A comparison of numerical schemes to solve the magnetic induction eigenvalue problem in a spherical geometry

DOI10.1080/03091920500404861zbMath1206.86033OpenAlexW1974729917MaRDI QIDQ3081196

Philip W. Livermore, Andrew D. Jackson

Publication date: 5 March 2011

Published in: Geophysical & Astrophysical Fluid Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03091920500404861

zbMATH Keywords

spectralconvergenceeigenvalueGalerkininduction equation

Mathematics Subject Classification ID

Spectral methods applied to problems in fluid mechanics (76M22) Finite element methods applied to problems in fluid mechanics (76M10) Magnetohydrodynamics and electrohydrodynamics (76W05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Geo-electricity and geomagnetism (86A25)

Related Items (6)

An implementation of the exponential time differencing scheme to the magnetohydrodynamic equations in a spherical shell ⋮ An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere ⋮ Spectral radial basis functions for full sphere computations ⋮ Taylor state dynamos found by optimal control: axisymmetric examples ⋮ Mean zonal flows induced by weak mechanical forcings in rotating spheroids ⋮ The optimal kinematic dynamo driven by steady flows in a sphere

Uses Software

• ARPACK

Cites Work

• A class of self-sustaining dissipative spherical dynamos
• Numerical solution of the kinematic dynamo problem for Beltrami flows in a sphere
• A spectral model for two-dimensional incompressible fluid flow in a circular basin. I: Mathematical formulation
• A class of sparse spectral operators for inversion of powers of the Laplacian in \(N\) dimensions
• A spectral method for polar coordinates
• Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry
• Hydrodynamic Stability Without Eigenvalues
• Finite amplitude convection and magnetic field generation in a rotating spherical shell
• On the linear instability of elliptic pipe flow
• On magnetic energy instability in spherical stationary flows
• Toroidal fluid motion at the top of the Earth's core
• On the thermal instability of a rotating-fluid sphere containing heat sources
• Numerical solutions of the kinematic dynamo problem
• Induction Effects in Terrestrial Magnetism Part I. Theory

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