Optimal Grids in the Finite Element Approximations to Compressible Flow Problems
| Autor: | Shin-Perng Chang, 張新鵬 |
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| Rok vydání: | 2006 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 94 The purpose of this work is to construct optimal grids for solving transonic flow problems based on least-squares finite element approximations. One major difficulty of transonic flow problems is the occurrence of the shocks on the supersonic region. The weighted least-squares finite element using the mesh redistribution algorithm will be considered for accurate shock capturing. The idea is to adjust the position of the grid points and produce a mesh with the same number of unknowns, which is more aptly graded for the given problem. Numerical studies which lead to an appropriate grading of optimal grids for the weighted least-squares finite element methods will be provided. Using the weighted least-squares methods the algorithm using mesh redistributions and mesh refinements will be presented for the transonic flow problem. An artificial compressibility method is used in the supersonic region to eliminate the expansion shock obtained from the weighted least-squares approximations. Theoretical results on the choice of weighting functions and numerical results of one and two dimensional convection dominated flow problems are also provided. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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