A new approach to solve multi-medium nonlinear transient heat conduction problems using interface integration BEM

Abstract

In order to solve multi-medium nonlinear transient heat conduction problems, based on interface integration boundary element method, a new approach, which can convert the multi-domain integrals to the boundary integrals with high precision, is firstly proposed in this paper. The boundary element method with the internal and exterior source is used to establish the interface integral equation of the multi-medium heat conduction problems, and then there are some new multi-domain integrals that should be converted to the boundary integrals. However, different from the domain integral in the single medium problems, the conventional transformation technique cannot be directly applied to convert multi-domain integrals. To maintain the advantage of only boundary discretization for the BEM and take the discontinuity of integrands in multi-domain integrals into consideration, a uniformly continuous function over additional topology domains is defined. Therefore, an improved method is presented to transform the multi-domain integrals to the boundary and interface integrals based on the conventional radial integration method (RIM). What's more, the idea of the proposed approach can theoretically prove the correctness of applying RIM to the complex models with multi-connected domain, which has been only confirmed from some numerical examples. Finally, two numerical examples of multi-medium nonlinear heat conduction problems are shown to demonstrate the correctness and feasibility of the new proposed method.