一种求解抛物化Navier-Stokes方程的空间推进算法

陈兵 徐旭 蔡国飙

doi:10.6052/0459-1879-2008-2-2007-440

一种求解抛物化Navier-Stokes方程的空间推进算法

陈兵徐旭蔡国飙

北京航空航天大学宇航学院北京航空航天大学宇航学院北京航空航天大学宇航学院

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出版历程
- 收稿日期: 2007-09-11
- 修回日期: 2007-10-29
- 刊出日期: 2008-03-17

A space-marching algorithm for solving the parabolized Navier-Stokes equations

Bing Chen, Xu Xu, Guobiao Cai

School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, ChinaSchool of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, ChinaSchool of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

摘要

摘要: 讨论了抛物化NS方程(parabolized Navier-Stokesequations, PNS)的数学性质，对比分析多种处理流向压力梯度的方法的优缺点. 以此为基础，成功地将LU-SGS隐式时间积分方法推广到PNS方程的流向空间积分上，发展了基于PNS方程的有限体积单次扫描空间推进算法(single-sweep parabolized Navier-Stokesalgorithm, SSPNS). 在该算法中，横向无黏数值通量和黏性通量分别采用混合型迎风格式和中心格式求解. 用SSPNS算法计算了4个典型流场，包括超声速平板流、15$^\circ$楔板压缩高超声速流、带攻角的高超声速锥形流和侧压式高超声速进气道流动. SSPNS计算结果与NASA UPS程序数值结果、文献提供的实验数据及理论分析结果符合得很好.对比研究表明，SSPNS 法与传统时间迭代法相比，二者计算精度相当，而SSPNS计算速度快1~2个量级，存储量至少低1个量级.关键词抛物化NS方程；空间推进算法；LU-SGS隐式积分方法；超声速/高超声速流动
- 抛物化NS方程 /
- 空间推进算法 /
- LU-SGS隐式积分方法 /
- 混合型迎风格式 /
- 超声速/高超声速流动
Abstract: A new implicit finite-volume Single-Sweep ParabolizedNavier-Stokes (SSPNS) algorithm is developed. Theoretical analysis isfocused on the mathematic properties about the parabolized Navier-Stokes(PNS) Equations, especially on the treatment of streamwise pressuregradient. Then the original implicit time iterative Lower-Upper SymmetricGauss-Seidel (LU-SGS) method is successfully extended to integrate the PNSEquations in the streamwise direction. The hybrid upwind schemes, includingAdvection Upstream Splitting Method (AUSM) family schemes and Low-DiffusionFlux-Splitting (LDFSS) schemes, are used to compute the crossflow inviscidfluxes, while central schemes for the viscous fluxes. Four typical flows,i.e., supersonic flat plate flow, 15$^\circ$ ramp hypersonic flow,10$^\circ$ coneflows with different angles of attack, and side-compression hypersonic inletflows are calculated with the SSPNS codes. Numerical results agree well withthose obtained from NASA's UPS PNS codes and experimental results by Tracy,Holden, or Holland et al. All the numerical results indicate that SSPNS is ahighly efficient, highly accurate, and also highly robust algorithm forsteady supersonic/hypersonic flows without any large streamwise separation.Comparison to the traditional time-iterative Full Navier-Stokes (FNS) flowsolvers, the SSPNS codes show 1~2 order of magnitude of computationalspeed faster and at least 1 order of magnitude of memory storage saving.