An efficient bem solution for three-dimensional transient heat conduction

• Published in: International journal of numerical methods for heat & fluid flow Vol. 5; no. 4; pp. 327 - 340
• Main Authors: Gupta, Anil, Sullivan, John M, Delgado, Hugo E
• Format: Journal Article
• Language: English
• Published: Bradford MCB UP Ltd 01.05.1995; Emerald Group Publishing Limited
• Subjects: Computational methods; Computer applications; Differential equations; Efficiency; Heat conduction; Heat transfer; Integral equations; Integrals; Integration; Mathematical functions; Mathematical models; Numerical methods; Pressure effects; Studies; Temperature; Thermal conductivity of solids; United States > US; Heat conduction; Transient; Boundary element; Series expansions
• ISSN: 0961-5539; 1758-6585
• DOI: 10.1108/EUM0000000004069

This paper presents a computationally efficient numerical solution scheme to solve transient heat conduction problems using the boundary element method (BEM) without volume discretization. Traditionally, a transient solution using BEM is very computer intensive due to the excessive numerical integration requirements at each time increment. In the present work a numerical solution scheme based on the separation of time and space integrals in the boundary integral equation through the use of an appropriate series expansion of the integrand (incomplete gamma function) is presented. The space integrals are evaluated only once in the beginning and within each time increment the additional integrals are obtained from the previously evaluated space integrals by a simple calculation. Three-dimensional applications are provided to compare the proposed strategy with that used traditionally. The CPU requirements are reduced substantially. The solution scheme presented allows for dynamically changing the time step size as the solution evolves. This feature is not practical in the traditional schemes based on boundary discretization only.