An Efficient Scheme Using Fourier Series for the Boundary Element Solution of Heat Transfer Problems
Maria Teresa Ibanez a Lecturer of Mathematics at the School of Engineering of the Central University of Venezuela has recently passed a PhD Viva at Wessex Institute of Technology. The title of her thesis was "An Efficient Scheme Using Fourier Series for the Boundary Element Solution of Heat Transfer Problems". The external examiner was professor Mark Cross, Pro-Vice-Chancellor for Research at Greenwich University, and renown for his work on Applied Mathematical Modelling. The internal examiner was Dr Youssef Rashed, Head of the Damage Mechanics Division at WIT.
Maria was complimented by the examiners for the quality of her work, and for the excellent presentation she gave. The main objective of her research was to develop an efficient BEM scheme for the numerical solution of heat transfer problems. The scheme developed was of a reinitialisation type in which the domain integrals are computed by a recursive relation, which depends on only the boundary temperature and the flux at the previous time steps.
The proposed reinitialisation approach was based on a Green function corresponding to zero temperature in a box containing the original domain, instead of using the classical free space fundamental solutions. The Green function given in terms of the original fundamental solution plus a regular solution of the heat equation inside the domain under consideration. The Green function can be obtained by the images method, and the resulting source series can also be re-written in terms of a double Fourier series, that is used to transform the domain integrals into equivalent surface integrals.
Maria implemented the proposed numerical scheme for the solution of several heat transfer problems, comparing results with analytical and other numerical solutions.
Maria was one of the many students who graduated at WIT under the terms of the link agreement between the Institute and the Central University of Venezuela. Her stay was initially supported, in part, by a major research project with the DTI (Department of Trade and Industry) and afterwards by the Alpha scheme of the E.U..