Towards a Scalable Fully-Implicit Fully-coupled Resistive MHD Formulation with Stabilized FE Methods

Journal Article · Fri Jan 01 04:00:00 EST 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.06.018· OSTI ID:985756

Shadid, John N. ^[1]; Pawlowski, R. P. P. ^[1]; Banks, Jeffrey W ^[1]; Chacon, Luis ^[2]; Lin, Paul T. ^[1]; Tuminaro, R. S. ^[1]

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1. Sandia National Laboratories (SNL)
2. ORNL

This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-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, including both low-Lundquist number (e.g., an MHD Faraday conduction pump and a hydromagnetic Rayleigh-Bernard linear stability calculation) and moderately-high Lundquist number (magnetic island coalescence problem) examples. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 985756
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 229 Vol. 229; ISSN 1090-2716; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPUTERIZED SIMULATION
FINITE ELEMENT METHOD
MAGNETOHYDRODYNAMICS
NONLINEAR PROBLEMS