International audienceWe present applications of the reduced basis method (RBM) to large-scale non-linear multi-physics problems connected to real industrial applications arising from the High Field Resistive Magnets development at the Laboratoire National des Champs Magnétiques Intenses

Daversin, Cécile

Prud'Homme, Christophe

Trophime, Christophe

Veys, Stéphane

Hal - Université Grenoble Alpes

Reduced Order modeling of high magnetic field magnetsCe´cile Daversin, Christophe Prud’Homme, Christophe Trophime, Ste´phaneVeysTo cite this version:Ce´cile Daversin, Christophe Prud’Homme, Christophe Trophime, Ste´phane Veys. ReducedOrder modeling of high magnetic field magnets. 17th U.S. National Congress on Theoretical& Applied Mechanics, Jun 2014, Michigan State University, East Lansing, Michigan, UnitedStates. <hal-00955232v2>HAL Id: hal-00955232https://hal.archives-ouvertes.fr/hal-00955232v2Submitted on 17 Apr 2014HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.17th U.S. National Congress on Theoretical and Applied MechanicsMichigan State University, 15-20 June 2014Abstract: C-07-646Reduced Order Modeling of High MagneticField MagnetsC. Daversin, Inst. de Recherches en Math. Appl., University of Strasbourg, Strasbourg, daversin@math.unistra.frC. Prudhomme, Inst. de Recherches en Math. Appl., University of Strasbourg, Strasbourg, prudhomme@unistra.frC. Trophime, Lab. Nat. des Champs Magne´tiques Intenses, CNRS-UJF-UPS-INSA, christophe.trophime@lncmi.cnrs.frS. Veys, Lab. Jean Kuntzmann, CNRS-University Joseph Fourier, stephane.veys@imag.frThe Laboratoire National des Champs Magne´tiques Intenses (LNCMI) is a French large scale facility[?] enabling researchers to perform experiments in the highest possible magnetic field (up to 35 T staticfield provided by water cooled resistive magnets connected with a 24 MW power supply). In the racefor higher field, existing magnet technologies are pushed to the limits in terms of material properties anddesign methods. This is even more true for magnets where either the field profile or the field homogeneity(eg. for NMR applications) is also targeted. The design and optimization of these magnets require fromFigure 1. On the left : a view of a 35 tesla magnet; on the right a detailled view of the inner part of themagnet with a zoom on the cooling channels and insulators. Temperature field within this part isdisplayed on the same figure.an engineering point of view the prediction of ”quantities of interest” or performance metrics, whichwe shall denote outputs namely magnetic field in the center, maximum stresses, maximum and averagetemperatures. These outputs are expressed as functionals of field variables associated with a set of coupledparametrized PDEs which describe the physical behavior of our magnets. The parameters, which we shalldenote inputs, represent characterization variables such as physical properties, heat transfer coefficients,water temperature and flowrate, and geometric variables in optimisation studies. To evaluate these implicitinput/output relationships, solutions of a multi-physics model involving electro-thermal, magnetostatics,electro-thermal-mechanical and thermo-hydraulics are requested. It should be noted that this model isnon-linear as the material properties depend on temperature. In practice these evaluations represent ahuge computational time but they are mandatory to improve the magnet design as we can no longer relyon common physical sense.To significantly reduce this computational time, we choose to use model order reduction strategies,and specifically to use the reduced basis method [?, ?, ?]. This method is well adapted in this contextof many model evaluations for parametric studies, inverse problems and uncertainty quantification. Wewill present the RB method applied to our non-linear coupled models starting with the example of the1Reduced Order Modeling of High Magnetic Field Magnets — 2/240608010012014030 50 70 90MeanTemperature(◦C)Current density (A/m2)CD-calc.01FEMCRBFigure 2. Parametric study of the mean temperature of a Bitter magnet sector.electro-thermal coupled problem which is the basis of our design. We build upon the feel++ reducedbasis framework ([?, ?]) and rely on the openturns (http://www.openturns.org/) library for uncertaintyquantifications. Validations and examples will be presented for small to large magnet models. Ungoingdevelopments to include more physics in our models (eg. electro-thermal-mechanical phenomena) will bediscussed.AcknowledgmentsWe acknowledge PRACE for awarding us access to resource SuperMUC based in Germany at LRZ.

Reduced Order modeling of high magnetic field magnets

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Reduced Order modeling of high magnetic field magnets

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Hal - Université Grenoble Alpes