Vincent M. Wheeler

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

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.

Ubiquitous Interactive Visualization of 3-D Mantle Convection through Web Applications Using Java

We have designed a new system for real-time interactive visualization of results taken directly from large-scale simulations of 3-D mantle convection and other large-scale simulations. This approach allows for intense visualization sessions for a couple of hours as opposed to storing massive amounts of data in a storage system. Our data sets consist of 3-D data for volume rendering with sets ranging as high as over 10 million unknowns at each timestep. Large scale visualization on a display wall holding around 13 million pixels has already been accomplished with extension to hand-held devices, such as the OQO and Nokia N800. We are developing web-based software in Java to extend the use of this system across long distances. The software is aimed at creating an interactive and functional application capable of running on multiple browsers by taking advantage of two AJAX-enabled web frameworks: Echo2 and Google Web Toolkit.

An overview of phonon-based heat conduction models and their solution

Purpose – The purpose of this paper is to provide an overview and some recent advances in the models, analysis and simulation of thermal transport of phonons as related to the field of microscale/macroscale heat conduction in solids. The efforts focus upon a fairly comprehensive overview of the subject matter from a unified standpoint highlighting the various approximations inherent in the thermal models. Subsequently, the numerical formulations and illustrations using the current state-of-the-art are provided. Design/methodology/approach – This paper is dedicated to the approximate solution to the relaxation time phonon Boltzmann equation (BE). While original contributions are pointed out and addressed appropriately, the efforts and contributions will be focussed on a relatively complete overview highlighting the field from one unified standpoint and clearly stating all assumptions that go into the approximations inherent to existing models. The contents will be divided as follows: In the first section t...