A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory

Abstract

It is well known that the boundary element method (BEM) is capable of converting a boundary- value equation into its discrete analog by a judicious application of the Green’s identity and complementary equation. However, for many challenging problems, the fundamental solution is either not available in a cheaply computable form or does not exist at all. Even when the fundamental solution does exist, it appears in a form that is highly non-local which inadvertently leads to a sys-tem of equations with a fully populated matrix. In this paper, fundamental solution of an auxiliary form of a governing partial differential equation coupled with the Green identity is used to discretize and localize an integro-partial differential transport equation by conversion into a boundary-domain form amenable to a hybrid boundary integral numerical formulation. It is observed that the numerical technique applied herein is able to accurately represent numerical and closed form solutions available in literature.