A General Algorithm for Evaluating Domain Integrals in 2D Boundary Element Method for Transient Heat Conduction

Abstract

A time-dependent boundary integral equation method named as pseudo-initial condition method is widely used to solve the transient heat conduction problems. Accurate evaluation of the domain integrals in the pseudo-initial condition formulation is of crucial importance for its successful implementation. As the time-dependent kernel in the domain integral is close to singular when small time step is used, a straightforward computation using Gaussian quadrature may produce large errors, and thus lead to instability of the analysis. To improve the computational accuracy of the domain integral, a coordinate transformation coupled with a domain cell subdivision technique is presented in this paper for 2D boundary element method. The coordinate transformation is denoted as (α, β) transformation, while the cell subdivision technique considers the position of the source point, the shape of the integration cell and the relations between the size of the cell and the time step. With the cell subdivision technique, more Gaussian points are shifted towards the source point, thus more accurate results can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.