Temperature maxima in stable two-dimensional shock waves

Abstract

We use molecular dynamics to study the structure of moderately strong shock waves in dense twodimensional fluids, using Lucy's pair potential. The stationary profiles show relatively broad temperature maxima, for both the longitudinal and the average kinetic temperatures, just as does Mott-Smith's model for strong shock waves in dilute three-dimensional gases. ͓S1063-651X͑97͒01507-9͔

Beyond the Navier–Stokes equations: Burnett hydrodynamics

“…It is very likely that these instabilities have the same origin as in the dilute regime from the complete set of equations, but since this work is outside the dilute regime we will not comment on it any further. However, notice should be made about the results from molecular dynamics for shock waves in dense fluids and in particular to the work done recently [173] that apparently exhibits a contradiction with Fourier's Law. Furthermore, for dense fluids evidence for divergent Burnett coefficients has been provided [174,175].…”

Maxwell and Cattaneo’s Time-Delay Ideas Applied to Shockwaves and the Rayleigh-Bénard Problem

“…Second, as is also shown in Figure 2, the shear stress (P yy − P xx )/2 and the heat flux Q x both lag behind the velocity gradient (dv x /dx) and the temperature gradients (dT xx /dx) and (dT yy /dx), suggesting the presence of Maxwell-type relaxation times [12,15]. Third, the fact that temperature is so very anisotropic makes it necessary to consider separate xx and yy contributions to the heat flux [8][9][10][11][12][13][14][15]:…”

“…Molecular dynamics shockwave simulations [6][7][8][9][10][11][12][13][14][15] have been carried out in the two different ways shown in Figure 1: (1) by following the two moving waves generated by the inelastic collision of two blocks of material; (2) by studying the single stationary wave formed with two boundary "treadmills" -on the left boundary cold fluid is introduced at the "shock speed" v s while at the right boundary hot fluid is extracted at the slower speed v s − v p , where v p is the "particle speed". In either case, in a coordinate frame centered on the shockwave the mass, momentum, and energy fluxes are all constant:…”

“…For "weak" shocks the Navier-Stokes-Fourier description is "good" [16]. For "stronger" shocks (twofold compression) several contradictions to this simple description arise [8][9][10][11][12][13][14][15]. To illustrate these points typical mechanical and thermal shockwave profiles are shown in Figure 2.…”

Higher moments of the velocity distribution function in dense-gas shocks

“…100, 000 nitrogen molecules are randomly distributed within the fluid portion of the domain and given random initial velocities and rotation rates drawn from a Maxwell-Boltzmann distribution. The rigid nitrogen molecule is modeled by a two-center Lennard-Jones (6,12) potential with σ LJ = 3.318 Å, ǫ LJ /k B = 35.6 K, and a bond length of 1.098 Å between the two Lennard-Jones centers. Each atom has a mass of 14 amu.…”