# Analysis of the Time Increment for the Diffusion Equation with Time-Varying Heat Source from the Boundary Element Method

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Roberto Pettres (2016). Analysis of the Time Increment for the Diffusion Equation with Time-Varying Heat Source from the Boundary Element Method. Mechanics, Materials Science & Engineering, Vol 7. doi:10.2412/mmse.8.968.954

Authors: Roberto Pettres

ABSTRACT. In this paper a Boundary Element Formulation for the one-dimensional transient heat flow problem is presented. The formulation employs a time-independent fundamental solution; consequently, a domain integral appears in the integral equations, which contains the potential time derivative and the time-dependent heat source term of the governing equation. Linear elements are used for the domain discretization. The time marching scheme is implemented with finite difference approximations. The performance of the formulation was assessed comparing the numerical results with an analytical solution. Convergence of the numerical results is evaluated with varying size time-increment during analysis.

Keywords: Boundary Element Method, diffusion equation, time increment, transient analyses

References

[1] Simmons , G. F. (1987). Calculus with Analytical Geometry – Vol. 2. McGraw Hill.

[2] Jacobs, D. (1979). The State of the Art in Numerical Analysis, Academic Press, New York, USA.

[3] Brebbia, C. A. (1978). The boundary element method for engineers. Pentech Press, London.

[4] Pettres, R.; Lacerda, L. A.; Carrer, J.A.M. (2015) A boundary element formulation for the heat equation with dissipative and heat generation terms. Engineering Analysis with Boundary Elements, vol. 51, Feb., pp 191-198, doi 10.1016/j.enganabound.2014.11.005

[5] Kreyszig, E. (2006). Advanced Engineering Mathematics 9th Edition. Wiley, Ohio.

[6] Greenberg, M. D. (1998). Advanced Engineering Mathematics (2nd Edition). Prentice-Hall, New Jersey.

[7] Application of Green’s Functions in Science and Engineering (1971).. Prentice-Hall, New Jersey.

[8] Vladimirov, V. S. (1979). Generalized Functions in Mathematical Physics. Nauka Publishers, Moscow.

[9] Curran, D. A. S., Cross, M. and Lewis, B. A. (1980). Solution of parabolic differential equations by the boundary element method using discretisation in time – Applied Mathematical Modelling, vol. 4, pp 398–400.

[10] Wrobel, L. C. (1981). Potential and Viscous Flow Problems Using the Boundary Element Method, U.K. Ph.D. Thesis, University of Southampton.

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