Isogeometric boundary element for analyzing steady-state heat conduction problems under spatially varying conductivity and internal heat source

Abstract

This paper proposes an isogeometric boundary element (IGABEM) with the aim to solve the 2D steady-state heat conduction problems under spatially varying conductivity and internal heat source. The IGABEM boundary-domain integral equation is derived underlying the divergence theorem of Gauss and the Laplace equation. The non-uniform rational B-spline (NURBS) basis used in the CAD/CAE industries is applied to approximate both the boundary of problem domain and the unknown physical quantities, and the radial integration method (RIM) is employed to deal with the domain integrals induced by the non-homogeneous thermal conductivity and the internal heat source. The present boundary-domain integral equation is firstly divided into several NURBS patches, upon which the IGABEM can be further defined. The main advantage of the NURBS basis in comparison with the standard piecewise polynomial basis is that there is almost no error in the boundary approximation with IGABEM, which plays a significant role in controlling the accuracy of numerical calculation. Four numerical examples consisting of square regions with cubic and exponential thermal conductivities (with or without internal heat source), annulus region with constant and quadratic conductivities as well as complex region with varying thermal conductivity and complex heat source are provided. The accuracy and convergence of the proposed method are assessed by comparing the present solution with the existing results obtained by several other researchers or ANSYS results, and excellent performance is achieved.