Stabilized bi-cubic Hermite Bézier finite element method with application to gas-plasma interactions occurring during massive material injection in tokamaks

Ashish Bhole (Corresponding author), Boniface Nkonga, José Costa, Guido Huijsmans, Stanislas Pamela, Matthias Hoelzl

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
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Abstract

Development of a numerical tool based upon the high-order, high-resolution Galerkin finite element method (FEM) often encounters two challenges: First, the Galerkin FEMs give central approximations to the differential operators and their use in the simulation of the convection-dominated flows may lead to the dispersion errors yielding entirely wrong numerical solutions. Secondly, high-order, high-resolution numerical methods are known to produce high wave-number oscillations in the vicinity of shocks/discontinuities in the numerical solution adversely affecting the stability of the method. We present the stabilized finite element method for plasma fluid models to address the two challenges. The numerical stabilization is based on two strategies: Variational Multiscale (VMS) and the shock-capturing approach. The former strategy takes into account (the approximation of) the effect of the unresolved scales onto resolved scales to introduce upwinding in the Galerkin FEM. The latter adaptively adds the artificial viscosity only in the vicinity of shocks. These numerical stabilization strategies are applied to stabilize the bi-cubic Hermite Bézier FEM in the computational framework of the nonlinear magnetohydrodynamics (MHD) code JOREK. The application of the stabilized FEM to the challenging simulation of Shattered Pellet Injection (SPI) in JET-like plasma is presented. It is shown that the developed numerical stabilization model improves the stability of the underlying numerical algorithm and the computational cost required to reveal the complex physics is reduced. The physical and numerical models presented can be used to perform expensive simulations of the plasma applications in large computational domains such as JET, and ITER.

Original languageEnglish
Pages (from-to)225-256
Number of pages32
JournalComputers and Mathematics with Applications
Volume142
DOIs
Publication statusPublished - 15 Jul 2023

Funding

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 \u2014 EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. The simulations presented here have been performed using the ITER HPC cluster, Marconi-Fusion supercomputer operated by Cineca, Italy, and JFRS-1 operated by IFERC-CSC in Japan.

Keywords

  • Bi-cubic Hermite Bézier FEM
  • Magnetohydrodynamics
  • Massive material injection in tokamak plasma
  • Shock-capturing stabilization
  • Stabilized FEM
  • Variational multi-scale methods

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