  Macroscopic models which distinguish the longitudinal and transverse
temperatures can provide improved descriptions of the microscopic shock
structures as revealed by molecular dynamics simulations. Additionally, we can
include three relaxation times in the models, two based on Maxwell's
viscoelasticity and its Cattaneo-equation analog for heat flow, and a third
thermal, based on the Krook-Boltzmann equation. This approach can replicate the
observed lags of stress (which lags behind the strain rate) and heat flux
(which lags behind the temperature gradient), as well as the eventual
equilibration of the two temperatures. For profile stability the time lags
cannot be too large. By partitioning the longitudinal and transverse
contributions of work and heat and including a tensor heat conductivity and
bulk viscosity, all the qualitative microscopic features of strong simple-fluid
shockwave structures can be reproduced.
