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KIAM Preprint ¹ 62, Moscow, 2024
Authors: Boykov D.S., Hunanyan H.A., Gasilov V.A.
Comparative analysis of projection and diffusion methods for ensuring the solenoidality of the calculated magnetic field
Abstract:
Numerical modeling of current-carrying plasma dynamics is based, as a rule, on multiphysics models, which include equations describing MHD waves, transport and and dissipative processes accompanying the exchange of momentum and energy with the electromagnetic field. To solve the equations describing the evolution of the magnetic field, including as a result of magnetic diffusion, the grid system of equations of the discrete MHD model is not always constructed in such a way that the magnetic field divergence constraint is satisfied “automatically”. As a result, numerical errors can accumulate, creating the effect of the appearance of non-physical “magnetic charges” and plasma flows caused by these charges that do not correspond to the true physical situation. To maintain the solenoidal condition, calibration of the calculated magnetic field is used. In this work, in computational experiments with the MHD MARPLE code (M.V. Keldysh Institute of Applied Mathematics RAS), the practical accuracy of calibration methods such as projection and diffusion is assessed. The magnetic field correction was calculated using a stabilized explicit scheme for solving parabolic equations. It has been shown via numerical experiments that the diffusion method is more accurate and is not inferior to the projection method in terms of efficiency.
Keywords:
MHD modeling, difference schemes, solenoidality constraint of a magnetic field
Publication language: russian,  pages: 26
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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About authors:
  • Boykov Dmitri Sergeevich,  orcid.org/0000-0001-8587-4994KIAM RAS
  • Hunanyan Harutyun Aramovich,  orcid.org/0000-0003-2629-6527National Research Nuclear University MEPhI
  • Gasilov Vladimir Anatolievich,  orcid.org/0000-0003-2629-6527KIAM RAS