Modifications to the XBR-2D Heat Conduction Code

Abstract : A study was conducted to evaluate different methods to improve the execution speed of the XBR-2D heat conduction code. When run in burst fire mode, the original XBR-2D code could require up to 20 hours of CPU time on a Cray computer. Two numerical methods were studied as alternatives to the explicit finite difference techniques employed in Version 1 of the code: an implicit finite difference method and a boundary element method (BEM). The BEM appeared to offer a promising and elegant approach to the solution of the heat conduction problem. A detailed explanation of the BEM is contained in this report; however, it was not implemented at the time because of its complexity. The final solution inserted into the code was an improved explicit finite difference method. Under this mechanism the execution time was reduced by up to two-thirds. The speed increase was largely obtained through improvements in coding efficiency and the use of a variable time step based on the maximum temperature gradient in the system