Some Numerical Results for Two Dimensional Incompressible Navier-Stokes Equations in Lagrangian Formulation Using Finite Element Method

• Main Authors: Chang-sheng Zhang, 張昶盛
• Other Authors: Arthur Cheng
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/94394139379405176187

碩士 === 國立中央大學 === 數學研究所 === 100 === In this thesis we propose a different point of view in solving Navier-Stokes equations on a fixed domain numerically. Instead of using the spatial coordinate to model the motion of the fluids, we formulate using the material coordinate and study the corresponding PDE by standard finite element method. The most important benifit of using the material coordinate is that a lot of free boundary problems can be theoretically solved in this fashion, while a main drawback of doing this is that it is very time-consuming. We compare the numerical results produced by these two different formulations, and conclude that the error between two sets of numerical results gets smaller as the mesh size approaches zero.