Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

Journal Article · Wed Sep 01 00:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.04.024· OSTI ID:21417240

Adams, Mark F ^[1]; Samtaney, Ravi ^[2]; Brandt, Achi ^[3]

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1. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY (United States)
2. Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ (United States)
3. Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot (Israel)

Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations - so-called 'textbook' multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.

• OSTI ID: 21417240
• Journal Information: Journal of Computational Physics, Vol. 229, Issue 18; Other Information: DOI: 10.1016/j.jcp.2010.04.024; PII: S0021-9991(10)00200-7; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ACCURACY
APPROXIMATIONS
BENCHMARKS
CORRECTIONS
EFFICIENCY
EQUATIONS
GEOMETRY
INTERPOLATION
MAGNETOHYDRODYNAMICS
NONLINEAR PROBLEMS
SIMULATION
TIME DEPENDENCE
CALCULATION METHODS
FLUID MECHANICS
HYDRODYNAMICS
MATHEMATICAL SOLUTIONS
MATHEMATICS
MECHANICS
NUMERICAL SOLUTION