A precise integration boundary element method for solving transient heat conduction problems

• RIBEM and PIM are combined to solve the transient heat conduction problems.
• The PIM can obtain highly precise results for a big time step.
• The computational time of PIM is almost same as FD without loss of precision.

In this paper, a combined approach of boundary element method and precise integration method is presented for solving transient heat conduction problems with heat sources. The boundary integral equation is derived by means of the Green’s function for the Laplace equation, and as a result, two domain integrals are involved in the derived integral equations. Firstly, the radial integration method is used to convert the domain integrals into equivalent boundary integrals, so the system of ordinary differential equations on the boundary integral equation can be obtained by the boundary element method. Then, the precise integration method is adopted to solve the system of ordinary differential equations. Finally, several numerical examples are given to demonstrate the performance of the present method. The results show that the present approach gives satisfactory performance even for very large time step size, and the results given by the present approach are independent of the time step size if some integrals involves boundary conditions and heat sources can be integrated analytically.