AN EFFECTIVE BOUNDARY INTEGRAL APPROACH FOR THE SOLUTION OF NONLINEAR TRANSIENT THERMAL DIFFUSION PROBLEMS

Abstract

Numerical calculations of nonlinear transient thermal diffusion problems have been carried out with a modified 'simple' boundary integral formulation known as the Green element method (GEM).  The theory of the formulation is based on the singular integral equation of the boundary element method (BEM) but its implementation is element-by-element like the ¯nite element method (FEM).  Domain integrals resulting from nonlinearity of the problems as well as those arising from the approximation of the time derivative are encountered but unlike the classical approach, they are resolved within the element domain.  Comparisons of GEM results with those obtained analytically or from the finite difference Newton-Richtmeyer's and the finite element method (FEM) serve to confirm the usefulness of the proposed formulation in handling nonlinearity in an unambiguous, straightforward and elegant manner without transforming or complicating the governing equations.