亚大气压六相交流电弧放电等离子体射流特性数值模拟

以临近空间高超声速飞行器和航天器再入大气环境飞行过程中其表面产生的高密度非平衡态等离子体为研究对象,基于本研究组所建立的多相交流电弧放电等离子体实验平台(MPX-2015),开展了非平衡态氩等离子体射流特性的二维数值模拟研究.在亚音速条件下二维、非平衡数值模拟所得到的计算结果与实验测量结果符合良好.超音速条件下的数值模拟结果表明,随着真空腔压强的降低,等离子体射流流速明显增大,覆盖钝体头部的等离子体鞘套的厚度先减小,而后又增加,鞘套的空间均匀性以及等离子体向钝体表面的总传热量均显著降低,而钝体头部的局部电子数密度则增大.数值模拟结果为在MPX-2015上开展超音速条件下的实验研究提供了理论指导.     

气体体积粘性对二维环形激波聚焦的影响

基于体积粘性系数ζ的分子运动论和连续介质理论,对二维环形激波聚焦（马赫数Ma=2.0）的体积粘性效应进行数值研究,结果表明：对于热完全气体,体积粘性使得激波汇聚中心点处的压力减小、温度增加、密度减小,聚焦点物理参数的改变量分别可达20%、10%、30%,体积粘性效应对环形激波聚焦的影响是不可忽略的;与转动模态相比,在振动模态下环形激波聚焦的体积粘性效应更为明显,因为激波聚焦点附近的体积粘性应力ζ▽·V与热力学压力p达到同一数量级,从而显著改变了流动参数.     

基于非结构网格间断有限元方法在可压缩流体中的应用

本文开发了一套基于非结构网格的间断有限元方法(DG)程序,并对与单元形状无关的斜率限制器进行了研究。此程序支持多种网格类型,能够方便应用于具有混合单元的非结构网格,具有处理复杂几何结构的能力,为研究叶轮机械内部复杂流动现象提供了有效的研究工具。本文利用该程序对若干典型无黏和黏性问题进行数值模拟,结果表明,该程序具有较高的可信度,能够处理具有混合单元的非结构网格,并给出良好的数值模拟结果。     

可压缩Navier-Stokes方程组球对称弱解的大时间行为

研究了可压缩Navier-Stokes方程组 球对称弱解的大时间行为. 假设压强 $p(\varrho)=\varrho^\gamma$, 绝热指数$\gamma>1$, 外力是球对称的. 证明了假如外力满足一定的正则性及某种结构性条件, 则当时间 趋于无穷大时, 密度将趋于其对应的静止问题的唯一解.     

三维动边值问题的迎风差分方法

可压缩可混溶油、水三维渗流动边值问题的研究,对重建盆地发育中油气资源运移、聚集的历史和评估油气资源的勘探与开发有重要的价值, 其数学模型是一组非线性耦合偏微分方程组的动边值问题. 该文对有界域的动边值问题提出一类新的二阶修正迎风差分格式, 应用区域变换、 变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧, 得到了最佳 $l^2$ 误差估计结果. 该方法已成功应用到油资评估的数值模拟中. 它对这一领域的模型分析, 数值方法和软件研制均有重要的价值.     

Basic function scheme of polynomial type

A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.     

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.     

Minimax principle on energy dissipation of incompressible shear flow

The energy dissipation rate is an important concept in the theory of turbulence. Doering-Constantin＇s variational principle characterizes the upper bounds （maxi- mum） of the time-averaged rate of viscous energy dissipation. In the present study, an optimization theoretical point of view was adopted to recast Doering-Constantin＇s formu- lation into a minimax principle for the energy dissipation of an incompressible shear flow. Then, the Kakutani minimax theorem in the game theory is applied to obtain a set of conditions, under which the maximization and the minimization in the minimax principle are commutative. The results explain the spectral constraint of Doering-Constantin, and confirm the equivalence between Doering-Constantin＇s variational principle and Howard- Busse＇s statistical turbulence theory.     

Simple waves for two-dimensional compressible pseudo-steady Euler system

A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that ＂the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow patterns＂ see Courant and Friedrichs＇s chassical book ＂Supersonic Flow and Shock Waves＂. This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems.     

可缩液体汽车减振器装置研究

对一种新型可压缩液体汽车减振器的基本结构和工作原理进行了分析,给出其内特性的数学模型。指出可压缩液体减振器由于腔内充满可压缩液体,其动作连续可靠,其外特性不会发生高频高速畸变,并提供了该减振器外特性试验。