On Two Iterative Least-Squares Finite Element Schemes for Solving the Incompressible Navier-Stokes Equations
| Autor: | Yun-Tsz Wang, 王韻詞 |
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| Rok vydání: | 2008 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 96 This thesis is devoted to a numerical study of two iterative least-squares finite element schemes on uniform meshes for solving the stationary incompressible Navier-Stokes equations with velocity boundary condition. Introducing vorticity as an additional unknown variable, the Navier-Stokes problem can be recast as a first-order quasilinear velocity-vorticity-pressure system. Two Picard-type iterative least-squares finite element schemes are proposed for approximating the solution to the nonlinear first-order problem. In each iteration, we apply the usual L2 least-squares scheme or a weighted L2 least-squares scheme to solve the corresponding Oseen problem. We concentrate on two-dimensional model problems using continuous piecewise polynomial finite elements on uniform meshes for both iterative least-squares schemes. Numerical evidences show that, for the same test problem with smooth exact solution, the L2 least-squares solutions are more accurate than the weighted L2 least-squares solutions for low Reynolds number flows, while for flows with relatively higher Reynolds numbers the weighted L2 least-squares approximations seem to be better than the L2 least-squares approximations. Finally, numerical results for driven cavity flows are also given to demonstrate the effectiveness of the iterative least-squares finite element approach. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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