The integral equation method for a steady kinematic dynamo problem

Xu, Mingtian; Stefani, Frank; Gerbeth, Günter

doi:10.1016/j.jcp.2003.10.034

Cited by 36 publications

(40 citation statements)

References 24 publications

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“…Hence Eqs. (2,3) represent an integral equation system which actually can be used to solve dynamo problems in arbitrary bounded domains [5]. It it also suitable for a systematic investigation of the non-linear induction effects as they appear already in the sub-critical regime of laboratory dynamos [6].…”

Section: Theorymentioning

confidence: 99%

Contactless inductive flow tomography

2004

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The three-dimensional velocity field of a propeller driven liquid metal flow is reconstructed by a contactless inductive flow tomography (CIFT). The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvin's theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of the new technique are shown to be in satisfactory agreement with ultrasonic measurements.

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Section: Theorymentioning

confidence: 99%

Contactless inductive flow tomography

2004

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“…In the employed finitedifference solver this problem was overcome by solving the Laplace equation in the exterior and using matching conditions at the interface to the dynamo domain. 14,28 A similar approach, although based on the finite element method, was presented by Guermond et al 30 Other methods of handling this boundary condition problem are the integral equation approach [31][32][33] and a hybrid boundary element/finite volume method. 34 For the Riga experiment, we also checked the use of simplified boundary conditions ͑so-called vertical field conditions 35 ͒ which led, however, to a significant 20% error in the determination of the critical Re m .…”

Section: Introductionmentioning

confidence: 99%

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

et al. 2006

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Magnetic fields of planets, stars, and galaxies result from self-excitation in moving electroconducting fluids, also known as the dynamo effect. This phenomenon was recently experimentally confirmed in the Riga dynamo experiment ͓A. Gailitis et al., Phys. Rev. Lett. 84, 4365 ͑2000͒; A. Gailitis et al., Physics of Plasmas 11, 2838 ͑2004͔͒, consisting of a helical motion of sodium in a long pipe followed by a straight backflow in a surrounding annular passage, which provided adequate conditions for magnetic-field self-excitation. In this paper, a first attempt to simulate computationally the Riga experiment is reported. The velocity and turbulence fields are modeled by a finite-volume Navier-Stokes solver using a Reynolds-averaged-Navier-Stokes turbulence model. The magnetic field is computed by an Adams-Bashforth finite-difference solver. The coupling of the two computational codes, although performed sequentially, provides an improved understanding of the interaction between the fluid velocity and magnetic fields in the saturation regime of the Riga dynamo experiment under realistic working conditions.

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“…However, real use of the method was only made later in the papers [36,37]. With [38] this integral equation method was then extended to the case of unsteady magnetic fields which requires an additional equation for the vector potential A which is related to the magnetic field by B = ∇ × A.…”

Section: Integral Equation Approachmentioning

confidence: 99%

Forward and inverse problems in fundamental and applied magnetohydrodynamics

Giesecke

Stefani

Wondrak

et al. 2013

Eur. Phys. J. Spec. Top.

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Abstract. This Minireview summarizes the recent efforts to solve forward and inverse problems as they occur in different branches of fundamental and applied magnetohydrodynamics. As for the forward problem, the main focus is on the numerical treatment of induction processes, including self-excitation of magnetic fields in non-spherical domains and/or under the influence of non-homogeneous material parameters. As an important application of the developed numerical schemes, the functioning of the von-Kármán-sodium (VKS) dynamo experiment is shown to depend crucially on the presence of soft-iron impellers. As for the inverse problem, the main focus is on the mathematical background and some first practical applications of the Contactless Inductive Flow Tomography (CIFT), in which flow induced magnetic field perturbations are utilized for the reconstruction of the velocity field. The promises of CIFT for flow field monitoring in the continuous casting of steel are substantiated by results obtained at a test rig with a low melting liquid metal. While CIFT is presently restricted to flows with low magnetic Reynolds numbers, some selected problems of non-linear inverse dynamo theory, with possible application to geo-and astrophysics, are also discussed.

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The integral equation method for a steady kinematic dynamo problem

Cited by 36 publications

References 24 publications

Contactless inductive flow tomography

Contactless inductive flow tomography

Coupled fluid-flow and magnetic-field simulation of the Riga dynamo experiment

Forward and inverse problems in fundamental and applied magnetohydrodynamics

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