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Advanced study for the numerical approximation of Navier-Stokes equations by implementation of a finite volume solver

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TimeLine.xlsx (15,60Kb) (Restricted access)
Budget.pdf (49,88Kb) (Restricted access)
DiagonalFlow_cpp.pdf (434,8Kb) (Restricted access)
LidDrivenCavity_cpp.pdf (329,7Kb) (Restricted access)
ParallelFlow_cpp.pdf (227,1Kb) (Restricted access)
1d_conduction_cpp.pdf (233,4Kb) (Restricted access)
SmithHuttonCaseUDS_cpp.pdf (272,8Kb) (Restricted access)
SmithHuttonCaseCDS_cpp.pdf (270,1Kb) (Restricted access)
20191008_Master_Thesis_Schubert_v1.pdf (1,290Mb) (Restricted access)
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hdl:2117/179390

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Schubert, Stefan
Tutor / directorPérez Segarra, Carlos DavidMés informacióMés informacióMés informació; Schröder, Wolfgang; Loosen, Simon
CovenanteeRheinisch-Westfälische Technische Hochschule Aachen
Document typeBachelor thesis
Date2019-10
Rights accessRestricted access - author's decision
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
The objective of the thesis is to build different fluid solvers from scratch, whereby the following three cases are considered: Resolution of diffusion problems, convection-diffusion and Navier-Stokes equations. In the process, the conservation equations are approximated in order to convert them into an algebraic system of equations. The code will be implemented in C++ and the equations will be solved either directly or iteratively. The investigation will be applied to incompressible and laminar flows. Within this thesis the finite volume (FV) discretization method is used. Furthermore, a cartesian coordinate system is chosen and the numerical grid applied is an orthogonal cell center mesh. The influence of the refinement of the mesh as well as the time step influence will be analyzed. Moreover, Neumann and Dirichlet boundary conditions will be applied. A different solver will be implemented for each case: First, pure conduction heat transfer in 1D and 2D will be discussed regarding the resolution of diffusion problems. The implementation with the help of the TDMA and line-by-line method will be carried out. The results will be compared to analytical values to prove the accuracy of the solver. Second, a resolution of the convectiondiffusion equation for 2D flows will be investigated. For this purpose, the Smith-Hutton case and a diagonal flow in a square domain will be used to test the code as a benchmark problem. Upwind-, central- and smart-difference schemes will be discussed. The results will be compared to numerical studies on different Peclet numbers. Finally, the resolution of the Navier-Stokes equations will be studied with the fractional step method. As a benchmark problem the driven cavity case will be used, for a 2D case. Upwind- and central- schemes will be covered. Moreover, the effect of different Reynolds numbers on the solution will be examined.
SubjectsNavier-Stokes equations, Heat -- Transmission, Heat -- Convection, Equacions de Navier-Stokes, Calor -- Transmissió, Calor -- Convecció
DegreeMOBILITAT INCOMING
Location
1: Kopernikusstraße 9, 52074 Aachen, Alemanya
URIhttp://hdl.handle.net/2117/179390
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  • Programes de Mobilitat Internacional - Programes de mobilitat 'incoming' (ESEIAAT) [42]
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FilesDescriptionSizeFormatView
TimeLine.xlsxBlocked15,60KbMicrosoft Excel 2007 Restricted access
Budget.pdfBlocked49,88KbPDFRestricted access
DiagonalFlow_cpp.pdfBlocked434,8KbPDFRestricted access
LidDrivenCavity_cpp.pdfBlocked329,7KbPDFRestricted access
ParallelFlow_cpp.pdfBlocked227,1KbPDFRestricted access
1d_conduction_cpp.pdfBlocked233,4KbPDFRestricted access
SmithHuttonCaseUDS_cpp.pdfBlocked272,8KbPDFRestricted access
SmithHuttonCaseCDS_cpp.pdfBlocked270,1KbPDFRestricted access
20191008_Master_Thesis_Schubert_v1.pdfBlocked1,290MbPDFRestricted access

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