Capturing and modeling shock wave profiles has a long history in computational analysis. Often artificial irreversibilities and/or smearing schemes are implemented in order to stabilize and resolve shock structures in large-scale simulations. This work presents a direct numeric simulation of the one-dimensional Navier-Stokes equations resolved without the use of artificial viscosity or shock smearing techniques. Initial simulations are compared to a perfect gas analytic solution to validate the technique, then several viscosity models are employed to study the role of temperature and pressure dependent viscosity models. The argon gas results indicated that the shock front thickness and entropy production are in good agreement with the analytic solution and experimental results. The liquid water results utilizing a Mie-Gruneisen equation of state do not compare as favorably.