Maxwell and Cattaneo's Time-Delay Ideas Applied to Shockwaves and the Rayleigh-Benard Problem

TL;DR

This paper applies Maxwell and Cattaneo's relaxation models to shockwaves and Rayleigh-Benard convection, showing good agreement with experiments for shockwaves and negligible effects on slower flows, with instability arising at large relaxation times.

Contribution

It demonstrates the application of Maxwell and Cattaneo relaxation approaches to shockwaves and convection, highlighting their effects and limitations in different flow regimes.

Findings

Good agreement with shockwave data for reasonable relaxation times

Instability occurs when viscous relaxation time is too large

Relaxation effects are negligible in slow subsonic flows

Abstract

We apply Maxwell and Cattaneo's relaxation approaches to the analysis of strong shockwaves in a two-dimensional viscous heat-conducting fluid. Good agreement results for reasonable values of Maxwell's relaxation times. Instability results if the viscous relaxation time is too large. These relaxation terms have negligible effects on slower-paced subsonic problems, as is shown here for two-roll and four-roll Rayleigh-Benard flows.