论粘性激波层理论的理论基础及其进一步发展

本文将Davis的量级分析方法改用匹配渐近展开方法,作为一级近似推导出了高超音速化学反应粘性激波层方程。证明了粘性激波层方程是NS方程在匹配渐近意义上的一级近似方程。进一步讨论了这一方程的基本假设条件。本文首次推导出的二级近似方程,是对Davis粘性激波层方程的修正。这种修正可以提高数值解的精度,有助于对问题获得更全面的了解,对进一步发展与完善高超音速钝头体绕流问题的数值求解方法起一定的作用。

ON THE THEORETICAL BASE OF VISCOUS SHOCK LAYER EQUATIONS AND THE FURTHER DEVELOPMENTS

In the present paper, the method of matched asymptotic expansions is introduced to the Davis' viscous shock layer theory, and the result of the first order of approximation leads to the same hypersonic chemically reacting viscous shock layer equations as with the Davis' method. Although the resulting equations are the same, the fundamental assumptions of the latter method is more restricteived. The result of the second order approximation given for me first time in the present paper leads to a theoretical modification to Davis' viscous shock layer theory and it is also a method to enhance the numerical solution precision. It is expected that this modification could play a certain role in the development of the numerical solution method to the hypersonic viscous flow problems over blunted bodies and could help us understand the details of some flow problems.