Notes on the structure of viscous and numerically-captured shocks

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Abstract
Summary: An exact expression for the flow variables through a viscous shock wave is obtained from the Navier-Stokes equations. The Prandtl number is taken to be ¾, which is close to the value for air, and the viscosity is assumed to be given by Sutherland's formula.By considering the limit as the viscosity tends to zero, it is shown that the solution to the Euler equations has an entropy spike at the shock wave. This explains certain, hitherto considered spurious, features of shock waves captured by numerical solutions of the Euler equations.

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