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Macroscopic models which distinguish the longitudinal and transversetemperatures can provide improved descriptions of the microscopic shockstructures as revealed by molecular dynamics simulations. Additionally, we caninclude three relaxation times in the models, two based on Maxwell'sviscoelasticity and its Cattaneo-equation analog for heat flow, and a thirdthermal, based on the Krook-Boltzmann equation. This approach can replicate theobserved lags of stress (which lags behind the strain rate) and heat flux(which lags behind the temperature gradient), as well as the eventualequilibration of the two temperatures. For profile stability the time lagscannot be too large. By partitioning the longitudinal and transversecontributions of work and heat and including a tensor heat conductivity andbulk viscosity, all the qualitative microscopic features of strong simple-fluidshockwave structures can be reproduced.

Flexible Macroscopic Models for Dense-Fluid Shockwaves: Partitioning  Heat and Work; Delaying Stress and Heat Flux; Two-Temperature Thermal  Relaxation