A direct boundary element approach for unsteady non-linear heat transfer problems

Abstract

Unsteady non-linear problems are usually solved based on the time marching scheme together with iterative methods. In this paper, we employed an example to illustrate a new direct boundary element technique, which can provide accurate solutions of unsteady non-linear problems without the need for iterations. The principle and validity of the technique is demonstrated by considering an unsteady non-linear hyperbolic heat transfer problem, together with a fully implicit difference scheme in the time domain. It illustrates that the proposed non-iterative boundary element approach is numerically rather efficient for unsteady non-linear problems. Thus, it provides an alternative to traditional iterative methods for unsteady non-linear problems.