An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time...

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Bibliographic Details
Published in:Journal of computational physics Vol. 454; p. 110967
Main Authors: Tang, Qi, Chacón, Luis, Kolev, Tzanio V., Shadid, John N., Tang, Xian-Zhu
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 01.04.2022
Elsevier Science Ltd
Elsevier
Subjects:
Adaptive algorithms
Adaptive mesh refinement
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Coalescing
Computational physics
Continuous finite element
Continuum modeling
Current sheets
Dusty plasmas
Dynamic loads
Finite element method
Grid refinement (mathematics)
Magnetohydrodynamics
Mathematical analysis
Multigrid methods
Numerical methods
Physics
Physics-based preconditioning
Plasma dynamics
Plasma physics
Plasmoid instability
Polynomials
Preconditioning
Streamline upwind Petrov-Galerkin
Visco-resistive implicit MHD
Visco-resistive implicit MHD
Continuous finite element
Plasmoid instability
Adaptive mesh refinement
Streamline upwind Petrov-Galerkin
Physics-based preconditioning
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) [3] to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥107) with the successful resolution of plasmoid instabilities and thin current sheets. •Fully implicit SUPG-based stabilized finite elements for resistive MHD.•Scalable physics-based preconditioning.•A parallel AMR algorithm with dynamic load balancing in MFEM.•Demonstration of excellent parallel and algorithmic scaling up to 4096 CPUs.•Multi-scale simulations for plasmoid instabilities of high Lundquist number.
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content type line 14
NERSC
LA-UR-21-25160
USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR)
89233218CNA000001; AC02-05CH11231; ERCAP0016552; ERCAP0016553
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2022.110967