Meshless Methods for Generalized Newtonian Fluid Flow and Heat Transfer

• Main Authors: Shu-Ping Hu, 胡淑評
• Other Authors: 楊德良
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/45682497659254896170

博士 === 國立臺灣大學 === 土木工程學研究所 === 98 === The present research aims to develop a meshless numerical model for the simulation of non-Newtonian fluid flows and heat transfer problems. The non-Newtonian fluid is simplified as a generalized Newtonian fluid (GNF). The viscosity of the GNF is descried by Power law model and Cross model. The numerical solution by a meshless method is expressed by a linear combination of radial basis functions (RBFs). No mesh generation and numerical integral are needed. The meshless numerical methods concerned in this dissertation consist of two types: 1. global method; and 2. local method. Global methods are the meshless analog equation method (MAEM), the combination of method of fundamental solutions and method of particular solutions (MFS-MPS), the method of particular solution (MPS). The adopted local method is the local radial basis function (LRBF) scheme. In this dissertation, the global methods are used to solve the steady equations of temperature and velocity; the local method is applied to solving unsteady 2D and 3D unsteady temperate-velocity coupling equations. The global meshless scheme has high accuracy due to the full consideration of weighting of global supporting nodes, but the global supporting nodes induce a highly ill-conditioned full matrix. It is time-consuming to solve the dense matrix equations. The global meshless methods are not easy to be extended to time dependent problems. Therefore, the local meshless method is introduced for solving unsteady problems. The LRBF scheme approximates the numerical solutions by a linear combination of supporting nodes in every local region. The memory requirement and the cost of CPU time are reduced. Moreover, mesh methods only provide the solution at mesh points, while the meshless method can interpolate the physical value and its derivatives everywhere with high accuracy. The advantages of the meshless methods are very useful for industrial applications. The numerical results by the present methods are compared with the results in the literature. The comparisons show the accuracy of the meshless methods and also demonstrate that the meshless methods are worth developing.