Adaptive finite element method and its application to CFD

• Main Authors: Wang Shi Jung, 王希勇
• Other Authors: CyhungYuan Huang
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/83045861133851624620

碩士 === 國立臺灣科技大學 === 機械工程研究所 === 83 === The aerodynamic characteristics of high speed flying vehicles are affected by many complex flow phenomena such as shock waves, boundary layer separation, vortex shedding, turbulence, etc. In recent years, the revolutionary progress of computational mechanics and the rapid development of computer hardware/ software provide an optimistic future for the realistic numerical simulation of these flow phenomena. The purpose of this study is to apply the recently developed h- adaptive finite elemen method to analyze inviscid, high speed, axisymmetric flow problems. The adaptive procedures make use of mathematically justified error indicator to evaluate the "goodness" of the numerical solution and they subsequently optimize the structure of the grid to deliver answers which satisfy user-specified levels of accuracy. The computational grid is adapted in order to reduce the error using a minimal number of degrees of freedom; this is achieved by employing nested local refinements (unrefinements) in regions of large (small) error. This type of grid-solution adaptive scheme automatically resolve shocks to a level of accuracy specified by the user and it employs minimal computational effort to achieve this task. The technical bottlenecks for implementing h- adaptive finite element method are : the treatment of constrained nodes and the design of associated data structures. In this study, a robust data structures are designed for efficiently implementing grid refinement and unrefinement. By modifying the local shape functions and the associated physical degrees of freedom in an element, the constrained nodes can be completely removed. To verify the proposed method, a series of high speed flow problems are solved and compared with either analytical solution or experimental data. The test results demonstrate that the accuracy of the numerical solution can be significantly improved by using the h-adaptive finite element method.