Name: José Antônio Ramiro Avelar
Type: MSc dissertation
Publication date: 15/04/2016
Advisor:

Namesort descending Role
Carlos Friedrich Loeffler Neto Advisor *

Examining board:

Namesort descending Role
Andre Bulcão External Examiner *
Carlos Friedrich Loeffler Neto Advisor *
Luciano de Oliveira Castro Lara Internal Examiner *

Summary: The research involved in this dissertation is based on the so-called DIBEM (Boundary
Element Method with Direct Interpolation) which directly interpolates the
inhomogeneous term of the government differential equation using the Boundary
Element Method (BEM). The DIBEM uses a primitive of the original interpolation
function in the kernel of the domain integral, allowing the latter processing a boundary
integral, similarly to that performed in the Dual Reciprocity, thus avoiding domain
discretization by cells
This new formulation has well succeeded in solving well known problems of great
interest and difficulty in engineering, such as the governed by the Poisson Equation
and the Helmholtz Equation. Following the natural scale of complexity, considering the
Generalized Scalar Field Equation as reference, the diffusive-advective problems
which evaluate the thermal effects of transport by a fluid (advection) together with
conduction are approached. This phenomenon is very common in engineering
problems such as: the formation of the boundary layer of a laminar fluid flow; the heat
transmission with the association between the spread in the continuous medium
(conduction) and transport by flow (advection). These problems continue to require
constant improvement in the implementation of numerical methods. Therefore, the
applicability and accuracy of DIBEM are tested for solving problems characterized by
unidirectional fluid flow on a control volume with different boundary conditions that are
governed by the diffusion-advection phenomenon. For this purpose, 42 different
meshes are generated to calculate both the flow and temperature as compared with
the respective analytical values.
KEYWORDS: Boundary Element Method, Radial Basis Function,
Equation diffusion and advection.

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