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L'étude du comportement d'un réservoir de gaz en nappe aquifère réclame une connaissance aussi précise que possible des caractéristiques géométriques et pétrophysiques des couches réservoirs. Les moyens d'investigation sont de deux natures : - forages permettant une connaissance locale des roches réservoirs ; - mesures sismiques conduisant à une estimation approximative des cotes de certains repères stratigraphiques, en des points situés le long de profils. Les données recueillies sont donc, par nature, fragmentaires et discrètes : là où elles sont absentes, il y a lieu d'estimer les grandeurs étudiées en tenant compte au mieux de notre connaissance de leur variabilité spatiale. Ce problème d'interpolation optimale a donné lieu, depuis une vingtaine d'années, à l'élaboration et la mise en pratique d'un outil théorique particulièrement bien adapté aux besoins exprimés par les techniciens des sciences de la terre : la théorie des variables régionalisées due à G. Matheron. Des programmes informatiques mettant en oeuvre cette théorie sont actuellement opérationnels. Des exemples d'application en sont donnés : - tracé automatique de cartes structurales à partir des données de forages et des mesures sismiques ; - estimation des incertitudes de prévision sur les profondeurs ; - tracé de plusieurs variantes de carte compatibles avec les données ; - établissement d'éléments statistiques relatifs à une grandeur caractéristique d'un stockage : volume stockable par exemple ; - génération automatique des données nécessaires à la mise en oeuvre d'un modèle maillé de réservoir. Predicting and monitoring the behavior of an aquifer gas-storage reservoir requires as precise a knowledge as possible of the geometric and petrophysical properties of the reservoir layer. Two ways of obtaining this information can be given: (a) Boreholes which provide local knowledge of the reservoir, and (b) Seismic measurements which lead to more or less accurate depth estimates for some stratigraphic markers at points located along profiles. Therefore, the data are inherently fragmentary. At points where they are lacking, we have to make the most of available information in order to estimate the unknown values. This problem of optimum interpolation has led to a new theoretical approach which is particularly suited to the earth sciences. This theory is called the theory of regionalized variablesby its author, G. Matheron. It has given rise to effective computer programs, and developments are still being made. Examples of possible applications are: (a) Computer-drawn structural maps based on borehole data and seismic measurements; assessment of the prediction uncertainty for the depth of the top-layer; alternative top-layer maps all of which are consistent with the data. (b) Probabilistic evaluation of the storage volume available. (c) Gridded input to reservoir models.

A coupling of the partial element equivalent circuit method with the finite element method for solving magneto-harmonic electromagnetic problems is proposed. The new formulation, which combines the main advantages of the previous methods, is particularly well suited for modeling electromagnetic complex devices including a large number of conductors. Index Terms--Finite element method, mutual matrix, partial element equivalent circuit, [T.sub.0]--[phi] formulation.

In order to improve the finite-element modeling of macroscopic eddy currents (associated with motion and/or a time- varying electrical excitation), an original error criterion for adaptive meshing, based on a local power conservation, is proposed. Then, the importance of the order element in the error computation is investigated. Finally, the criterion is coupled to a 'bubble' mesh generator, and an adaptive meshing of a 2-D induction heating case is performed. Index Terms--Adaptive meshing, eddy currents, error criterion, power conservation.

The aim of this paper is to propose and argue specific electromagnetic formulations including dynamic electric and magnetic properties of soft materials, working with transient signals and time harmonics within the quasi-static approximation. Special attention will be paid to origin, nature, and relevance of these so-called dynamic properties, which will act on both the diffusion process and coupling between regions. Nonlinear transient experimental identifications of a homogenized dynamic magnetic property are also carried out and discussed. It can provide useful experimental data of soft magnetic materials for simulation and conception purposes. Index Terms--Dynamic hysteresis and properties, eddy currents, experimental characterization, fields coupling, magnetization reversal processes, materials modeling.

Thermal constraint is one of the major cause of capacitor failures. In this paper, a loss model, based on electrode current distribution, is first established to determine, by numerical simulation, a temperature mapping of capacitor. This mapping is successfully compared to measurements. Then a shape optimization, coupling losses computing and finite-element method, is led in order to find parameters that give the best lifespan and the larger reactive power provided. Very interesting new geometries have been found out; they allow an increase in reactive power greater than the increase in volume. Index Terms--Capacitor lifespan, capacitor losses, metallized film capacitors, shape optimization.

In this paper, we consider taking both microscopic excess and macroscopic classical induced losses and damping, occurring within bulk and laminated soft magnetic materials, into account. We will not detail actual eddy currents distributions but use homogenizing techniques and variational principles to derive a dedicated formulation with respect to the reduced magnetic vector potential AM, and still including specific material dynamic properties. At last, some 2-D computations are carried out and first results are discussed. Index Terms--Dynamic hysteresis and eddy currents, homogenization of bulk and laminated materials, quasi-static electromagnetic fields formulations.

This paper investigates a new approach to face the problem of dynamic hysteresis and extra-losses in soft magnetic materials. Thanks to a spatial averaging technique and a variational principle, a dedicated formulation is derived. It takes microscopic magnetization mechanisms and domain wall motion-induced Joule losses into account. Implementation with the finite element method is dicussed and first simple two dimensions and three dimensions calculations are carried out. The method is shown to be suitable whithin the linear dynamic approximation and far from saturation, which only requires additional non linear properties and numerical methods. Index Terms--Dynamic hysteresis, eddy currents, magnetic materials, sensors, transformers, transient formulations.

High frequency electrical machine modeling based on lumped parameter equivalent circuit requires that eddy currents effects be taken into account for R and L coefficient derivation. Substituting hysteretic materials (complex permeability) to conductive materials makes it possible to accurately approximate proximity losses and shielding effect while considering realistic meshes for finite element methods computation. Three-dimensional magnetodynamic simulations of transformer test-cases using anisotropie complex permeability for magnetic core and windings have shown a good agreement with the standard models results. Index Terms--Eddy currents, electromagnetic transient analysis, finite element methods (FEMs), hysteresis, losses.

This paper deals with the modeling of eddy currents generated by are motion during opening phases of low voltage circuit breakers. Two kinds of modeling are tested. While the first one consists in determining eddy currents in splitter plates, the second one is devoted to the calculation of eddy currents in electrodes. All simulations are carried out with a T--[PHI] finite-element method formulation and no new mesh at each time step is required. Index Terms--Circuit breakers, eddy currents, finite-element method, magnetic forces.

Magnetic silencing is required for specific naval applications, especially for some oceanographic or military ships. It is therefore necessary to study the field radiated by electrical propulsion motors. This can be achieved using a numerical modeling based on magnetic moments. In the present paper, this model is presented and then compared to some experimental signatures for validation. Index Terms--Electrical propulsion motor, magnetic moment, magnetic silence, modeling.

Different methods can be proposed to determine the global force on Magnets (equivalent models, Maxwell stress tensor, virtual work principle...). The same value is obtained whatever the method while the local force distribution differs. This problem (i.e. different local force distributions on permanent magnets) has not been solved yet. Though, the determination of the physical distribution of forces is a crucial point, both for practical applications and for theory. Thus, the different methods allowing the calculation of the local force distribution in permanent magnets are described and compared. Evidences are given that only the method based on the virtual work principle provides reliable results. Index terms: permanent magnet, magnetic force densities, magnetic charge, magnetising current, Maxwell stress tensor, virtual work.

Finite Element Methods are used to model the magneto-mechanical characteristics of a magnetostrictive rod. Optimisation of the shapes and dimensions of the heavy magnetostrictive actuator is done. As magnetostrictive material characteristics are non-linear, the modelling methods use an iterative process. A new modelling method has been developed so as to use the available experimental characteristic of magnetostrictive rod: [Lambda](H).

In order to take into account the eddy current in conducting bodies that are supplied by an electrical circuit, a relation linking the global current and the voltage in a massive coil is presented and proved. This relation is introduced in the T-[T.sub.0]-[Phi] formulation for modelling coupled problem of 3D eddy current and electrical circuit. The use of the magnetic scalar potential in this formulation makes it very attractive in terms of computation cost. The validation of the method is realised by comparing calculated results with those obtained with the AV formulation. A contactor validates the case of filament coils. Index terms: coupled problems, circuit equation, scalar formulation, finite elements

To calculate magnetic global force on permanent magnets, several approaches can be used with the Finite Element Method (FEM). They are either based on Maxwell's stress tensor, on the energetic principle or on the equivalent source models. The accuracy of the results for a given mesh is an important criterion for the choice between them. Description and comparison of these methods applied to the calculation of magnetic global forces on rigid permanent magnets (constant magnetization) is done. Results for two different meshes are compared with analytical reference. Index terms - magnetic global force, permanent magnet, magnetizing current, magnetic charge, Maxwell's stress tensor, virtual work.

Two dual formulations are proposed for the calculation of the electromagnetic forces in permanent magnets. The formulations are based on the virtual work principle with the use of nodal elements. Both methods allow the calculation of global force as well as local force densities. These densities depend on the expression of the magnetic energy or co-energy of the magnet. The energies of a permanent magnet are discussed on physical basis. Index terms: local force densities, permanent magnet, virtual work, magnetic energy.

An original permanent magnet flux source is designed in order to generate a magnetic field of several Tesla. The magnet configuration and discretization of the structure are optimized with the help of numerical simulation software developped at LEG (DIPOLE-3D, FLUX2D & FLUX3D). The model of spheroidal flux source presented in the paper creates a field in excess of 4.3 T in a central volume of 0 6 mm x h 2.8 mm with external diameter [approximately equal to] 0 100 mm. A prototype is in the final assembly stage, designed for X-ray dichroism experiments at the European Synchrotron Radiation Facility (ESRF) in Grenoble. Indexing terms - rare earth permanent magnet, magnetic flux source, intense magnetic field, synchrotron.

Since the traditional formulation in terms of a current vector potential T and a magnetic scalar potential [Psi] enforces zero net current in conductors, they cannot be used to solve current driven eddy current problems. For this reason, an alternative using T-[T.sub.0]-[Psi] formulation where [T.sub.0] described an arbitrary current distribution with the given net current in conductors has been proposed some years ago. In this paper, an alternative finite element T-[H.sub.j]-[Phi] formulation using cutting surfaces is proposed. A cutting surface describing the given net current in the conductor is introduced in the nonconducting multi-connected region in order to allow a discontinuity of the scalar potential. This method also avoids cancellation errors in permeable regions and ensures a good numerical stability of the finite element scheme. The present method is validated with a 3-D current driven eddy current problem. Results are compared to T-[T.sub.0]-[Psi] formulation computation.

Following up previous research, concerning low frequency electromagnetic emission from a grounding system, the authors suggest methodology which allows a complete electromagnetic study by Finite Element Method (FEM) of a grounding system in the significant frequential spectrum of a stroke of lightning or a short circuit (f[less than or equal to]1MHz). In this study, as well as calculating the electromagnetic field at any point in space (ground and air), we shall pay particular attention to variation with frequency of the impedance of a grounding system. Suggested modelling will take into account eddy currents in buried conductors and ground and non-linear phenomena (ionization of the ground) around the buried conductors when high currents flow via the earth. It will also deal with displacement currents when their effect becomes noticeable in the earth for high frequency. The interest of this work lies in providing data needed to implement an optimal grounding system in non-homogeneous medium. All the results of calculations will be compared with measurements made by the French Electricity Board (E.D.F, France).

Nowadays many softwares already allow carrying out multiple coupling, however, they are often destined to only one type of coupling and it can prove difficult to integrate a new physical field. So, we have developed an adapted finite element toolbox to do generic coupling. Thanks to an object oriented approach, it becomes possible to carry out multiple coupling. Overall, it's easy to add a new coupling transparently with a minimum of developments. With the choice of indirect coupling method, one can integrate specific solving methods, independently developed. We present the implantation in S.I.C. (Systeme Interactif de Conception) software, one of the first finite element software using an object approach. We have chosen it for its object manager in FORTRAN and the included various physic models. Finally, we have validated all our developments on a physical process of induction heating.

The paper describes a combination of methods for the three dimensional magnetic field simulation of rotating machines using the finite element method. The modelling takes into account both external circuit and movement of the rotor. The electric coils are represented in a mesh-independent fashion by the line current model. The equations from a nodal analysis of the electric circuit are solved simultaneously with the finite element equation system at each time step. The movement is treated using a finite element connection between the two independent stator and rotor meshes.

This paper describes a method for finite element modelling of transient 2D eddy currents in the nonlinear moving conductor of an electromagnetic retarder. The magnetic vector potential A formulation is used, with a general single-step time-marching algorithm, and the fixed and moving coordinate systems are compared. A homogenization technique, inspired by the lamination modelling, is used to make the geometry of a moving region invariant along the speed direction, in order to use a more direct method to compute the steady state eddy currents in the whole rotor. Results are compared to measurements.

This paper develops a basic idea which allows low frequency electromagnetic fields generated by cylindrical conductors, with very small radii compared with their lengths, to be calculated. The proposed method can be applied to both overhead conductors and those buried in a conducting environment. The paper presents a direct application for this concept which consists in calculating electromagnetic fields created by a substation grounding system following an accidental short circuit or a stroke of lightning. The Finite Element Method (FEM) with several formulations will be used. Currents in the cylindrical conductors which make up the earth network grid are taken into account without volume meshing; simple line discretization of these will be carried out. Electromagnetic fields generated by leakage currents and currents induced underground are taken into account. Furthermore, open boundaries of both air and earth environments are processed by introducing a spatial transformation. This application for an earth network enables us to show the advantages of FEM processing compared with the method traditionally used in antenna theory for this kind of problem.

Application of the 'diffuse approximation' to the post-treatment and the computation of electromagnetic fields is investigated. This numerical method is very attractive since it does not require a mesh and leads to continuous estimates of the unknown function and its derivatives. The diffuse element method behaviour is observed on several numerical examples.

Finite Element Method transient modelling is used to study the behaviour of Linear Induction Launchers. A coupling between electrical and magnetic equation allows one to model all kinds of conductors as well as connections with electrical circuits. A local remeshing around the moving part is applied at the beginning of each time step in order to take into account the displacement of the conductors. Moreover, a thermal coupling enables one to take into consideration the variations of the main characteristics of materials.

This paper is devoted to the computation of the magnetic field radiated by static inductors and a rotating machine. The authors used a 3D finite element program in which the open boundary space was represented either by a geometrica transformation or by the coupling of finite element and boundary integral methods. A comparison of the computed values given by the two methods will be presented along with experimental results measured a long distance from the magnetic devices that has been tested.

A method to take into account movement in finite element modelling of Linear Moving System is presented. It avoids new mesh generation for each time step as well as introduction of speed terms due to movement. Just a few user's routines have to be added to a classical finite element software as FLUX2D. Using this method, a multi-section induction electromagnetic launcher is modelled.

The non-linear analysis of electrical devices is often limited by the complexity of the power supply. In effect, in the case of solid conductors, the voltage is required, while in the case of stranded conductors, the current must be known. These restrictions are due to the nature of the field equations. A new formulation is proposed which offers the possibility of choosing the power supply as well as any kind of connection between components. Two types of 'electromagnetic conductors' are considered: solid conductors, in which eddy current can be induced, and stranded conductors without eddy current. An equation combining the magnetic potential, the current, and the voltage is established for each conductor. This equation is used in a conventional circuit analysis method. The magnetic field and circuit equations can be solved simultaneously in the resulting system. An implicit method is used to discretize the equations in time. A Newton-Raphson linearization algorithm is used to handle problems that include materials with nonlinear properties. This formulation has been implemented in the commercial program FLUX2D. To illustrate one of the many applications, an A.C. electromagnet is studied.

This paper reviews the formulations and numerical methods for two-dimensional eddy current problems in which conductors with eddy currents are connected by external circuits. A general formulation valid for arbitrary circuit connections is obtained using the loop current method.