Study On Boundary Element Method And Develop Numerical System Of 3-D Unsteady Heat Conduction

There are many practical problems related to heat conduction in life.The range of the problems which the analytic method can solve is extremely limited. It is a trend to solve complex problems with numerical methods. Whether in theory analysis or in numerical method, some research has been made in the heat conduction field for many years. The methods which we usually use are the Finite Element Method and the Finite Difference Method. But the error of the above methods for solving infinite field problems is large, because it is artificially to determine boundaries and impose boundary conditions. However, Boundary Element Method has the absolute advantages in these aspects, such as reducing dimension of the questions and having the higher computational precision, and it is strictly established in mathematics for the infinite field problems. Consequently, the Boundary Element Method is choosed to research the heat conduction problems in this thesis.In this thesis, a simple solution of transient heat conduction problems is proposed, which is based on the potential theory of the Boundary Element Method. Firstly, the field and boundary integral equations which based on the unsteady heat conduction equation, fundamental solutions and Dirac Function are proposed. Then, discrete equations of unsteady heat conduction is derived by dispersing the time and space. By the above algorithm, the Fortran language is used for compiling the computational program of three-dimensional transient heat conduction equations. Then the numerical system of BEM for 3-D unsteady heat conduction is developed,A number of technical problems have been solved in the process of developing the system. And the Time Integral Method and the Step Wise Method theory are derived, nay, the system is developed.Finally, this system is verified by numerical models. The result demonstrates it has high computational precision and is reliable.