The study examines the Projection method and the simultaneousapproximation-term (SAT) method as boundary treatment for the dynamic beam equation using summation-by-parts (SBP) operators for handling the inner domain. The methods are examined for both the homogeneous constant coefficient case, and the inhomogeneous piecewise constant coefficient case with a coupled interface. The outer boundaries are handled by SAT or Projection, the coupled interfaced is handled by Projection or a mix between Projection and SAT. Solutions are integrated in time with finite central difference schemes and compared to analytical solutions. A convergence study is conducted with respect to the spatial discretization to measure the accuracy, and the stability is examined by numerical simulations of the CFL-condition. The study shows that Projection has the same accuracy as SAT for most boundary conditions while allowing for a larger timestep. A discontinuity in the medium is found to be handled equally accurate by Projection and the Projection and SAT mixture for all but one case studied, where the mixture was slightly more accurate.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-416818 |
| Date | January 2020 |
| Creators | Wik, Niklas, Niemelä, David, Wagner Zethrin, Valter |
| Publisher | Uppsala universitet, Avdelningen för beräkningsvetenskap, Uppsala universitet, Avdelningen för beräkningsvetenskap, Uppsala universitet, Avdelningen för beräkningsvetenskap |
| 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 ; 20006 |
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