Comparison of finite element and general finite difference methods for transient heat flow

Abstract

AbstractThe need for calculating transient temperature fields during solidification of ingots and static-mould metal castings of various shapes has stimulated interest in the application of finite element (FEM) and finite difference methods. The present study shows that the general finite difference (GFD) method, utilizing a computational grid with irregular nodal positions, is a computationally effective technique which allows not only the treatment of curved boundaries, but also the improvement of accuracy by selective placement of nodes in regions of rapid temperature changes. Moreover, the computing time requirements of the GFD method are theoretically less and the computation more efficient than that of the FEM. In the present work, a general purpose computer program based on the GFD method is constructed, incorporating two proposed techniques for the treatment of latent heat and convective boundary conditions along curved boundaries. Using two numerical examples, the accuracy and stability of this i...