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Finite Element Approximations of 2D Incompressible Navier-Stokes Equations Using Residual Viscosity
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences.
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences.
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Chorin’s method, Incremental Pressure Correction Scheme (IPCS) and Crank-Nicolson’s method (CN) are three numerical methods that were investigated in this study. These methods were here used for solving the incompressible Navier-Stokes equations, which describe the motion of an incompressible fluid, in three different benchmark problems. The methods were stabilized using residual based artificial viscosity, which was introduced to avoid instability. The methods were compared in terms of accuracy and computational time. Furthermore, a theoretical study of adaptivity was made, based on an a posteriori error estimate and an adjoint problem. The implementation of the adaptivity is left for future studies. In this study we consider the following three well-known benchmark problems: laminar 2D flow around a cylinder, Taylor-Green vortex and lid-driven cavity problem. The difference of the computational time for the three methods were in general relatively small and differed depending on which problem that was investigated. Furthermore the accuracy of the methods also differed in the benchmark problems, but in general Crank-Nicolson’s method gave less accurate results. Moreover the stabilization technique worked well when the kinematic viscosity of the fluid was relatively low, since it managed to stabilize the numerical methods. In general the solution was affected in a negative way when the problem could be solved without stabilization for higher viscosities.

Place, publisher, year, edition, pages
2018. , p. 40
Series
TVE-F ; 18 010
Keywords [en]
Finite element method, incompressible Navier-Stokes equations, residual based artificial viscosity, stabilization, adaptive method, Chorin's method, IPCS, Crank-Nicholson's method, benchmark problems, CPU-time, accuracy
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-354590OAI: oai:DiVA.org:uu-354590DiVA, id: diva2:1221880
Educational program
Master Programme in Engineering Physics
Supervisors
Examiners
Available from: 2018-08-10 Created: 2018-06-20 Last updated: 2018-08-10Bibliographically approved

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CiteExportLink to record
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