基于修正N-S方程本构关系的气体动理论耦合方法

随着稀薄程度的增加,Navier-Stokes方程的线性本构关系难以正确描述稀薄气体输运特性,高阶非线性本构关系往往数学形式极为复杂,对数值求解造成稳定性差等问题。为了发展适宜于近空间飞行器气动特性分析的高超声速稀薄流动模拟方法,本文利用求解Boltzmann模型方程的气体动理论统一算法(Gas Kineitc Unified Algorithm,GKUA)对应力张量、热流等宏观量数值积分求解的优势,提出了一种基于数值修正N-S方程本构关系的气体动理论耦合方法。通过将GKUA获得的应力张量及热流用于修正N-S方程的本构关系,实现了存在局部稀薄效应的流动模拟,并且通过可压缩平板边界层、圆柱绕流问题的数值模拟,验证了方法的有效性。

Kinetic hybrid method based on correction of N-S constitutive relation

As rarefaction effect becomes stronger for flight vehicles in the near space,the linear constitutive relation in the Navier-Stokes equations is not able to describe the transportation process of rarefied gas properly,while the high-order nonlinear constitutive relation is too complicated in its mathematical form,which can cause troubles,such as instability,for finding the numerical solutions.To tackle this issue,a kinetic hybrid method based on the correction of the linear constitutive relation has been proposed in the present study.In this method,the stress tensor and heat flux obtained from the Gas Kinetic Unified Algorithm(GKUA)are used to correct the linear constitutive relation of the Navier-Stokes equations such that it is capable to simulation flows with local rarefaction effects.The new method is validated by two testing cases,i.e.,rarefied flows on a compressible flatplate boundary layer and around a circular cylinder,respectively.