Classical Navier–Stokes equations fail to predict shock wave profiles accurately. In this paper, the Navier–Stokes system is fully transformed using a velocity variable transformation. The transformed equations termed the recast Navier–Stokes equations display physics not initially included in the classical form of the equations. We then analyze the stationary shock structure problem in a monatomic gas by solving both the classical and the recast Navier–Stokes equations numerically using a finite difference global solution (FDGS) scheme. The numerical results are presented for different upstream Mach numbers ranging from supersonic to hypersonic flows. We found that the recast Navier–Stokes equations show better agreement with the experimentally measured density and reciprocal shock thickness profiles.

中文翻译：

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使用 Navier-Stokes 方程重新解释冲击波结构预测

经典 Navier-Stokes 方程无法准确预测冲击波剖面。在本文中，Navier-Stokes 系统使用速度变量变换进行了完全变换。转换后的方程称为重铸 Navier-Stokes 方程，显示了最初未包含在方程经典形式中的物理。然后，我们通过使用有限差分全局解 (FDGS) 方案以数值方式求解经典和重铸 Navier-Stokes 方程来分析单原子气体中的稳态激波结构问题。给出了从超音速到高超音速流动的不同上游马赫数的数值结果。我们发现重铸的 Navier-Stokes 方程与实验测量的密度和倒数冲击厚度剖面显示出更好的一致性。