Dolores Gomez | University of Santiago de Compostela (original) (raw)
Papers by Dolores Gomez
Mathematical and Computer Modelling, 2011
A coupled problem arising in induction heating furnaces is studied. The thermal problem, which in... more A coupled problem arising in induction heating furnaces is studied. The thermal problem, which involves a change of phase, has a nonlocal radiation boundary condition. Convective heat transfer in the liquid is also included which makes necessary to compute the liquid motion. For the space discretization, we propose finite element methods which are combined with characteristics methods in the thermal and flow models to handle the convective terms. In the electromagnetic model they are coupled with boundary element methods (BEM/FEM). An iterative algorithm is introduced for the whole coupled model and numerical results for an industrial induction furnace are presented.
Advances in Computational Mathematics, 2006
This paper concerns the mathematical modelling and numerical solution of thermoelectrical phenome... more This paper concerns the mathematical modelling and numerical solution of thermoelectrical phenomena taking place in an axisymmetric induction heating furnace. We formulate the problem in a two-dimensional domain and propose a finite element method and an iterative algorithm for its numerical solution. We also provide a family of one-dimensional analytical solutions which are used to test the two-dimensional code and to predict the behaviour of the furnace under special conditions. Some numerical results for an industrial furnace used in silicon purification are shown.
Advances in Induction and Microwave Heating of Mineral and Organic Materials, 2011
Lecture Notes in Computational Science and Engineering, 2015
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Journal of Computational and Applied Mathematics, 2019
Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads t... more Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads to a nonlinear and multivalued behavior, making their modeling and control difficult. Even though the analysis and mathematical properties of classical or rate-independent hysteresis models are known, this is not the case for dynamic models where current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics, both being crucial in practice. This paper deals with the description and mathematical analysis of the dynamic Preisach hysteresis model. Toward that end, we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field H and the magnetic induction B, in which, the values of B not only depends on the present values of H but also on the past history and its velocity. We first analyze mathematically some important properties of the model and compare them with known results for the static Preisach model. Then, we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. Under suitable assumptions, we show the well posedness of a weak formulation of the problem and solve it numerically. Finally, we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic Preisach model.
Hysteresis in Engineering [Working Title], 2021
In this chapter we recall the well-known hysteresis Preisach model, widely employed in the area o... more In this chapter we recall the well-known hysteresis Preisach model, widely employed in the area of magnetism. Some applications of this model in electrical engineering are also described, with a specific focus on the estimation of electromagnetic losses in electrical machines, the simulation of magnetization-demagnetization processes arising in magnetic particle inspection, and the mathematical modeling of batteries for electric vehicles.
Applied Mathematical Modelling, 2021
SSRN Electronic Journal, 2021
It is well known that alternating currents (AC) differ significantly from direct currents (DC) in... more It is well known that alternating currents (AC) differ significantly from direct currents (DC) in large electrodes for Submerged Arc Furnaces (SAFs). The skin effect concentrates AC to the periphery of each electrode, while the proximity effect causes higher current concentration towards the leading electrode. In a presentation at INFACON XV it was further shown that there is also a significant proximity effect between electrode currents and induced currents in the furnace steel shell. Here, we will focus on differences and similarities between AC and DC below the electrodes. In many processes the current runs primarily vertically in a coke bed from each electrode to a metal bath, where it distributes to the other electrodes. In such coke beds we find no significant difference between AC and DC. In the highly conductive metal, there will be horizontal currents and a significant AC skin effect. Horizontal currents will also be present in the materials above the metal, depending on the electrical conductivity in this region. A simple model shows that there is a strong proximity effect between such adjacent currents, “pushing” the currents upwards within the slag/coke bed region. A simple estimate, based on furnace dimensions and assumed conductivities, will show whether this effect is significant, in which case DC computations are inadequate to estimate the current paths. The same proximity effect will significantly enhance induced currents in an electrically conductive lining. Finally, since the underlying Maxwell’s equations are linear, the fundamental current paths in 3-phase AC SAFs can be studied by computing two independent single-phase cases for a given geometry and distribution of electrical conductivities. Any other current distribution will be a linear combination of these two solutions.
Finite Elements in Analysis and Design, 2017
This paper presents a novel algorithm for the computation of transient electromagnetic fields in ... more This paper presents a novel algorithm for the computation of transient electromagnetic fields in nonlinear magnetic media with hysteresis. We deal with an axisymmetric transient eddy current problem where the constitutive relation between H and B is given by a hysteresis operator, i.e., the values of the magnetic induction B depend not only on the present values of the magnetic field H but also on its past history. First, we introduce the mathematical model of the problem and, by applying some abstract result, we show the well posedness of a weak formulation written in terms of the magnetic field. For the numerical solution, we consider the Preisach model as hysteresis operator, a finite element discretization by piecewise linear functions, and the backward Euler time discretization. By taking into account the monotonicity property of the Preisach model, we propose a fixed point algorithm to deal with hysteresis effects which is numerically validated: we report a numerical test in order to assess the order of convergence and we compare the results with experimental data. For the later, we consider a physical application: the numerical computation of eddy current and hysteresis losses in laminated media as those used in transformers or electric machines.
Mathematics in Industry, 2008
This paper deals with mathematical modelling and numerical simulation of induction heating furnac... more This paper deals with mathematical modelling and numerical simulation of induction heating furnaces for axisymmetric geometries. The mathematical model presented consists in a coupled thermo-magneto-hydrodynamic problem with phase change. We propose a finite element method and an iterative algorithm to solve the equations. Some numerical results for an industrial furnace used for silicon purification are shown.
Mathematics in Industry, 2006
The aim of this work is to introduce and numerically solve an axisymmetric mathematical model for... more The aim of this work is to introduce and numerically solve an axisymmetric mathematical model for thermoelectrical simulation of an induction heating furnace.
Mathematical Models and Methods in Applied Sciences, 2013
This paper deals with an axisymmetric transient eddy current problem in conductive nonlinear magn... more This paper deals with an axisymmetric transient eddy current problem in conductive nonlinear magnetic media. This means that the relation between the magnetic field and the magnetic induction, the so-called H-B curve, is nonlinear. The source of the problem is the magnetic flux across a meridian section of the device, which leads to a parabolic nonlinear problem with nonlocal boundary conditions. First, by applying some abstract results, we prove the existence and uniqueness of the solution to a weak formulation written in terms of the magnetic field. Then, we compute the numerical solution of the problem by using a finite element method combined with a backward Euler time discretization. We derive error estimates in appropriate norms for both the semidiscrete (in space) and the fully discrete problems. Finally, we show numerical results which allow us to confirm the theoretical estimates and to assess the performance of the proposed scheme.
International Journal for Numerical Methods in Engineering, 2007
Computers & Mathematics with Applications, 2013
Applied Numerical Mathematics, 2009
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:
IEEE Transactions on Magnetics
Mathematical and Computer Modelling, 2011
A coupled problem arising in induction heating furnaces is studied. The thermal problem, which in... more A coupled problem arising in induction heating furnaces is studied. The thermal problem, which involves a change of phase, has a nonlocal radiation boundary condition. Convective heat transfer in the liquid is also included which makes necessary to compute the liquid motion. For the space discretization, we propose finite element methods which are combined with characteristics methods in the thermal and flow models to handle the convective terms. In the electromagnetic model they are coupled with boundary element methods (BEM/FEM). An iterative algorithm is introduced for the whole coupled model and numerical results for an industrial induction furnace are presented.
Advances in Computational Mathematics, 2006
This paper concerns the mathematical modelling and numerical solution of thermoelectrical phenome... more This paper concerns the mathematical modelling and numerical solution of thermoelectrical phenomena taking place in an axisymmetric induction heating furnace. We formulate the problem in a two-dimensional domain and propose a finite element method and an iterative algorithm for its numerical solution. We also provide a family of one-dimensional analytical solutions which are used to test the two-dimensional code and to predict the behaviour of the furnace under special conditions. Some numerical results for an industrial furnace used in silicon purification are shown.
Advances in Induction and Microwave Heating of Mineral and Organic Materials, 2011
Lecture Notes in Computational Science and Engineering, 2015
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
Journal of Computational and Applied Mathematics, 2019
Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads t... more Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads to a nonlinear and multivalued behavior, making their modeling and control difficult. Even though the analysis and mathematical properties of classical or rate-independent hysteresis models are known, this is not the case for dynamic models where current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics, both being crucial in practice. This paper deals with the description and mathematical analysis of the dynamic Preisach hysteresis model. Toward that end, we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field H and the magnetic induction B, in which, the values of B not only depends on the present values of H but also on the past history and its velocity. We first analyze mathematically some important properties of the model and compare them with known results for the static Preisach model. Then, we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. Under suitable assumptions, we show the well posedness of a weak formulation of the problem and solve it numerically. Finally, we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic Preisach model.
Hysteresis in Engineering [Working Title], 2021
In this chapter we recall the well-known hysteresis Preisach model, widely employed in the area o... more In this chapter we recall the well-known hysteresis Preisach model, widely employed in the area of magnetism. Some applications of this model in electrical engineering are also described, with a specific focus on the estimation of electromagnetic losses in electrical machines, the simulation of magnetization-demagnetization processes arising in magnetic particle inspection, and the mathematical modeling of batteries for electric vehicles.
Applied Mathematical Modelling, 2021
SSRN Electronic Journal, 2021
It is well known that alternating currents (AC) differ significantly from direct currents (DC) in... more It is well known that alternating currents (AC) differ significantly from direct currents (DC) in large electrodes for Submerged Arc Furnaces (SAFs). The skin effect concentrates AC to the periphery of each electrode, while the proximity effect causes higher current concentration towards the leading electrode. In a presentation at INFACON XV it was further shown that there is also a significant proximity effect between electrode currents and induced currents in the furnace steel shell. Here, we will focus on differences and similarities between AC and DC below the electrodes. In many processes the current runs primarily vertically in a coke bed from each electrode to a metal bath, where it distributes to the other electrodes. In such coke beds we find no significant difference between AC and DC. In the highly conductive metal, there will be horizontal currents and a significant AC skin effect. Horizontal currents will also be present in the materials above the metal, depending on the electrical conductivity in this region. A simple model shows that there is a strong proximity effect between such adjacent currents, “pushing” the currents upwards within the slag/coke bed region. A simple estimate, based on furnace dimensions and assumed conductivities, will show whether this effect is significant, in which case DC computations are inadequate to estimate the current paths. The same proximity effect will significantly enhance induced currents in an electrically conductive lining. Finally, since the underlying Maxwell’s equations are linear, the fundamental current paths in 3-phase AC SAFs can be studied by computing two independent single-phase cases for a given geometry and distribution of electrical conductivities. Any other current distribution will be a linear combination of these two solutions.
Finite Elements in Analysis and Design, 2017
This paper presents a novel algorithm for the computation of transient electromagnetic fields in ... more This paper presents a novel algorithm for the computation of transient electromagnetic fields in nonlinear magnetic media with hysteresis. We deal with an axisymmetric transient eddy current problem where the constitutive relation between H and B is given by a hysteresis operator, i.e., the values of the magnetic induction B depend not only on the present values of the magnetic field H but also on its past history. First, we introduce the mathematical model of the problem and, by applying some abstract result, we show the well posedness of a weak formulation written in terms of the magnetic field. For the numerical solution, we consider the Preisach model as hysteresis operator, a finite element discretization by piecewise linear functions, and the backward Euler time discretization. By taking into account the monotonicity property of the Preisach model, we propose a fixed point algorithm to deal with hysteresis effects which is numerically validated: we report a numerical test in order to assess the order of convergence and we compare the results with experimental data. For the later, we consider a physical application: the numerical computation of eddy current and hysteresis losses in laminated media as those used in transformers or electric machines.
Mathematics in Industry, 2008
This paper deals with mathematical modelling and numerical simulation of induction heating furnac... more This paper deals with mathematical modelling and numerical simulation of induction heating furnaces for axisymmetric geometries. The mathematical model presented consists in a coupled thermo-magneto-hydrodynamic problem with phase change. We propose a finite element method and an iterative algorithm to solve the equations. Some numerical results for an industrial furnace used for silicon purification are shown.
Mathematics in Industry, 2006
The aim of this work is to introduce and numerically solve an axisymmetric mathematical model for... more The aim of this work is to introduce and numerically solve an axisymmetric mathematical model for thermoelectrical simulation of an induction heating furnace.
Mathematical Models and Methods in Applied Sciences, 2013
This paper deals with an axisymmetric transient eddy current problem in conductive nonlinear magn... more This paper deals with an axisymmetric transient eddy current problem in conductive nonlinear magnetic media. This means that the relation between the magnetic field and the magnetic induction, the so-called H-B curve, is nonlinear. The source of the problem is the magnetic flux across a meridian section of the device, which leads to a parabolic nonlinear problem with nonlocal boundary conditions. First, by applying some abstract results, we prove the existence and uniqueness of the solution to a weak formulation written in terms of the magnetic field. Then, we compute the numerical solution of the problem by using a finite element method combined with a backward Euler time discretization. We derive error estimates in appropriate norms for both the semidiscrete (in space) and the fully discrete problems. Finally, we show numerical results which allow us to confirm the theoretical estimates and to assess the performance of the proposed scheme.
International Journal for Numerical Methods in Engineering, 2007
Computers & Mathematics with Applications, 2013
Applied Numerical Mathematics, 2009
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:
IEEE Transactions on Magnetics