Numerical simulation of the Dynamic Beam Equation using the SBP-SAT method
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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.
Place, publisher, year, edition, pages
2014. , 39 p.
TVE, TVE 14 046 juni
Dynamic beam equation, finite difference methods, stability, boundary treatment
IdentifiersURN: urn:nbn:se:uu:diva-227121OAI: oai:DiVA.org:uu-227121DiVA: diva2:728594
Master Programme in Engineering Physics
Sjödin, MartinStrømme, Maria