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抛物化NS方程得到广泛应用,已经成为工业标准气动计算的基础。现有的八种抛物化NS方程有不同的名称,方程中粘性项的形式略有不同,其中的PNS和薄层(TL)NS方程应用最多。但是这些方程都具有类似的数学性质,例如,当流向方向上马赫数大于1时,他们都是抛物型方程,可以采用空间推进算法(SMA)进行求解。与采用时间推进算法求解的NS方程或雷诺平均(RA)NS方程相比,PNS-SMA计算降低了空间的维数,节省了大量的存储空间和CPU计算时间。PNS-SMA算法也获得了巨大的进展。但是,早期PNS研究在理论上是相当模糊的,高智在1990年提出的粘性/无粘干扰剪切流理论(ISF)弥补了这一不足。ISF理论概括了PNS方程所能描述的基本流动,提出了其流动的运动规律及数学定义式,所导出的ISF方程组也属于PNS方程的一种。为了不增加新的名称,我们将ISF方程组也称为高氏PNS理论和方程组。这一理论在NS方程和RANS方程的计算中均有重要的应用。例如,计算最优坐标系的选择以减少伪扩散,网格尺度选择及局部网格加密设计以捕捉高超声速流动中物体表面热流等的急剧变化,壁面压力边界条件的选择以及由高PNS导出的壁面判据来进行NS和RANS近壁数值解可信度评估。本文评述了一些初步的应用,进一步的应用和综合PNS-SMA,RANS-SMA以及PSE-SMA计算值得深入研究,这里PSE指抛物化稳定性方程。
Parabolic NS equations are widely used and have become the basis for industrial-standard aerodynamic calculations. The existing eight kinds of parabolic NS equations have different names, and the form of the viscous terms in the equation is slightly different. Among them, the PNS and the thin layer (TL) NS equations are the most widely used. However, these equations all have similar mathematical properties. For example, when the Mach number in the flow direction is greater than 1, they are all parabolic equations that can be solved by using the space propulsion algorithm (SMA). Compared with the NS or Reynolds-averaged (RA) NS equations solved by time-propulsion algorithm, PNS-SMA computation reduces the dimension of space and saves a lot of storage space and CPU time. PNS-SMA algorithm has also made great progress. However, the earlier PNS research was rather fuzzy in theory. The theory of viscous / viscous interference shear flow (ISF) proposed by Gao Zhi in 1990 made up for this problem. ISF theory summarizes the basic flow that can be described by PNS equation, and proposes the law of its flow and its mathematical definition. The derived ISF equations also belong to one of the PNS equations. In order not to add a new name, we also call the ISF equations Gospel PNS theory and equations. This theory has important applications in the calculation of both NS and RANS equations. For example, the choice of the optimal coordinate system is calculated to reduce pseudo-diffusion, grid-scale selection, and local mesh-encryption design to capture sharp changes in object surface heat flow, etc. in hypersonic flow, selection of wall pressure boundary conditions, Wall criteria to assess the reliability of numerical solutions of NS and RANS near-walls. This paper reviews some preliminary applications, further applications and comprehensive calculations of PNS-SMA, RANS-SMA and PSE-SMA deserve further study, where PSE refers to the parabolic stability equation.