TITLE:
A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory
AUTHORS:
Okey Oseloka Onyejekwe
KEYWORDS:
Boundary Element Method, Green’s Identity, Complementary Equation, Fundamental Solution, Hybrid Formulation, Integro-Differential Transport Equation
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.11,
July
12,
2016
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.