Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations
| dc.contributor.advisor | Malan, Arnaud G | |
| dc.contributor.advisor | Nordstrom, Jan | |
| dc.contributor.author | Nchupang, Mojalefa Prince | |
| dc.date.accessioned | 2021-01-29T14:12:59Z | |
| dc.date.available | 2021-01-29T14:12:59Z | |
| dc.date.issued | 2020 | |
| dc.date.updated | 2021-01-29T14:09:38Z | |
| dc.description.abstract | Numerical simulations of incompressible flows are unequivocally important due to their numerous industrial applications. These applications ranges from the large-scale fluid's flow modelling such as aerodynamics [1], atmospheric-ocean modelling [2] to a simple pipe flows in the petroleum industry [3]. This study is devoted to develop a provably stable and high order approximation for the incompressible laminar boundary layer equations. A new set of energystable boundary conditions are derived using the energy method. It is shown that both the weak and strong implementation of these boundary conditions yields an energy estimate. The semidiscrete problem is formulated by discretizing the continuous spatial derivatives using high order finite difference approximations on summation-by-parts form. The boundary conditions are implemented weakly using the simultaneous approximation terms methods. The discrete energy estimate is derived by mimicking the continuous analysis and hence, the numerical approximation is proved to be stable. The accuracy and linear stability of the developed scheme is also validated by solving the celebrated laminar flat plate flow problem. This is done by injecting the Blasius solution into the coefficient matrix as well as weak boundary conditions | |
| dc.identifier.apacitation | Nchupang, M. P. (2020). <i>Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations</i>. (). ,Faculty of Engineering and the Built Environment ,Department of Mechanical Engineering. Retrieved from http://hdl.handle.net/11427/32732 | en_ZA |
| dc.identifier.chicagocitation | Nchupang, Mojalefa Prince. <i>"Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations."</i> ., ,Faculty of Engineering and the Built Environment ,Department of Mechanical Engineering, 2020. http://hdl.handle.net/11427/32732 | en_ZA |
| dc.identifier.citation | Nchupang, M.P. 2020. Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations. . ,Faculty of Engineering and the Built Environment ,Department of Mechanical Engineering. http://hdl.handle.net/11427/32732 | en_ZA |
| dc.identifier.ris | TY - Master Thesis AU - Nchupang, Mojalefa Prince AB - Numerical simulations of incompressible flows are unequivocally important due to their numerous industrial applications. These applications ranges from the large-scale fluid's flow modelling such as aerodynamics [1], atmospheric-ocean modelling [2] to a simple pipe flows in the petroleum industry [3]. This study is devoted to develop a provably stable and high order approximation for the incompressible laminar boundary layer equations. A new set of energystable boundary conditions are derived using the energy method. It is shown that both the weak and strong implementation of these boundary conditions yields an energy estimate. The semidiscrete problem is formulated by discretizing the continuous spatial derivatives using high order finite difference approximations on summation-by-parts form. The boundary conditions are implemented weakly using the simultaneous approximation terms methods. The discrete energy estimate is derived by mimicking the continuous analysis and hence, the numerical approximation is proved to be stable. The accuracy and linear stability of the developed scheme is also validated by solving the celebrated laminar flat plate flow problem. This is done by injecting the Blasius solution into the coefficient matrix as well as weak boundary conditions DA - 2020 DB - OpenUCT DP - University of Cape Town KW - mechanical engineering LK - https://open.uct.ac.za PY - 2020 T1 - Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations TI - Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations UR - http://hdl.handle.net/11427/32732 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/32732 | |
| dc.identifier.vancouvercitation | Nchupang MP. Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations. []. ,Faculty of Engineering and the Built Environment ,Department of Mechanical Engineering, 2020 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/32732 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Mechanical Engineering | |
| dc.publisher.faculty | Faculty of Engineering and the Built Environment | |
| dc.subject | mechanical engineering | |
| dc.title | Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations | |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MSc |