Direct And Inverse Heat Conduction Problems Solving By The Boundary Element Method

Boundary element method has been developed in recent years. In 1978, Brebbia has preliminarily constructed the theoretical system for boundary element method through adopting the weighted residual method to derive the boundary integration equation, which represents the mature of the boundary element method. Although the boundary element method was developed no more than forty years, it has become a new and effective tool for modern engineering analysis. Additionally, the boundary element method has advantages of reduced order, high precision and speed, it is of the vital importance comparing with the finite difference method and finite element method in the field of modern numerical solutions.Direct heat conduction and inverse heat conduction problems are significant for simulations of heating, ventilating and air-conditioning. Numerical studies of direct heat conduction problem far preceded that of boundary element method. At present, commercial software for solving the heat conduction problem has been developed in terms of finite difference method, finite volume method or finite element method. However, the unified and mature software for solving the inverse heat conduction problem has never been created until now, due to the fact that the inverse heat conduction problem is of ill-pose.In 1970s, the boundary element method has been firstly used to study the direct heat conduction problem. In the subsequent 1980s, it has been developed to study the inverse heat conduction problem combining with the'least squares'or'minimum energy'practices.In this thesis, the boundary element method has been systemically used to solve the direct heat conduction problem, especially that with discrete heat sources. Additionally, the inverse heat conduction problem of cooling solid-block has been successfully solved via combining the least squares practice and the boundary element method, which is of vital importance for real applications. General VB procedure for solving direct and inverse heat conduction problems has been developed basing on the boundary element method, and it has advantages of friendly-interface, convenience and adaptation. Numerical results demonstrate that the boundary element method is feasible and reliable for solving the direct and inverse heat conduction problems, and it has greatly abbreviated the code and enhanced the calculation speed and accuracy.