| In many engineering fields,heat conduction problems will be involved.Among them,the effective solution of structural heat dissipation problem is of great significance for engineering guidance.Finite volume method,finite element method and other commonly used numerical methods need to divide the whole calculation domain,which is large-scale and time-consuming.The boundary element method only needs to divide the elements on the boundary of the problem calculation domain.The number of elements is small and the calculation efficiency is high.There are two main difficulties in the application of boundary element method in heat transfer problems.One is that it is difficult to find the basic solution of the corresponding problem.There will be domain integration in the integral equation.Effectively dealing with domain integration is an important step in the implementation of boundary element method;The second is to solve the obtained ordinary differential equations,which affects the numerical stability and accuracy of the whole boundary element method.Effective treatment of the above two difficulties is of great significance to the boundary element method.In this thesis,the dual reciprocity boundary element method and different numerical methods are mainly used to solve the transient heat conduction problem.The main work is as follows:(1)The precise integration method and dual reciprocity boundary element method are coupled to solve the heat dissipation problem of structures without heat source.The dual reciprocity method is used to deal with the domain integration in the integral equation,and the precise integration method is used to deal with the first-order differential equations with constant coefficients.Numerical examples show that the precise integration dual reciprocity boundary element method(PI-DRBEM)has high accuracy in structural heat dissipation.(2)For the first time,Runge Kutta method and dual reciprocity boundary element method are coupled to form a new numerical algorithm:Runge Kutta-dual reciprocity boundary element method(RK-DRBEM).The internal heat source term is considered to solve the three-dimensional transient convection heat transfer problem.For the time-dependent firstorder differential equations with constant coefficients,the temperature of nodes in the domain is solved by the fourth-order Runge Kutta method.Finally,compared with the finite element method and the dual reciprocity precise integration method,the effectiveness of the new algorithm is verified.(3)Three boundary conditions are introduced into the system matrix for the first time.Through the analysis of the boundary conditions,the three boundary conditions are naturally loaded into the system matrix in a unified form.Whether PI-DRBEM or RK-DRBEM can naturally solve the three boundary types of problems.The boundary element method proposed in this thesis can be applied to a variety of transient heat conduction problems.Among them,Runge Kutta boundary element method has very high calculation accuracy,which provides a good scheme to improve the numerical stability of boundary element method,is conducive to the application and popularization of boundary element method in heat transfer,and provides a good reference for other numerical methods. |
