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

Abstract

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 scalemore » 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.« less

Authors:

Tang, Qi  ^[1];

• Search DOE PAGES for author "Tang, Qi"
• Search DOE PAGES for ORCID "0000-0001-9614-1075"

Chacón, Luis  ^[1];

• Search DOE PAGES for author "Chacón, Luis"
• Search DOE PAGES for ORCID "0000-0002-4566-8763"

Kolev, Tzanio V. ^[2]; Shadid, John N. ^[3]; Tang, Xian-Zhu  ^[1]

• Search DOE PAGES for author "Tang, Xian-Zhu"
• Search DOE PAGES for ORCID "0000-0002-4036-6643"

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+ Show Author Affiliations

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

Publication Date:

Fri Jan 14 00:00:00 EST 2022

Research Org.:

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

Sponsoring Org.:

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

OSTI Identifier:

1860664

Alternate Identifier(s):

OSTI ID: 1841945

Report Number(s):

LLNL-JRNL-822748; LA-UR-21-25160
Journal ID: ISSN 0021-9991; 1035320; TRN: US2305407

Grant/Contract Number:  

AC52-07NA27344; 89233218CNA000001; AC02-05CH11231; ERCAP0016552; ERCAP0016553

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Computational Physics

Additional Journal Information:

Journal Volume: 454; Journal Issue: N/A; Journal ID: ISSN 0021-9991

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; visco-resistive implicit MHD; continuous finite element; streamline upwind Petrov-Galerkin; physics-based preconditioning; adaptive mesh refinement; plasmoid instability