GS4-1 Computational Framework for Heat Transfer Problems: Part 1—Linear Cases with Illustration to Thermal Shock Problem

Abstract

A computational framework of time integrators, termed GS4-1, is described for use in first-order transient heat transfer problems. The framework consists of a family of algorithms by design with desirable features including second-order accuracy, unconditional stability, and zero-order overshoot. Of noteworthy mention and significance is the fact that the present computational framework naturally inherits features that permit selective control of the high-frequency damping for the primary variable and its time derivative, respectively, which is a new feature not available in existing methods. Consequently, the developments enable physically representative and accurate solutions of both variables. We first present, in Part 1, the derivation of such a framework with application to linear heat transfer problems. The significance of the present developments in capturing the problem physics via the selective control feature is demonstrated through an application to a simple illustrative one-dimensional problem for which an analytic solution is available. The extension of the framework for nonlinear cases is presented in Part 2.

Acknowledgments

The authors are very pleased to acknowledge support and funding from Mighty River Power, New Zealand, under research contract number E5653. Acknowledgment is also due the Minnesota Supercomputer Institute (MSI), Minneapolis, Minnesota, for computer grants.