Numerical solution of ideal MHD equilibrium via radial basis functions collocation and moving least squares approximation methods. (English) Zbl 1403.76148
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.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
Keywords:
magnetohydrodynamic (MHD); Grad-Shafranov (GS) equation; radial basis functions (RBFs); moving least squares (MLS); meshfree methodReferences:
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