A stable boundary treatment of the dynamic beam equation (DBE) with two different sets of boundary conditions has been conducted using the summation-by-parts-simultaneous-approximation-term (SBP-SAT) method. As the DBE involves a fourth derivative in space the numerical boundary treatment is highly non-trivial. Using SBP-SAT operators together with suitable time integration schemes the DBE has been simulated and a convergence study has been made. The results show that the SBP-SAT method produces a stable discretistation that is accurate enough to capture the dispersive nature of the dynamic beam equation. In additions simulations were made presenting the importance of a stable boundary treatment showing that the numerical solutions diverge when the boundaries were not handled correctly.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-227121 |
| Date | January 2014 |
| Creators | Stiernström, Vidar |
| 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 | TVE ; TVE 14 046 juni |
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