Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions
We introduce two finite element formulations to approximate magneto-static problems with discontinuous electric potential based respectively on the electrical scalar potential and the magnetic field. This work is motivated by our interest in Liquid Metal Batteries (LMBs), a promising technology for...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-04-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.184/ |
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| author | Bénard, Sabrina Cappanera, Loic Herreman, Wietze Nore, Caroline |
| author_facet | Bénard, Sabrina Cappanera, Loic Herreman, Wietze Nore, Caroline |
| author_sort | Bénard, Sabrina |
| collection | DOAJ |
| description | We introduce two finite element formulations to approximate magneto-static problems with discontinuous electric potential based respectively on the electrical scalar potential and the magnetic field. This work is motivated by our interest in Liquid Metal Batteries (LMBs), a promising technology for storing intermittent renewable sources of energy in large scale energy storage devices. LMBs consist of three liquid layers stably stratified and immiscible, with a light liquid metal on top (negative electrode), a molten salt in the middle (electrolyte) and a heavier liquid metal on bottom (positive electrode). Energy is stored in electrical potential differences that can be modeled as jumps at each electrode-electrolyte interface. This paper focuses on introducing new finite element methods for computing current and potential distributions, which account for internal voltage jumps in liquid metal batteries. Two different formulations that use as primary unknowns the electrical potential and magnetic field, respectively, are presented. We validate them using various manufactured test cases, and discuss their applications for simulating the current distribution during the discharge phase in a liquid metal battery. |
| format | Article |
| id | doaj-art-a3e1739cd60c4f939ef1e5a94151a8c6 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-04-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-a3e1739cd60c4f939ef1e5a94151a8c62025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-04-01351S1537210.5802/crmeca.18410.5802/crmeca.184Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributionsBénard, Sabrina0Cappanera, Loic1Herreman, Wietze2Nore, Caroline3Université Paris-Saclay, CNRS, LISN, 91400 Orsay, FranceDepartment of Mathematics, University of Houston, Houston, Texas 77204, USAUniversité Paris-Saclay, CNRS, FAST, 91400 Orsay, FranceLaboratoire Interdisciplinaire des Sciences du Numérique; LISN, Université Paris-Saclay, Bât 507, Campus Universitaire F-91405 Orsay, FranceWe introduce two finite element formulations to approximate magneto-static problems with discontinuous electric potential based respectively on the electrical scalar potential and the magnetic field. This work is motivated by our interest in Liquid Metal Batteries (LMBs), a promising technology for storing intermittent renewable sources of energy in large scale energy storage devices. LMBs consist of three liquid layers stably stratified and immiscible, with a light liquid metal on top (negative electrode), a molten salt in the middle (electrolyte) and a heavier liquid metal on bottom (positive electrode). Energy is stored in electrical potential differences that can be modeled as jumps at each electrode-electrolyte interface. This paper focuses on introducing new finite element methods for computing current and potential distributions, which account for internal voltage jumps in liquid metal batteries. Two different formulations that use as primary unknowns the electrical potential and magnetic field, respectively, are presented. We validate them using various manufactured test cases, and discuss their applications for simulating the current distribution during the discharge phase in a liquid metal battery.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.184/magnetohydrodynamicsfinite element methodsinterior penalty techniquesdiscontinuous electric potentialliquid metal batteries |
| spellingShingle | Bénard, Sabrina Cappanera, Loic Herreman, Wietze Nore, Caroline Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions Comptes Rendus. Mécanique magnetohydrodynamics finite element methods interior penalty techniques discontinuous electric potential liquid metal batteries |
| title | Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions |
| title_full | Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions |
| title_fullStr | Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions |
| title_full_unstemmed | Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions |
| title_short | Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions |
| title_sort | magnetic field based finite element method for magneto static problems with discontinuous electric potential distributions |
| topic | magnetohydrodynamics finite element methods interior penalty techniques discontinuous electric potential liquid metal batteries |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.184/ |
| work_keys_str_mv | AT benardsabrina magneticfieldbasedfiniteelementmethodformagnetostaticproblemswithdiscontinuouselectricpotentialdistributions AT cappaneraloic magneticfieldbasedfiniteelementmethodformagnetostaticproblemswithdiscontinuouselectricpotentialdistributions AT herremanwietze magneticfieldbasedfiniteelementmethodformagnetostaticproblemswithdiscontinuouselectricpotentialdistributions AT norecaroline magneticfieldbasedfiniteelementmethodformagnetostaticproblemswithdiscontinuouselectricpotentialdistributions |