Numerical simulation of the linearised Korteweg-de Vries equation: Diploma work (15 HP) Uppsala University Division of scientific computing
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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
SBP, SAT, SBP-SAT, Korteweg, de, Vries, linearised, numerical, approximation, simulation
Other Engineering and Technologies not elsewhere specified
IdentifiersURN: urn:nbn:se:uu:diva-229330OAI: oai:DiVA.org:uu-229330DiVA: diva2:736264
Master Programme in Engineering Physics
Sjödin, MartinStrömme, Maria, Professor