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

Tang, Qi; Chacón, Luis; Kolev, Tzanio V.; Shadid, John N.; Tang, Xian-Zhu

doi:10.1016/j.jcp.2022.110967

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

Journal Article · Fri Jan 14 00:00:00 EST 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.110967· OSTI ID:1860664

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^[1]; Kolev, Tzanio V. ^[2]; Shadid, John N. ^[3];

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)

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. Additionally, 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) 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.

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Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR); National Energy Research Scientific Computing Center (NERSC); NERSC

Grant/Contract Number:: AC52-07NA27344; 89233218CNA000001; AC02-05CH11231; ERCAP0016552; ERCAP0016553

OSTI ID:: 1860664

Alternate ID(s):: OSTI ID: 1841945

Report Number(s):: LLNL-JRNL-822748; LA-UR-21-25160; 1035320; TRN: US2305407

Journal Information:: Journal of Computational Physics, Vol. 454, Issue N/A; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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71 CLASSICAL AND QUANTUM MECHANICS
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Title: An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

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References (51)

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