EFGM Based Solutions For The Identification Of Boundary Configuration And Phase Change Problems In Heat Transfer And Adaptive EFGM Computing

Identification of boundary configurations and phase change in heat transfer problems have important application background in engineering and research value in theory. As these two problems involve changing boundaries, how to avoid the difficulties because of remeshing is a very important problem in numerical simulation. The Element-Free Galerkin Method (EFGM) builds the approximation using nodes only, thus it can avoid the generation and remeshing for mesh with good accuracy, stability and convergence. Hence, this thesis studies the identification of boundary configurations and phase change in heat transfer problems based on EFGM solutions.The adaptive EFGM computing can only refine the region where accuracy is not satisfied, so in comparision with uniform refinement, it can improve the accuracy and reduce the number of nodes needed, which achieve a significant decrease of computation cost. Hence, besides above two heat transfer problems, the adaptive EFGM computing is also researched in this thesis.The contribution of this thesis includes:1. Presenting a numerical model for the identification of boundary configurations in heat transfer problems combining EFG and Level set method (LSM). The remeshing is avoided in solving temperature field with changing boundary; LSM is an easy way to discrible shape evolution convieniently and accurately on a fixed grid. The proposed numerical model is verified via an identification of a curvilinear boundary, and the effects of initial guess, number of probing points, measurement error, and density of EFGM nodes and the LSM FD grid are considered. Satisfactory results are obtained.2. Presenting a smoothed effective heat capacity numerical model for phase change heat transfer problems combining EFG and function smoothing technique. The Sigmoid function is used to achieve a discontinuous and smooth effective heat capacity, which avoids the error caused by the discontinuous step-jump of the effective heat capacity, and it is efficient for either lumped or non-lumped heat capacity matrix. The proposed numerical model is verified via solidifications of slab and coner region examples, and the EFG nodes, the parameter relevant with Sigmoid function and the comparison with traditional averaging method are considered. Satisfactory results are obtained.3. Presenting an adaptive EFGM numerical model based on a node-based error estimator, this model is applied in elasticity problems. This node-based error estimator effectively reduces the spurious oscillation of estimated error between nodes. In comparison with the adaptive computing using Chung-Belytschko error estimator, the proposed model can achieve higher accuracy with fewer nodes introduced. 4. Presenting an adaptive EFGM model for direct couple-stress problems, in which the EFG avoids the inconvenience that may be caused by C1 continuity requirement in the implementation of FEM, and the adaptive refinement increases computational accuracy with significantly reducing the computational cost compared with uniform refinement. This thesis also builds a numerical model for solving multi-variables inverse couple-stress problems based on EFGM and Gauss-Newton algorithm. This model is effective for single/combined identification for material parameters/load in case of regional inhomogeneity.This thesis provides a valuable reference for further research/application of meshless and other numerical solutions for relevant problems.