“Application of boundary integral solution to thermal diffusion problem by edge based basis functions”

Abstract

In this research paper, heat diffusion problem is solved using the new numerical simulation method called boundary integral equation formulation and boundary element solution method. Three dimensional irregular thermal bodies are addressed by introducing the new edge based basis and weighting functions. The three numerical formulations defined on the edges are Single Layer Formulation (EBSLF), Double Layer Formulation (EBDLF) and Combined Layer Formulation (EBCLF) are presented for higher accuracy of the results for heat dissipation. The triangular patch modeling method is used to divide the arbitrary irregular geometry of the body into triangular patches so that above edge based function are defined on those edge of the patches for numerical solution. Numerically, the solution method is developed by defining the basis functions on the Edge of the triangles, instead of on the nodes as followed in the regular BEM solutions. The temperature diffusion results from the hot surface body are plotted for analysis. Also the convergence study is done to get the result convergence towards the exact solution for the different new numerical formulations. The errors are treated in two different ways. The actual error and the absolute errors are used to determine the best model among all the combinations of numerical formulations and different mesh sizes.