Accurate method for calculating currents in wires in the vicinity of curved geometries

International audiencePrecise methods to calculate currents are required for low frequency EMC simulations dealing with vehicles struck by lightning. The current model used resolves Maxwell’s equations combined with a Line model based on Holland’s thin wire formalism [1]. The challenge is related to the approximation of the source fields obtained with Yee’s scheme [2]. These sources are then used for the thin wire equations. In the vicinity of structures, the errors due to the staircase meshes representing surfaces corrupt the fields’ values. In order to bypass this issue, it was suggested to apply non structured meshes such as Finite Volume (FV) [3]. Difficulties are encountered when introducing thin oblique wires [4] in this last approach, in particular for the calculation of the local self inductance L, a numerical parameter required by the line model equations.In choosing a FV solver, difficulties will arise in terms of calculation resources due to the calculation procedure of the latter and to the unstructuredness of the meshes. To overcome this obstacle, a hybrid Non Structured-Structured (NST-ST) FV scheme which can also incorporate oblique Line models is proposed.To illustrate the advantage of this new approach, an open cylindrical structure with wires running along its walls will be taken into account. It will be illuminated by a plane wave and we shall compare the obtained results in terms of current and field values retrieved inside and also in the vicinity of the cables

Study of a hybrid finite volume / finite difference method and of a model for thin slanted wires for applications in electromagnetic compatibility

Dans des cas applicatifs de CEM industrielle des problématiques de complexité géométrique et électromagnétique s'imposent lors de la résolution des équations de Maxwell dans le domaine temporel. Des modèles et des méthodes numériques ont chacun été conçu pour résoudre des équations sur des géométries spécifiques (la méthode FDTD pour les géométries cartésiennes, la méthode FVTD pour les géométries courbes, les méthodes d’ordre élevé FEM et GD pour les problèmes de cavité et enfin un modèle TLM pour les structures filaires). Afin de travailler sur des systèmes ayant un aspect multi-échelles et en tenant compte de la courbure de leurs géométries il est envisager de combiner ces modèles et méthodes numériques par le biais d'un schéma hybride. Un couplage volumes finis/différences finies/TLM stable et convergent sera proposé dans un premier temps. La consistance et l'ordre de convergence d'un tel schéma seront étudiées. Des développements sur une architecture parallèle à mémoire distribuée et/ou sur une architecture GPU seront effectués dans un deuxième temps. Une fois que les travaux seront aboutis, des applications réalistes seront mis en œuvre afin de valider et quantifier les performances calcul de ces derniers.In the realm of industrial EMC applications, issues such as electromagnetic or geometric complexity could be encountered as one resolves Maxwell's equations in a time domain TD. Numerical methods and models have been designed to solve these equations on particular geometries (FDTD method in Cartesian geometries, FVTD method in curved geometries, High order methods such as FEM and GD for problems involving cavities and finally the TLM method for wire structures). In order to work on systems with a multi-scaled form and take in account their geometries' curvature, it is anticipated to combine these models and numerical methods with the use of a hybrid scheme. As a first step, a stable coupling of the finite volume/finite difference/transmission line methods which converges shall be proposed. The order of convergence and consistency of such a scheme will be studied. Secondly, algorithms will be implemented on a DMP (distributed memory parallel) machine and/or for a GPU architecture. Upon the fulfilment of these tasks, realistic applications will be launched to validate and quantify the computing performances of the algorithms