This work outlines and applies a new simulation method for the efficient study of shock wave fronts. This novel approach achieves a significantly improved efficiency in the generation of individual steady-state shock front states, and allows for the study of shocks as a function of a continuous shock strength parameter, vp. This is, to our knowledge, the first attempt to map the continuous Hugoniot curve.; The Continuous Hugoniot Method is applied to shock single-crystal Lennard-Jonesium along the 100> direction. Excellent agreement is found with both the published Lennard-Jones Hugoniot, and results of traditional shock simulation methods presented in this work.; The method is further applied to study the shock melt of single-crystal beta-tin along the 100> direction, using the Modified Embedded Atom Method (MEAM). Our continuum of Sn shock state results shows good agreement, within 6%, with the individual shock data points provided by experiment and agree perfectly with traditional shock simulation methods. Temperature profiles, density profiles, and melt length scales are determined as a function of shock strength.
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