2003/01/31 by M. Xu, Mingtian Xu, F. Stefani +2 · 3 citations
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Physics and Astronomy · #Geomagnetism and Paleomagnetism Studies #Geophysics and Gravity Measurements #Solar and Space Plasma Dynamics #astro-ph
paper · pdf · doi:10.1016/j.jcp.2003.10.034
published as J.Comput.Phys.196:102-125,2004 · 22 pages, 18 figures, to appear in J. Comp. Phys
arxiv created 2003/12/19 · openalex publication_date 2003/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust and accurate tools for the numerical solution of many problems in other fields of physics. The paper is intended to facilitate the use of integral equation solvers in dynamo theory. In concrete, the integral equation method is employed to solve the eigenvalue problem for a hydromagnetic dynamo model with a spherically symmetric, isotropic helical turbulence parameter alpha. Three examples of the function alpha(r) with steady and oscillatory solutions are considered. A convergence rate proportional to the inverse squared of the number of grid points is achieved. Based on this method, a convergence accelerating strategy is developed and the convergence rate is improved remarkably. Typically, quite accurate results can be obtained with a few tens of grid points. In order to demonstrate its suitability for the treatment of dynamos in other than spherical domains, the method is also applied to alpha2 dynamos in rectangular boxes. The magnetic fields and the electric potentials for the first eigenvalues are visualized.