Going beyond an old shockwave conjecture for improving upon Navier-Stokes.

Nonequilibrium molecular dynamics (NEMD) computer simulations of steady shockwaves in dense fluids and rarefied gases produce detailed shockwave profiles of mechanical and thermal properties. The Boltzmann equation, under the assumption of local thermodynamic equilibrium (LTE), leads to the first-order (linear) continuum theory of hydrodynamic flow: Navier-Stokes-Fourier (NSF). (Expansion of the LTE Boltzmann equation in higher powers of gradients yields so-called Burnett second-order terms, etc.

Mesodynamics with implicit degrees of freedom.

Mesoscale phenomena--involving a level of description between the finest atomistic scale and the macroscopic continuum--can be studied by a variation on the usual atomistic-level molecular dynamics (MD) simulation technique. In mesodynamics, the mass points, rather than being atoms, are mesoscopic in size, for instance, representing the centers of mass of polycrystalline grains or molecules. In order to reproduce many of the overall features of fully atomistic MD, which is inherently more expensive, the equations of motion in mesodynamics must be derivable from an interaction potential that is faithful to the compressive equation of state, as well as to tensile de-cohesion that occurs along the boundaries of the mesoscale units.

Burnett-Cattaneo continuum theory for shock waves.

We model strong shock-wave propagation, both in the ideal gas and in the dense Lennard-Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic-temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by a rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shock-wave solution of linear Navier-Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with nonequilibrium molecular-dynamics simulations under strong shock-wave conditions, using relaxation parameters obtained from the reference solution.

Heat-flow equation motivated by the ideal-gas shock wave.

We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front.

Test of a new heat-flow equation for dense-fluid shock waves.

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions.