Reply to comment on ?variational formulation for the equilibrium condition of a conducting fluid in an electric field?

1985 ◽  
Vol 36 (3) ◽  
pp. 171-174 ◽  
Author(s):  
M. Chung ◽  
P. H. Cutler ◽  
T. E. Feuchtwang ◽  
E. Kazes ◽  
N. M. Miskovsky
Keyword(s):  
Electric Field ◽  
Equilibrium Condition ◽  
Variational Formulation ◽  
Conducting Fluid

Variational formulation for the equilibrium condition of a conducting fluid in an electric field

1983 ◽  
Vol 32 (2) ◽  
pp. 55-61 ◽  
Author(s):  
N. Sujatha ◽  
P. H. Cutler ◽  
E. Kazes ◽  
J. P. Rogers ◽  
N. M. Miskovsky
Keyword(s):  
Electric Field ◽  
Equilibrium Condition ◽  
Variational Formulation ◽  
Conducting Fluid

KALB-RAMOND VORTICITY VARIATIONAL FORMULATION OF RELATIVISTIC PERFECTLY CONDUCTING FLUID THEORY

1994 ◽  
Vol 03 (01) ◽  
pp. 15-21 ◽  
Author(s):  
Brandon CARTER
Keyword(s):  
Variational Formulation ◽  
Conducting Fluid ◽  
Variation Principle ◽  
Fluid Theory

Use of a Kalb-Ramond type formulation is shown to allow standard perfect (electrically or neutrally) conducting fluid theory to be described by a variation principle in which the relevant vorticity forms act as independent convective field variables, a feature that is potentially useful for the purpose of constructing more general theories to allow for the macroscopic effect of vortex quantisation in superfluids.

Application of a modified variational formulation of the vector finite element method for modelling a harmonic electric field in areas with curved shields

2021 ◽  
pp. 26-41
Author(s):  
Дарья Владимировна Добролюбова ◽  
Элла Петровна Шурина
Keyword(s):  
Electric Field ◽  
Variational Formulation ◽  
Computational Cost ◽  
Surface Current ◽  
Local Source ◽  
Current Loop ◽  
Surface Current Density ◽  
Field Source ◽  
The Media ◽  
Cylindrical Shield

Рассматриваются особенности применения модифицированной вариационной постановки векторного метода конечных элементов (ВМКЭ), основанной на замене тонких сильнопроводящих объектов токонесущими поверхностями, для моделирования гармонического электрического поля в областях с криволинейными экранами при различном типе возбуждения поля. Исследуется применимость модифицированной вариационной постановки в широком диапазоне частот Purpose. The paper addresses applicability of the modified variational formulation of vector FEM for the harmonic electric field to the media with cylindrical shields. Thin highly conductive objects are treated as surfaces with the equivalent surface current density. We consider the excitation of the field by a local source (current loop) located either inside or outside the cylindrical shield. Methodology. The simulations are carried out on unstructured tetrahedral meshes. Since the modified variational formulation treats thin highly conductive objects as surfaces, only the surface of a cylinder is discretized. The results yielded by the modified variational formulation are compared with the results of the classic vector FEM. Findings. For the frequency range between 100 KHz and 100 MHz, the modified variational formulation provides correct results when the field source is located outside the cylindrical shield. The modified variational formulation reduces computational cost, since the volume of the thin shield is not discretized. When the field source is located inside the shield, the modified variational formulation gives valid results only in the proximity of the source. Originality/value. The limitations for the application of the reduced variational formulation for the modelling of harmonic electric field in the media with hollow cylindrical shields are investigated

A reduced formulation for modelling time-harmonic electromagnetic field in the media with thin highly conductive inclusions

2018 ◽  
Author(s):  
Э.П. Шурина ◽  
Д.В. Добролюбова ◽  
Е.И. Штанько
Keyword(s):  
Electric Field ◽  
Variational Formulation ◽  
Computational Cost ◽  
Surface Current ◽  
Wide Frequency Range ◽  
Geometrical Shape ◽  
Frequency Range ◽  
Surface Current Density ◽  
Time Harmonic ◽  
The Media

При решении задач электромагнетизма в широком частотном диапазоне в областях с тонкими пластинами, оболочками и экранами численными методами возникает проблема резкого роста сеточной дискретизации вблизи внутренних структур с разномасштабными габаритными размерами. В работе предложена модификация вариационной постановки векторного метода конечных элементов, основанная на снижении размерности модели в окрестности тонких включений, которая позволяет преодолеть эту проблему за счет специфического учета таких структур на уровне вариационной постановки. Так как редуцирование модели обычно приводит к появлению ограничений на область ее применимости, выполнено исследование диапазона допустимых частот, контрастности электрофизических характеристик матрицы и включений, геометрических особенностей внутренней структуры, для которых предложенная модель позволяет получить корректные с точки зрения физики результаты. Purpose. In this paper, we propose a reduced variational formulation for the Helmholtz equation for the electric field, in which thin highly conductive objects are approximated by surfaces with the equivalent surface current density. We conduct a study aimed at defining the range of application for the reduced variational formulation, focusing on highly contrasting thin objects of various geometrical shape and arrangement in a wide frequency range. Methodology. The modelling is performed on unstructured tetrahedral meshes. Since the reduced variational formulation treats thin highly conductive objects as surfaces, no volume mesh is constructed inside of them.We compare the results obtained by the vector FEM using the proposed variational formulation with the results obtained using standard formulation. Findings. Due to the fact that the proposed variational formulation does not require volume meshing of the thin objects, its computational cost is significantly lower. However, the reduced formulation yields correct results in a restricted frequency range. It also imposes some limitations on the minimal contrast and maximal thickness of the thin highly conductive objects. Originality/value. The proposed reduced variational formulation can be applied to simulate the time-harmonic electric field in the media with thin highly conductive inclusions of either regular or chaotic arrangement, as well as thin shielding plates or casings of various geometrical forms.

Stabilized Variational Formulation for Solving Cell Response to Applied Electric Field

2019 ◽  
pp. 627-634
Author(s):  
Cesar Augusto Conopoima ◽  
Bernardo Martins Rocha ◽  
Iury Igreja ◽  
Rodrigo Weber Dos Santos ◽  
Abimael Fernando Dourado Loula
Keyword(s):  
Electric Field ◽  
Cell Response ◽  
Applied Electric Field ◽  
Variational Formulation
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