Salam Adel Al-Bayati and Luiz C. Wrobel
The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one…
Abstract
Purpose
The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction.
Design/methodology/approach
The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence.
Findings
The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency.
Originality/value
Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.
Details
Keywords
Paul W. Partridge and Luiz C. Wrobel
The purpose of this paper is to present an inverse analysis procedure based on a coupled numerical formulation through which the coefficients describing non‐linear thermal…
Abstract
Purpose
The purpose of this paper is to present an inverse analysis procedure based on a coupled numerical formulation through which the coefficients describing non‐linear thermal properties of blood perfusion may be identified.
Design/methodology/approach
The coupled numerical technique involves a combination of the dual reciprocity boundary element method (DRBEM) and a genetic algorithm (GA) for the solution of the Pennes bioheat equation. Both linear and quadratic temperature‐dependent variations are considered for the blood perfusion.
Findings
The proposed DRBEM formulation requires no internal discretisation and, in this case, no internal nodes either, apart from those defining the interface tissue/tumour. It is seen that the skin temperature variation changes as the blood perfusion increases, and in certain cases flat or nearly flat curves are produced. The proposed algorithm has difficulty to identify the perfusion parameters in these cases, although a more advanced genetic algorithm may provide improved results.
Practical implications
The coupled technique allows accurate inverse solutions of the Pennes bioheat equation for quantitative diagnostics on the physiological conditions of biological bodies and for optimisation of hyperthermia for cancer therapy.
Originality/value
The proposed technique can be used to guide hyperthermia cancer treatment, which normally involves heating tissue to 42‐43°C. When heated up to this range of temperatures, the blood flow in normal tissues, e.g. skin and muscle, increases significantly, while blood flow in the tumour zone decreases. Therefore, the consideration of temperature‐dependent blood perfusion in this case is not only essential for the correct modelling of the problem, but also should provide larger skin temperature variations, making the identification problem easier.
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Iwona Nowak, Andrzej J. Nowak and Luiz C. Wrobel
This paper discusses an algorithm for phase change front identification in continuous casting. The problem is formulated as an inverse geometry problem, and the solution procedure…
Abstract
This paper discusses an algorithm for phase change front identification in continuous casting. The problem is formulated as an inverse geometry problem, and the solution procedure utilizes temperature measurements inside the solid phase and sensitivity coefficients. The proposed algorithms make use of the boundary element method, with cubic boundary elements and Bezier splines employed for modelling the interface between the solid and liquid phases. A case study of continuous casting of copper is solved to demonstrate the main features of the proposed algorithms.
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Nelson F.F. Ebecken, Edison C.P. de Lima, Luiz Landau, Lauro H.M. Chueiri and Adilson C. Benjamin
The applicability of a non‐linear finite element method for the determination of the static strength of tubular joints is examined. In order to establish static strength…
Abstract
The applicability of a non‐linear finite element method for the determination of the static strength of tubular joints is examined. In order to establish static strength, non‐linear elasto‐plastic models are implemented. Techniques for automatically generating finite element meshes in stress analysis of tubular intersections are used. The analysis is carried out on a typical X‐joint under axial brace loads and the model represents only one‐eighth of the joint. The results are obtained by two different element procedures: three node flat shell element (Ilyushin yield criterion); eight node isoparametric shell element (von Mises yield criterion). The objective of this work is to discuss the modelling and computational aspects which are required for dealing with this elasto‐plastic analysis and to determine the necessary degree of refinement in order to obtain reliably the loads at which ultimate failure occurs.