A Laplace Transform Boundary Element Method Approach to the Solution of Large-Scale Transient Heat Conduction Problems
Heat conduction has been a topic in engineering design for countless years. Many engineering devices, such as turbine engines, operate for long hours at steady conditions, and as such require steady-state conduction analysis. There are however becoming a growing number of devices that have short operational lives in areas such as missile and rocket propulsion systems. Although this research will focus specifically on heat conduction, its ideas can be applied to areas such as stress and acoustics, where transient calculations are also of great importance.
It is the objective of this thesis to develop and implement an efficient algorithm to solve large-scale, time dependent heat conduction problems using a Laplace transform boundary element method. In order to accomplish this task, an iterative, parallel, domain decomposition scheme is used to significantly reduce the computational and storage requirements typically encountered in large-scale problems. The decomposed subdomains are distributed through the nodes of a statically balanced computer cluster, where each transient heat conduction problem is solved independently for the specified time value. The independent solutions are merged at the artificially created interfaces using an iteration method which averages temperatures, resolves the problem, and averages flux magnitudes to ensure continuity at each iteration level. Accurate results are reported for several cases in regular and irregular geometries, with varying boundary conditions.
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Bachelor of Science (B.S.)
College of Engineering and Computer Science
Dissertations, Academic -- Engineering; Engineering -- Dissertations, Academic; Boundary element methods; Heat -- Conduction; Laplace transformation
Length of Campus-only Access
Honors in the Major Thesis
Erhart, Kevin, "A Laplace Transform Boundary Element Method Approach to the Solution of Large-Scale Transient Heat Conduction Problems" (2004). HIM 1990-2015. 378.