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## I. INTRODUCTION 

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A leftmoving piston, impacting a fluid with velocity − u$_{p}$ , generates a leftmoving shock- wave with velocity − u$_{s}$ . Throughout this paper we analyze such a shockwave from the viewpoint of a coordinate system moving leftward, so as to keep pace with the shock. See Figures 1 and 2. In this special uniformly-translating coordinate frame the shockwave is stationary, simplifying theoretical analyses. One-dimensional stationary shockwaves 1–14 provide a useful computational laboratory for the study of stationary far-from-equilibrium states. In such a shockwave a cold fluid is converted irreversibly to a hot one. As the fluid moves from left to right, in the shock-centered coordinate frame of the Figures, at speed u ( x ), the x coordinate increases; typically, the corresponding density, the longitudinal component of the pressure tensor, and the energy all increase too, in just such a way that the spatial structure of the wave is stationary: 

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