dc.subjectEquidistribution principleen
dc.subjectMagnetic reconnectionen
dc.subjectMHDen
dc.subjectMonge-Ampère equationen
dc.subjectMonge-Kantorovich optimizationen
dc.subjectNKSen
dc.subjectR-Refinementen
dc.subjectStructured griden
dc.titleNumerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarzen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionDepartment of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, United Statesen
dc.contributor.institutionTheory and Computation Department, Princeton Plasma Physics Laboratory, Princeton, NJ 08540, United Statesen
dc.contributor.institutionDepartment of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, United Statesen
kaust.authorKeyes, David E.en
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