On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

Bonilla deToro, Jesus; Shadid, John N.; Tang, Xian Zhu; Crockatt, Michael M.; Ohm, Peter; Phillips, E. G.; Pawlowski, R. P.; Conde, Sidafa; Beznosov, Oleksii

doi:10.1016/j.cma.2023.116359

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

Journal Article · Wed Aug 23 00:00:00 EDT 2023 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2023.116359· OSTI ID:1998134

^[1]; Shadid, John N. ^[2]; ^[1]; ^[3]; ^[4]; Phillips, E. G. ^[3]; Pawlowski, R. P. ^[3]; ^[3]; ^[1]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); University of New Mexico, Albuquerque, NM (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
RIKEN Center for Computational Science, Kobe (Japan)

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1998134

Alternate ID(s):: OSTI ID: 2216965

Report Number(s):: LA-UR--23-25833

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: Part B Vol. 417; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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