AbstractMaxwell’s laws state that the divergence of a magnetic field always remains zero. In thecontinuous setting this is true for the magnetohydrodynamics equations. However, in thediscrete setting, the solution does not always remain divergence-free. The goal of this project isto find two-dimensional finite element meshes for which the magnetic field solution to themagnetohydrodynamics equations remained divergence-free. The report includes the derivationfor a condition of a divergence-free mesh, examples of meshes for which this condition holdstrue, and lastly numerical results to confirm that the solutions using these meshes aredivergence-free.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-506010 |
| Date | January 2023 |
| Creators | Björklund, Erik, Mårtensson, Peter, Waltman, Noah |
| Publisher | Uppsala universitet, Institutionen för informationsteknologi |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | MATVET-F ; 23030 |
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