-0.5 -0.3 -0.1 0.1 0.3 -3.5 < x < +3.5 T$_{xx > yy}$ Q v η = η = 1  0.0 0.5 1.0 1.5 2.0 2.5 xx > yy -3.5 < x < +3.5 P e ρ τ = 3, κ = 6 Figure 9: Solution of the generalized Navier-Stokes-Fourier equations with both heat and work contributing solely to T$_{xx}$ and with the heat flux Q = − κ ( ∇ T$_{xx}$ +7 ∇ T$_{yy}$ ) / 8. The shear viscosity, bulk viscosity, heat conductivity, and thermal relaxation times are respectively 1, 1, 6, and 3. Gr¨ uneisen’s γ is 0.3 and ck = 2 k . Gr¨ uneisen equations of state are useful components of a kinetic shockwave model. By apportioning the longitudinal and transverse thermal portions of the work, heat, and heat flux vector a variety of useful models can be developed and used to reproduce results from simulations. A forward-in-time fourth-order Runge-Kutta (as opposed to backward Euler) integration of the cell and nodal motion equations results in accurate and stable continuum dynamics. One of the recent observations from molecular dynamics is that the stress and heat flux lag somewhat behind the strainrate and the temperature gradient $^{12}$. It is desirable that models be generalized to reflect these lags. Some study of time-delayed differential equations is necessary to model this phenomenon. A significant goal is the extension of these same ideas to the fluctuating stress and heat flows of two and three dimensional fluids. A comparison of results from molecular dynam- ics with those from two and three-dimensional two-temperature continuum simulations should provide useful tools for describing fluctuations within the overall one-dimensional flows. These results show that even far-from-equilibrium shocks can be treated in a semi- quantitative way by relating the tensor parts of the energy flows to one another in a relatively simple way. An intriguing result of some model calculations is the stable rever- sal of the direction of the heat flux vector. Though this reversal seems unphysical, there is no difficulty in obtaining stable numerical profiles which include flux reversal.