Nonlinear impedance boundary condition for 2D BEM

2018 ◽  
Vol 37 (2) ◽  
pp. 772-783 ◽  
Author(s):  
Carlo de Falco ◽  
Luca Di Rienzo ◽  
Nathan Ida ◽  
Sergey Yuferev
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Diffusion Equation ◽  
Efficient Implementation ◽  
Impedance Boundary Condition ◽  
Computational Domain ◽  
Impedance Boundary ◽  
Content Type ◽  
The Magnetic Field ◽  
Element Method

PurposeThe purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors. Design/methodology/approachAn approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields. FindingsThe results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost. Research limitations/implicationsLimitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor. Originality/valueThe efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

CHOICE OF CONDITIONS FOR MHD SIMULATIONS ABOVE THE ACTIVE REGION, ALLOWING THE STUDY OF THE SOLAR FLARE MECHANISM

2021 ◽  
Vol 44 ◽  
pp. 92-95
Author(s):  
A.I. Podgorny ◽  
◽  
I.M. Podgorny ◽  
A.V. Borisenko ◽  
N.S. Meshalkina ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Solar Flare ◽  
Magnetic Energy ◽  
Solar Radius ◽  
Computational Domain ◽  
Mhd Simulations ◽  
Flare Energy ◽  
Numerical Instabilities ◽  
The Magnetic Field

Primordial release of solar flare energy high in corona (at altitudes 1/40 - 1/20 of the solar radius) is explained by release of the magnetic energy of the current sheet. The observed manifestations of the flare are explained by the electrodynamical model of a solar flare proposed by I. M. Podgorny. To study the flare mechanism is necessary to perform MHD simulations above a real active region (AR). MHD simulation in the solar corona in the real scale of time can only be carried out thanks to parallel calculations using CUDA technology. Methods have been developed for stabilizing numerical instabilities that arise near the boundary of the computational domain. Methods are applicable for low viscosities in the main part of the domain, for which the flare energy is effectively accumulated near the singularities of the magnetic field. Singular lines of the magnetic field, near which the field can have a rather complex configuration, coincide or are located near the observed positions of the flare.

Magnetohydrodynamic effects on flow structures and heat transfer over two cylinders wrapped with a porous layer in side

2016 ◽  
Vol 26 (5) ◽  
pp. 1416-1432 ◽  
Author(s):  
Saman Rashidi ◽  
Javad Abolfazli Esfahani ◽  
Mohammad Sadegh Valipour ◽  
Masoud Bovand ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Flow Field ◽  
Porous Layer ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Circular Cylinders ◽  
Flow Structures ◽  
Content Type ◽  
The Magnetic Field

Purpose – The analysis of the flow field and heat transfer around a tube row or tube banks wrapped with porous layer have many related engineering applications. Examples include the reactor safety analysis, combustion, compact heat exchangers, solar power collectors, high-performance insulation for buildings and many another applications. The purpose of this paper is to perform a numerical study on flows passing through two circular cylinders in side-by-side arrangement wrapped with a porous layer under the influence of a magnetic field. The authors focus the attention to the effects of magnetic field, Darcy number and pitch ratio on the mechanism of convection heat transfer and flow structures. Design/methodology/approach – The Darcy-Brinkman-Forchheimer model for simulating the flow in porous medium along with the Maxwell equations for providing the coupling between the flow field and the magnetic field have been used. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Stuart and Darcy numbers are varied within the range of 0 < N < 3 and 1e-6 < Da < 1e-2, respectively, and Reynolds and Prandtl numbers are equal to Re=100 and Pr=0.71, respectively. Findings – The results show that the drag coefficient decreases for N < 0.6 and increases for N > 0.6. Also, the effect of magnetic field is negligible in the gap between two cylinders because the magnetic field for two cylinders counteracts each other in these regions. Originality/value – To the authors knowledge, in the open literature, flow passing over two circular cylinders in side-by-side arrangement wrapped with a porous layer has been rarely investigated especially under the influence of a magnetic field.

Numerical Simulation of the Effect of Magnetic Fields on Soot Formation in Laminar Non-Premixed Flames

2021 ◽  
Author(s):  
Edison E. Chukwuemeka ◽  
Ingmar M. Schoegl
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Volume Fraction ◽  
Soot Formation ◽  
Premixed Flames ◽  
Premixed Flame ◽  
Pollutant Emissions ◽  
Chemical Mechanism ◽  
Computational Domain ◽  
The Magnetic Field

Abstract Characteristics of non-premixed flames such as flame height and lift-off height are affected by the presence of magnetic fields due to the paramagnetic properties of some combustion species. However, it is unknown whether magnetic fields can be used to reduce the emission of pollutants in non-premixed flames. In general, pollutant emissions are reduced in combustion systems if the mixing of combustion species is enhanced during the process. Since paramagnetic combustion species such as O2, O, OH, HO2, etc have a preferential motion direction in the presence of magnetic fields, there is a potential to harness this effect of mixing by imposing a magnetic field on the flame. This study seeks to provide some insights on the effect of magnetic field on pollutants generated in a laminar non-premixed flame numerically. The non-premixed flame is simulated using a detailed chemical mechanism for propane-air combustion and a modified Moss-Brookes soot model. To simulate the effect of magnetism on the paramagnetic chemical species, the species paramagnetic susceptibility is computed using the Curie relation. The non-premixed flame is placed at three different locations within the magnetic field. The computation predicted that the amount of average pollutants reduction is dependent on the location of the flames within the magnetic fields with respect to magnetic gradients. The mass weighted average of the soot volume fraction over the computational domain decreased when the non-premixed flame is located at certain locations within the magnetic field of the solenoid with respect to the absence of the magnetic fields, but increases in other locations.

Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions

2003 ◽  
Vol 125 (6) ◽  
pp. 952-962 ◽  
Author(s):  
C. Midya ◽  
G. C. Layek ◽  
A. S. Gupta ◽  
T. Ray Mahapatra
Keyword(s):  
Magnetic Field ◽  
Flow Separation ◽  
Separation Zone ◽  
Transverse Magnetic ◽  
Mhd Equations ◽  
Staggered Grid ◽  
Solution Technique ◽  
Computational Domain ◽  
Pressure Poisson Equation ◽  
The Magnetic Field

An analysis is made of the flow of an electrically conducting fluid in a channel with constrictions in the presence of a uniform transverse magnetic field. A solution technique for governing magnetohydrodynamic (MHD) equations in primitive variable formulation is developed. A coordinate stretching is used to map the long irregular geometry into a finite computational domain. The governing equations are discretized using finite difference approximations and the well-known staggered grid of Harlow and Welch is used. Pressure Poisson equation and pressure-velocity correction formulas are derived and solved numerically. It is found that the flow separates downstream of the constriction. With increase in the magnetic field, the flow separation zone diminishes in size and for large magnetic field, the separation zone disappears completely. Wall shear stress increases with increase in the magnetic field strength. It is also found that for symmetrically situated constrictions on the channel walls, the critical Reynolds number for the flow bifurcation (i.e., flow asymmetry) increases with increase in the magnetic field.

scholarly journals Unstructured PEEC method with the use of surface impedance boundary condition

2020 ◽  
Vol 39 (5) ◽  
pp. 1017-1030 ◽  
Author(s):  
Gerard Meunier ◽  
Quang-Anh Phan ◽  
Olivier Chadebec ◽  
Jean-Michel Guichon ◽  
Bertrand Bannwarth ◽  
...  
Keyword(s):  
Finite Element ◽  
Surface Impedance ◽  
Computational Effort ◽  
Impedance Boundary Condition ◽  
Surface Mesh ◽  
Impedance Boundary ◽  
Content Type ◽  
Magnetic Effects ◽  
Coupled Circuits ◽  
Simply Connected

Purpose This paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation. Design/methodology/approach Because of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed. Findings The new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh. Research limitations/implications The propagation effects are not taken into account in the proposed formulation. Originality/value The formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.

scholarly journals Low-degree mixed modes in red giant stars with moderate core magnetic fields

2019 ◽  
Author(s):  
Shyeh Tjing Loi ◽  
John C B Papaloizou
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Magnetic Fields ◽  
Differential Equations ◽  
Order Perturbation ◽  
First Order ◽  
Low Degree ◽  
Mixed Modes ◽  
The Magnetic Field ◽  
First Order Perturbation

Abstract Observations of pressure-gravity mixed modes, combined with a theoretical framework for understanding mode formation, can yield a wealth of information about deep stellar interiors. In this paper, we seek to develop a formalism for treating the effects of deeply buried core magnetic fields on mixed modes in evolved stars, where the fields are moderate, i.e. not strong enough to disrupt wave propagation, but where they may be too strong for non-degenerate first-order perturbation theory to be applied. The magnetic field is incorporated in a way that avoids having to use this. Inclusion of the Lorentz force term is shown to yield a system of differential equations that allows for the magnetically-affected eigenfunctions to be computed from scratch, rather than following the approach of first-order perturbation theory. For sufficiently weak fields, coupling between different spherical harmonics can be neglected, allowing for reduction to a second-order system of ordinary differential equations akin to the usual oscillation equations that can be solved analogously. We derive expressions for (i) the mixed-mode quantisation condition in the presence of a field and (ii) the frequency shift associated with the magnetic field. In addition, for modes of low degree we uncover an extra offset term in the quantisation condition that is sensitive to properties of the evanescent zone. These expressions may be inverted to extract information about the stellar structure and magnetic field from observational data.

Optimization of magnetic hat for quartz flexible accelerometer

Sensor Review ◽  
2016 ◽  
Vol 36 (1) ◽  
pp. 71-76 ◽  
Author(s):  
Cuo Wang ◽  
Xingfei Li ◽  
Ke Kou ◽  
Chunguo Long
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Cylindrical Symmetry ◽  
Air Gap ◽  
Magnetic Sensors ◽  
Magnetic Field Distribution ◽  
Navigation Systems ◽  
Pole Piece ◽  
Content Type ◽  
The Magnetic Field

Purpose – This study aims to ameliorate the strength and uniformity of the magnetic field in the air-gap of quartz flexible accelerometers. Quartz flexible accelerometers (QFAs), a type of magneto-electric inertial sensors, have wide applications in inertial navigation systems, and their precision, linearity and stability performance are largely determined by the magnetic field in operation air-gap. To enhance the strength and uniformity of the magnetic field in the air-gap, a magnetic hat structure has been proposed to replace the traditional magnetic pole piece which tends to produce stratiform magnetic field distribution. Design/methodology/approach – Three-dimensional analysis in ANSYS workbench helps to exhibit magnetic field distribution for the structures with a pole piece and a magnetic hat, and under the hypothesis of cylindrical symmetry, two-dimensional finite element optimization by ANSYS APDL gives an optimal set of dimensions of the magnetic hat. Findings – Three structures of the QFA with a pole piece, a non-optimized magnetic hat and an optimized magnetic hat are compared by the simulation in ANSYS Maxwell and experiments measuring the electromagnetic rebalance force. The results show that the optimized hat can supply stronger and more uniform magnetic field, which is reflected by larger and more linear rebalance force. Originality/value – To the authors ' knowledge, the magnetic hat and its dimension optimization have rarely been reported, and they can find significant applications in designing QFAs or other similar magnetic sensors.

Spin Hall Effect in a Magnetic Field

2001 ◽  
Vol 690 ◽  
Author(s):  
Shufeng Zhang
Keyword(s):  
Magnetic Field ◽  
Diffusion Equation ◽  
Electric Field ◽  
Hall Effect ◽  
Transverse Electric ◽  
Spin Current ◽  
Magnetic Semiconductor ◽  
Hall Voltage ◽  
Spin Polarized ◽  
The Magnetic Field

ABSTRACTWhen a spin-polarized current is injected into a non-magnetic semiconductor, a transverse electric field known as Hall voltage is generated. By using a macroscopic diffusion equation, we derive the Hall voltage in the presence of both spin current and magnetic field. Novel features such as oscillating Hall signals as a function of the magnetic field and geometrical dependence of Hall signals are predicted.

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