Well-Posed Two-Temperature Constitutive Equations for Stable Dense Fluid Shockwaves using Molecular Dynamics and Generalizations of Navier-Stokes-Fourier Continuum Mechanics

TL;DR

This paper develops a generalized two-temperature continuum model for dense fluid shockwaves, incorporating anisotropic temperatures guided by molecular dynamics, leading to stable and accurate shockwave profiles.

Contribution

It introduces a novel two-temperature continuum framework that captures anisotropic temperature effects in dense fluid shockwaves, validated against molecular dynamics simulations.

Findings

Profiles fit molecular dynamics results well

Model captures anisotropic temperature effects

Provides stable solutions for shockwave structures

Abstract

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.