Up-wind finite element solution of travelling magnetic field problems

Ito, M.; Takahashi, Toshihiko; Odamura, Motomi

doi:10.1109/20.124007

Cited by 20 publications

(5 citation statements)

References 5 publications

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“…Application of the GFEM/FEM and the finite difference method (FDM) to (4), results in same set of difference equation [6,19]. The difference equation for nth node…”

Section: Analysis On Instabilitymentioning

confidence: 99%

“…Equation 16, has a constant part given by lΔz and an oscillatory part given by (c 2 (r m c −1 − r m c ))/Δz. Comparing with the analytical solution given in (12), oscillatory part can be identified to be the major part of the error in the The magnitude of the oscillation present in the analytical solution of the difference equation is given by (18) and (19) for the respective inputs (i.e. A sy and B x , respectively).…”

Section: Location and Value Of The Maximum Errormentioning

confidence: 99%

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Augmenting numerical stability of the Galerkin finite element formulation for electromagnetic flowmeter analysis

Subramanian

Kumar

2016

IET Science, Measurement & Technology

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“…Application of the GFEM/FEM and the finite difference method (FDM) to (4), results in same set of difference equation [6,19]. The difference equation for nth node…”

Section: Analysis On Instabilitymentioning

confidence: 99%

Section: Location and Value Of The Maximum Errormentioning

confidence: 99%

Augmenting numerical stability of the Galerkin finite element formulation for electromagnetic flowmeter analysis

Subramanian

Kumar

2016

IET Science, Measurement & Technology

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“…Clearly, (3) has the same form as the convection-diffusion equation dealt in fluid dynamics [3], [6], [21]. Application of the GFEM to (3) leads to difference equation [3], [15], which for n th node takes the form,…”

Section: Analysis With the 1d Version Of The Problemmentioning

confidence: 99%

“…This issue of numerical instability has been adequately addressed in the fluid dynamics literature [3] mostly for the nodal formulation. Among the methods suggested, the Streamline upwinding/Petrov-Galerkin (SU/PG) scheme [5] [6] is commonly employed in the electromagnetic literature [7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Stable Galerkin finite‐element scheme for the simulation of problems involving conductors moving rectilinearly in magnetic fields

Subramanian

Kumar

2016

IET Science, Measurement & Technology

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For the simulation of rectilinearly moving conductors across a magnetic field, the Galerkin finite element method (GFEM) is generally employed. The inherent instability of GFEM is very often addressed by employing Streamline upwinding/Petrov-Galerkin (SU/PG) scheme. However, the SU/PG solution is known to suffer from distortion at the boundary transverse to the velocity and the remedial measures suggested in fluid dynamics literature are computationally demanding. Therefore, simple alternative schemes are essential. In an earlier effort, instead of conventional finite-difference based approach, the numerical instability was analyzed using the Ztransform. By employing the concept of pole-zero cancellation, stability of the numerical solution was achieved by a simple restatement of the input magnetic flux in terms of associated vector potential. This approach, however, is restricted for input fields, which vary only along the direction of the velocity. To overcome this, the present work proposes a novel approach in which the input field is restated as a weighted elemental average. The stability of the proposed scheme is proven analytically for both 1D and 2D cases. The error bound for the small oscillations remnant at intermittent Peclet numbers is also deduced. Using suitable numerical simulations, all the theoretical deductions are verified.

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“…7.7. Since only the solid parts have to be discretized, the preprocessing, especially in (22,33,44,55,59]: When the coil is driven by a voltage signal, the interaction between the resulting electric current and the magnetic field in the airgap leads to an axial magnetic force (Lorentz force), acting on the coil.…”

Section: Moving Current/voltage-loaded Coilmentioning

confidence: 99%

Numerical Simulation of Mechatronic Sensors and Actuators

Kaltenbacher¹

2004

185

254

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PrefaceThe focus of this book is concerned with the modeling and precise numerical simulation of mechatronic sensors and actuators. These sensors, actuators, and sensor -actuator systems are based on the mutual interaction of the mechanical field with a magnetic, an electrostatic or an electromagnetic field. In many cases the transducer is immersed in an acoustic fluid and the solid-fluid coupling has to be taken into account. Examples are: piezoelectric stack actuators for common-rail injection systems, micromachined electrostatic gyro sensors used in stabilizing systems of automobiles or ultrasonic imaging systems for medical diagnostics.The modeling of mechatronic sensors and actuators leads to so-called multifield problems, which are described by a system of nonlinear partial differential equations. Such systems can not be solved analytically and, thus a numerical calculation scheme has to be applied. The schemes discussed in this book are based on the finite element (FE) method, which is capable of efficiently solving the partial differential equations. The complexity of the simulation of multifield problems consists in the simultaneous computation of the involved single fields as well as in the coupling terms, which introduce additional nonlinearities. Examples are: moving conductive (electrically charged) body within a magnetic (an electric) field, electromagnetic and/or electrostatic forces.The goal of this book is to present a comprehensive survey of the main physical phenomena of multifield problems and, in addition, to discuss calculation schemes for the efficient solution of coupled partial differential equations applying the FE method. We will concentrate on electromagnetic, mechanical, and acoustic fields with the following mutual interactions: • Coupling Electric Field -Mechanical FieldThis coupling is either based on the piezoelectric effect or results from the force on an electrically charged structure in an electric field (electrostatic force). VI Preface • Coupling Magnetic Field -Mechanical FieldThis coupling is two-fold. First, we have the electromotive force (emf), which describes the generation of an electric field (electric voltage respectively current) when a conductor is moved in a magnetic field, and secondly, the electromagnetic force. • Coupling Mechanical Field -Acoustic FieldVery often a transducer is surrounded by a fluid or a gaseous medium in which an acoustic wave is launched (actuator) or is impinging from an outside source towards the receiving transducer.In Chap. 2, we give an introduction to the finite element (FE) method. Starting from the strong form of a general partial differential equation we describe all the steps concerning spatial as well as time discretization to arrive at an algebraic system of equations. Both nodal and edge finite elements are introduced. Special emphasis is put on an explanation of all the important steps necessary for the computer implementation.A detailed discussion on electromagnetic, mechanical, and acoustic fields including their numerical c...

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Up-wind finite element solution of travelling magnetic field problems

Cited by 20 publications

References 5 publications

Augmenting numerical stability of the Galerkin finite element formulation for electromagnetic flowmeter analysis

Augmenting numerical stability of the Galerkin finite element formulation for electromagnetic flowmeter analysis

Stable Galerkin finite‐element scheme for the simulation of problems involving conductors moving rectilinearly in magnetic fields

Numerical Simulation of Mechatronic Sensors and Actuators

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