Shock waves are of great interest in many fields of science and engineering, but the mechanisms of their formation, maintenance and dissipation are still not well understood. While all transport processes existing in a shock wave contribute to its compression and irreversibility, they are not of equal importance. To figure out the roles of viscosity and heat conduction in shock transition, the existence of smooth shock solutions and the counter-intuitive entropy overshoot phenomenon (the specific entropy is not monotonically increasing and exhibits a peak inside the shock front) are theoretically and numerically investigated, with emphasis on the effects of viscosity and heat conduction. Instead of higher-order hydrodynamics, the Navier–Stokes formalism is employed for its stability and simplicity. Supplemented with nonlinear thermodynamically consistent constitutive relations, the Navier–Stokes equations are adequate to demonstrate the general nature of shock profiles. It is found that heat conduction cannot sustain strong shocks without the presence of viscosity, while viscosity can maintain smooth shock transition at all strengths, regardless of heat conduction. Hence, the critical role in shock compression is played by viscosity rather than heat conduction. Nevertheless, the dispensability of heat conduction would not compromise its essential role in the emergence of an entropy peak. It is the entropy flux resulting from heat conduction that neutralises the positive entropy production and thus prevents the decreasing entropy from violating the second law of thermodynamics. This mechanism of entropy overshoot has not been addressed previously in the literature and is revealed using the entropy balance equation.

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粘性和热传导在冲击波中的作用的综合研究

冲击波在科学和工程的许多领域引起了极大的兴趣，但其形成、维持和消散的机制仍不清楚。虽然冲击波中存在的所有传输过程都有助于其压缩和不可逆性，但它们的重要性并不相同。为了弄清楚粘性和热传导在激波转变中的作用，从理论上和数值上研究了光滑激波解的存在性和反直觉的熵超调现象（比熵不是单调增加的，并且在激波前沿内呈现峰值） ，重点是粘度和热传导的影响。纳维-斯托克斯形式主义因其稳定性和简单性而被采用，而不是高阶流体动力学。辅以非线性热力学一致的本构关系，纳维-斯托克斯方程足以证明冲击曲线的一般性质。研究发现，如果没有粘度，热传导就无法承受强烈的冲击，而无论热传导如何，粘度都可以在所有强度下保持平稳的冲击过渡。因此，冲击压缩中的关键作用是由粘度而不是热传导发挥的。然而，热传导的可有可无并不会损害其在熵峰出现中的重要作用。热传导产生的熵通量中和了正熵的产生，从而防止熵减少违反热力学第二定律。这种熵超调的机制在之前的文献中尚未得到解决，而是使用熵平衡方程来揭示的。