The two-dimensional adiabatic relaxation method for MHD modelling
type: Item
instance of: scholarly article
title: The two-dimensional adiabatic relaxation method for MHD modelling
zbMATH Open document ID: 0632.76126
DOI: 10.1016/0021-9991(87)90111-2
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: The adiabatic relaxation method is extended to two dimensions using a moving finite element model. The MHD equations are split into ideal and diffusion parts by employing a fractional timestep. The ideal equations are expressed in variational form using Hamilton's principle. Finite element discretisation of the variational principle leads to equations for studying equilibria, time dependent MHD and stability. It is shown that conjugate gradient accelerated SSOR is effective in solving the nonlinear minimisation problem arising in finding equilibria. Aligning the finite elements with flux surfaces causes surface averaged transport to emerge naturally from the diffusion part of the timestep.
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 70H99
zbMATH DE Number: 4029204
zbMATH Keywords: adiabatic relaxation method
zbMATH Keywords: moving finite element model
zbMATH Keywords: MHD equations
zbMATH Keywords: Hamilton's principle
zbMATH Keywords: Finite element discretisation
zbMATH Keywords: variational principle
zbMATH Keywords: equilibria
zbMATH Keywords: conjugate gradient accelerated SSOR
zbMATH Keywords: nonlinear minimisation problem
author: James W. Eastwood
describes a project that uses: ERATO
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90111-2
OpenAlex ID: W1987027539
cites work: Q3691250
cites work: Nonlinear, two-dimensional magnetohydrodynamic calculations
cites work: G2M, a two-dimensional diffusion time scale tokamak code
cites work: The Lagrangian solution of transient problems in hydrodynamics using a triangular mesh
cites work: Q3994787
cites work: Q4196165
cites work: Q4404383
cites work: An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
Recommended article: An adaptive moving mesh method for two-dimensional relativistic magnetohydrodynamics
Recommended article: An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
Recommended article: Q4357769
Recommended article: Relativistic MHD with adaptive mesh refinement
Recommended article: Q3770242
Recommended article: Two-dimensional MHD solver by fluctuation splitting and dual time stepping
Recommended article: An effective two-dimensional model for MHD flows with transverse magnetic field
Recommended article: Two-dimensional magnetohydrodynamic equilibria
Recommended article: Q4521720
Recommended article: On a two-dimensional magnetohydrodynamic problem. I. Modelling and analysis
description: scientific article; zbMATH DE number 4029204