稀薄流非线性模型方程离散速度坐标法有限差分解  

Finite difference solution of nonlinear model equations for rarified gas using discrete velocity ordinate method

作　　者：王强[1] 程晓丽[1] 庄逢甘[2] 

机构地区：[1]航天空气动力技术研究院,北京100074 [2]北京航空航天大学流体力学研究所,北京100083

出　　处：《计算力学学报》2006年第2期235-241,共7页Chinese Journal of Computational Mechanics

基　　金：国防预研基金(99J13.3.3HT7104);航天创新基金(20HTZ0602)资助项目

摘　　要：从一般非线性Bo ltzm ann方程出发,发展并实现了一套适于大范围K nudsen数稀薄流问题数值模拟的统一算法。采用BGK模型和Shakov模型近似碰撞项,进而引入两个二速度无量纲简化分布函数,通过关于分子速度第三分量取矩积分,将三速度单一模型方程变换为二速度微分方程组。基于G auss-H erm ite积分公式和正交多项式G auss积分公式,借助离散速度坐标法消除简化模型方程对分子速度空间的连续依赖性,从相空间到物理空间得到一组带源项双曲守恒离散方程,并给出其显式和隐式二阶迎风TVD有限差分解。以二维圆柱A r气体超声速绕流算例,验证了数值算法的有效性,比较分析了漫反射和镜面反射两种气体分子壁面反射模型的计算结果。Considering the general nonlinear Boltzmann eq to simulate rarified flows at a wide Knudsen numbe approximated by BGK model and Shakov distribution functions are introduced. The si velocity differential equation system throug model, and uation,a uniform algorithm has been developed r range numerically. The collision term is two bi-velocity non-dimensionalized reduced ngle tri-velocity model equation is transformed into a bi- h integrating weightedly the non-dimensionalized model equation about the third component of molecule velocity. The discrete velocity ordinate method associated with Gauss-Hermite quadrature and orthogonal polynomial quadrature is used to eliminate dependency of the reduced model equations on continuous molecule velocity space, then a set of hyperbolic conservative discrete equations with source terms are obtained from phase space to physical space,and a finite difference method related to a second-order upwind TVD scheme is selected to solve them both explicitly and implicitly. A two- dimensional supersonic Ar-gas flow around a cylinder is computed to show the effectivity of algorithm. Moreover,numerical results of two wall reflection models of gas molecules, namely diffuse reflection model and specular reflection model, are compared and analyzed.

关 键 词：稀薄流 BOLTZMANN方程 离散坐标法 数值积分 有限差分 

分 类 号：V211.25[航空宇航科学与技术—航空宇航推进理论与工程]