Numerical solution of ideal MHD equilibrium via radial basis functions collocation and moving least squares approximation methods

In this study, two different meshfree methods consisting of the Radial Basis Functions (RBFs) and the Moving Least Square Method (MLS) are applied to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of plasma in the tokamak. The validity and the effectiveness of the proposed s...

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Bibliographic Details
Published in:Engineering analysis with boundary elements Vol. 67; pp. 126 - 137
Main Authors: Ghasemi, Maryam, Amrollahi, Reza
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.06.2016
Subjects:
Grad–Shafranov (GS) equation
Magnetohydrodynamic (MHD)
Magnetohydrodynamics
Mathematical analysis
Mathematical models
Meshfree method
Meshless methods
MHD
Moving least squares (MLS)
Partial differential equations
Radial basis function
Radial basis functions (RBFs)
Tokamak devices
Moving least squares (MLS)
Radial basis functions (RBFs)
Magnetohydrodynamic (MHD)
Grad–Shafranov (GS) equation
Meshfree method
ISSN:0955-7997, 1873-197X
Online Access:Get full text
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Summary:In this study, two different meshfree methods consisting of the Radial Basis Functions (RBFs) and the Moving Least Square Method (MLS) are applied to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of plasma in the tokamak. The validity and the effectiveness of the proposed schemes are studied by several test problems through absolute and Root Mean Squared (RMS) errors. Although, during the past few years, a meshfree method is normally applied in magnetohydrodynamic (MHD) studies to the numerical solution of partial differential equations (PDEs) but to the best of our knowledge, its application in MHD equilibrium of the tokamak plasma investigations is rare. The future more extensive studies regarding this numerical method would definitely have a significant impact on improving tokamak numerical tools.
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ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2016.02.008