On the Applicability of an Isochronous Integration Framework for Parabolic/Hyperbolic Heat Conduction Type Problems

Abstract

We demonstrate the applicability of a new isochronous integration (iIntegration) computational framework for the analysis of transient first/second-order systems via the new generalized single step single solve (GS4) family of algorithms, capable of simultaneously being applied to first- and second-order systems in time while providing attractive numerical and order-preserving attributes to capture the problem physics. To illustrate, we consider a recently developed model of heat conduction that was proposed to govern thermal transport from nano- to macro-scales, and is known in the literature as the C- and F-processes heat conduction model. This model inherits unique features and can represent either first- or second-order parabolic/hyperbolic heat conduction governing equations. A derivation of the model is first summarized, followed by the numerical discretization procedure and illustrative examples demonstrating the practicality and convenience of the new unified approach for modeling and analysis.

Notes

¹The development of an “Algorithms by Design”-based family of explicit schemes is currently underway.

²Note, that because of this assignment, {θ} no longer participates in the solution.

³Note, that these situations are often simulated using models that account for these small time scales, such as the hyperbolic heat equation considered in section 5.1, or a two-temperature model [36].