shock waves的结构，作为Brenner对纳维-斯托克斯方程修正的检验
The structure of shock waves as a test of Brenner's modifications to the Navier-Stokes equations
摘要：
布伦纳最近提出了对纳维-斯托克斯方程的修正，这些修正基于理论论证，但仅得到范围相当有限的实验的支持。这些修改涉及流体体积的扩散，这对于具有高密度梯度的流动是重要的。因此，气体中激波的粘性结构应该为这个新模型提供一个很好的测试案例。在本文中，我们详细的冲击结构的问题，并提出指数的气体粘度-温度关系的基础上的经验粘度数据是独立的冲击实验。然后，我们用纳维-斯托克斯方程模拟马赫数1.0-12.0范围内的激波，有和没有Brenner修正。初步模拟表明，布伦纳的修改显示非物理行为时，体积扩散系数超过运动粘度。我们随后的分析归因于这两个行为的不稳定性的时间扰动和一个虚假的相速度-频率关系。然而，在将体积扩散率等同于运动粘度时，我们发现Brenner修正的结果明显优于标准纳维-斯托克斯方程的结果，并且与包括Burnett方程的扩展流体动力学模型家族的结果大致相似。Brenner的修正只在纳维-斯托克斯方程中增加了两项，数值实现比传统的扩展流体动力学模型简单得多，特别是在边界条件方面。我们建议对一些不同的基准非平衡流情况进行进一步的调查和测试。
英文摘要：
Brenner has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume that would be significant for flows with high density gradients. So the viscous structure of shock waves in gases should provide an excellent test case for this new model. In this paper we detail the shock structure problem and propose exponents for the gas viscosity-temperature relation based on empirical viscosity data that is independent of shock experiments. We then simulate shocks in the range Mach 1.0-12.0 using the Navier-Stokes equations, both with and without Brenner's modifications. Initial simulations showed Brenner's modifications display unphysical behaviour when the coefficient of volume diffusion exceeds the kinematic viscosity. Our subsequent analyses attribute this behaviour to both an instability to temporal disturbances and a spurious phase velocity-frequency relationship. On equating the volume diffusivity to the kinematic viscosity, however, we find the results with Brenner's modifications are significantly better than those of the standard Navier-Stokes equations, and broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. Brenner's modifications add only two terms to the Navier-Stokes equations, and the numerical implementation is much simpler than conventional extended hydrodynamic models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases.
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