一种求解抛物化Navier-Stokes方程的空间推进算法  

A SPACE-MARCHING ALGORITHM FOR SOLVING THE PARABOLIZED NAVIER-STOKES EQUATIONS

作　　者：陈兵[1] 徐旭[1] 蔡国飙[1] 

机构地区：[1]北京航空航天大学宇航学院,北京100083

出　　处：《力学学报》2008年第2期162-170,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：中国博士后科学基金(20070410455);国家863高技术项目(2006AA705306)资助.

摘　　要：讨论了抛物化NS方程(parabolized Navier-Stokes equations,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-Stokes algorithm,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°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.A new implicit finite-volume Single-Sweep Parabolized Navier-Stokes （SSPNS） algorithm is developed. Theoretical analysis is focused on the mathematic properties about the parabolized Navier-Stokes （PNS） Equations, especially on the treatment of streamwise pressure gradient. Then the original implicit time iterative Lower-Upper Symmetric Gauss-Seidel （LU-SGS） method is successfully extended to integrate the PNS Equations in the streamwise direction. The hybrid upwind schemes, including Advection Upstream Splitting Method （AUSM） family schemes and Low-Diffusion Flux-Splitting （LDFSS） schemes, are used to compute the crossflow inviscid fluxes, while central schemes for the viscous fluxes. Four typical flows, i.e., supersonic flat plate flow, 15° ramp hypersonic flow, 10° cone flows with different angles of attack, and side-compression hypersonic inlet flows are calculated with the SSPNS codes. Numerical results agree well with those 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 a highly efficient, highly accurate, and also highly robust algorithm for steady supersonic/hypersonic flows without any large streamwise separation. Comparison to the traditional time-iterative Full Navier-Stokes （FNS） flow solvers, the SSPNS codes show 1-2 order of magnitude of computational speed faster and at least 1 order of magnitude of memory storage saving.

关 键 词：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 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]