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Numerical simulation of the linearised Korteweg-de Vries equation: Diploma work (15 HP) Uppsala University Division of scientific computing
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The first main focus in the present project was to analyse the boundary treatment of the linearised Korteweg-de Vries equation. The second main focus was to derive a stable numerical solution using a high-order finite difference method. Since the model involved a third derivative in space, the numerical treatment of the boundaries was highly nontrivial. To aid the boundary treatment high-order accurate first and third derivative finite difference operators were employed. The boundaries are based on the summation-by-parts (SBP) framework, thereby guaranteeing linear stability. The boundary conditions were imposed using a penalty technique. A convergence study was performed where the derived numerical solution was compared with an analytical one. Fourth order accurate Runge-Kutta was used to time-integrate the numerical approximation. Measuring the rate of convergence, q, yielded q = 4 for 4th order accurate SBP-operators and q = 5.5 for 6th order accurate SBP-operators. Thus the convergence study proved the accuracy and stability of the numerical solution derived with the SBP-methodology.

Place, publisher, year, edition, pages
2014. , 29 p.
TVE, TVE 14 030 juni
Keyword [en]
SBP, SAT, SBP-SAT, Korteweg, de, Vries, linearised, numerical, approximation, simulation
National Category
Other Engineering and Technologies not elsewhere specified
URN: urn:nbn:se:uu:diva-229330OAI: oai:DiVA.org:uu-229330DiVA: diva2:736264
Educational program
Master Programme in Engineering Physics
Available from: 2014-08-13 Created: 2014-08-05 Last updated: 2014-08-13Bibliographically approved

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