Upwind finite element solution for saturated traveling magnetic field problems

Odamura, Motomi

doi:10.1002/eej.4391050416

Cited by 10 publications

(7 citation statements)

References 2 publications

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“…This exercise clearly indicates that the boundary error in the solution is strongly correlated with the existence of ∇ • A = 0 in the weak solution through SU/PG scheme. It is worth noting here that the Coulombs gauge is commonly employed in moving conductor literature [7], [11]- [13], [27] especially for the nodal formulation. The following vector identity is employed most of the times:…”

Section: (B)mentioning

confidence: 99%

“…The upwinding schemes are the earliest and popular ones suggested in the fluid dynamics literature and these have been extensively adopted in the moving conductor literature as well [7]- [17]. It can be worth noting here that the occurrence of numerical oscillations at higher velocities is common to many numerical schemes including the edge element method and there are few upwinding remedies suggested in the literature [18], [19].…”

Section: Introductionmentioning

confidence: 99%

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On Overcoming the Transverse Boundary Error of the SU/PG Scheme for Moving Conductor Problems

2022

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Conductor moving in magnetic field is quite common in electrical equipment. The numerical simulation of such problem is vital in their design and analysis of electrical equipment. The Galerkin finite element method (GFEM) is a commonly employed simulation tool, nonetheless, due to its inherent numerical instability at higher velocities, the GFEM requires upwinding techniques to handle moving conductor problems. The streamline upwinding/Petrov-Galerkin (SU/PG) scheme is a widely acknowledged upwinding technique, despite its error peaking at the transverse boundary. This error at the transverse boundary is found to be leading to non-physical solutions. Several remedies have been suggested in the allied fluid dynamics literature, which employs non-linear, iterative techniques. The present work attempts to address this issue, by retaining the computational efficiency of the GFEM. By suitable analysis, it is shown that the source of the problem can be attributed to the Coulomb's gauge. Therefore, to solve the problem, the Coulomb's gauge is taken out from the formulation and the associated weak form is derived. The effectiveness of this technique is demonstrated with pertinent numerical results.

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Section: (B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Overcoming the Transverse Boundary Error of the SU/PG Scheme for Moving Conductor Problems

2022

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“…This exercise clearly indicate that the boundary error in the solution is strongly correlated with the existence of ∇ • A = 0 in the weak solution through SU/PG scheme. It is worth noting here that the Coulombs gauge is commonly employed in moving conductor literature [7], [11]- [13], [27] especially for the nodal formulation. The following vector identity is employed most of the times,…”

Section: A Analysis With 2d Version Of the Problemmentioning

confidence: 99%

“…across the elements 1 and 2. Thus, neglecting the boundary integral in (7), helps to maintain the continuity of magnetic field intensity across the element interface. Therefore, the weak formulation contains only the volume integral term in the proposed approach and the complete SU/PG-weak formulation of ( 1) and ( 2) are provided in the Appendix A.…”

Section: A Analysis With 2d Version Of the Problemmentioning

confidence: 99%

On Overcoming the Transverse Boundary Error of the SU/PG Scheme for Moving Conductor Problems

Subramanian,

Kumar,

Bhowmick

2021

Preprint

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Conductor moving in magnetic field is quite common in electrical equipment. The numerical simulation of such problem is vital in their design and analysis of electrical equipment. The Galerkin finite element method (GFEM) is a commonly employed simulation tool, nonetheless, due to its inherent numerical instability at higher velocities, the GFEM requires upwinding techniques to handle moving conductor problems. The Streamline Upwinding/Petrov-Galerkin (SU/PG) scheme is a widely acknowledged upwinding technique, despite its error-peaking at the transverse boundary. This error at the transverse-boundary, is found to be leading to non-physical solutions. Several remedies have been suggested in the allied fluid dynamics literature, which employs non-linear, iterative techniques. The present work attempts to address this issue, by retaining the computational efficiency of the GFEM. By suitable analysis, it is shown that the source of the problem can be attributed to the Coulomb's gauge. Therefore, to solve the problem, the Coulomb's gauge is taken out from the formulation and the associated weak form is derived. The effectiveness of this technique is demonstrated with pertinent numerical results.

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“…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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Upwind finite element solution for saturated traveling magnetic field problems

Cited by 10 publications

References 2 publications

On Overcoming the Transverse Boundary Error of the SU/PG Scheme for Moving Conductor Problems

On Overcoming the Transverse Boundary Error of the SU/PG Scheme for Moving Conductor Problems

On Overcoming the Transverse Boundary Error of the SU/PG Scheme for Moving Conductor Problems

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

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