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Navier–Stokes Equations01:28

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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Going beyond an old shockwave conjecture for improving upon Navier-Stokes.

Brad Lee Holian1, Michel Mareschal2, Ramon Ravelo1,3

  • 1Theoretical Division, <a href="https://ror.org/01e41cf67">Los Alamos National Laboratory</a>, Los Alamos, New Mexico 87545, USA.

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Summary

This study enhances continuum theories for shockwaves by incorporating Burnett nonlinearity and non-equilibrium Maxwell relaxation. This approach accurately models nonequilibrium molecular dynamics simulations across various shock strengths and fluid types.

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Area of Science:

  • Computational Physics
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • Continuum theories like Navier-Stokes-Fourier (NSF) struggle to model strong shockwaves due to limitations in local thermodynamic equilibrium (LTE).
  • Nonequilibrium molecular dynamics (NEMD) simulations reveal detailed shockwave profiles that deviate from NSF predictions, especially under high gradients.

Purpose of the Study:

  • To develop a more accurate continuum theory for shockwave profiles by incorporating Burnett nonlinearity and non-equilibrium effects.
  • To improve the modeling of both weak and strong shockwaves in dense fluids and rarefied gases.

Main Methods:

  • Incorporating Burnett nonlinearity into an LTE continuum theory.
  • Applying Maxwell relaxation directly to hydrodynamic variables, moving beyond gradient-based relaxation.
  • Comparing theoretical predictions with NEMD simulation data for shockwave profiles.

Main Results:

  • The enhanced continuum theory with Burnett nonlinearity successfully reproduces the initial shock rise and slope observed in NEMD simulations for both weak and strong shocks.
  • Holian's conjecture, while including Burnett nonlinearity, fails to capture the post-shock relaxation dynamics.
  • Non-LTE Maxwell relaxation applied to hydrodynamic variables is essential for accurately modeling the entire shockwave profile, particularly the slow return to equilibrium.

Conclusions:

  • Burnett nonlinearity is crucial for accurately describing the shock front in continuum theories.
  • Standard LTE continuum theories, including Holian's conjecture, are insufficient for modeling the complete shockwave relaxation process.
  • Non-equilibrium Maxwell relaxation is the key to achieving full agreement between continuum theory and NEMD simulations of shockwaves.