Boundary element formulation using relative quantity for unsteady heat conduction problem

Abstract

It has been found that the boundary integral equations for the field functions in the steady problems such as potential and displacement can be regularized by introduction of their relative quantities. This report describes that the same techniques are also applicable to the unsteady problems for regularization of the integral equations. Integral equations with relative quantity for potential are obtained by superposing a particular solution under the condition of time-independent uniform potential upon the usual integral equations. These new equations give accurate numerical results at any points in the whole domain. In addition, since the integral equations for boundary and inside become continuous, the integral equation for boundary temperature gradient, which is absent hitherto in the usual formulations, has been readily obtained. Through two- and three-dimensional examples, the present integral equations are verified to be valid and useful.