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.
Highlights
IntroductionThe governing equation for a convective-dispersive transport phenomenon is given by:
The governing equation for a convective-dispersive transport phenomenon is given by:∂c + ∇ ⋅(vc) − ∇ ⋅( D ⋅∇c) = Rin Ω × (0,T ] (1)dt where c is concentration; v is the flow velocity; D is the dispersive tensor; t is the time variable and Ris theHow to cite this paper: Onyejekwe, O.O. (2016) A Domain-Boundary Integral Treatment of Transient Scalar Transport with Memory
Numerical attempts to deal with this include that of Schanz and Antes [8]. They studied a boundary element method (BEM) viscoelastic formulation based on the so called convolution integral method proposed by Lubich [9] in 1988
Summary
The governing equation for a convective-dispersive transport phenomenon is given by:. Numerical attempts to deal with this include that of Schanz and Antes [8] They studied a BEM viscoelastic formulation based on the so called convolution integral method proposed by Lubich [9] in 1988. The hybrid boundary-integral-finite element procedure adopted employs the Green’s function of the Laplace operator, and retains the time marching feature of classical BEM, but its spatial discretization enlists a local support feature that is similar to that of the finite element This guarantees some attractive outcomes; it facilitates the hybridization process especially for schemes that are element or nodal based (Onyejekwe [10] [11]) and establishes a hybrid computational method which exploits the strengths of its composite parts.
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