紧致差分格式的分辨率与精度的实例比较与讨论

通过比较先前建立的4阶最优紧致差分格式,以及传统的6阶和8阶紧致差分格式,来研究精度和分辨率之间的关系,主要比较了空间离散格式的有效波数范围、实际数值计算精度、以及对小尺度波动的模拟能力.数值试验结果表明:(1)这3种格式的计算精度都可以达到理论精度,并且此时精度越高,误差越小;(2)对于小尺度波动,最优4阶紧致格式比6阶和8阶紧致格式具有更高的分辨率;(3)对于行波问题,最优4阶紧致格式能够更加准确地模拟波动的传播行为.理论分析和数值算例的比较结果均表明,数值格式的精度和分辨率并不能互相替代,而是要根据计算问题的需要选择具有合适的精度和分辨率的数值格式.     

三维双调和方程的高阶紧致差分格式及其多重网格方法

提出一类求解三维双调和方程的高精度紧致差分格式.该类格式是以泊松方程的高精度格式为基础的四阶精度19点紧致差分格式和六阶精度27点紧致差分格式.采用多重网格方法求解由高精度紧致差分格式所形成的代数方程组,并与低精度方法进行比较.讨论多重网格方法中不同松驰算子的迭代收敛效果.数值实验结果验证四阶紧致差分格式和六阶紧致差分格式的精度以及多重网格方法的可靠性和高效性.     

多项式拟合数值边界格式及其稳定性分析

根据构造无反射数值边界格式的基本思想,采用多项式拟合的方法,构造了一种高精度的数值边界格式(SFEBS).理论分析表明:SFEBS边界格式与4阶紧致差分格式相结合,既能保持格式的G-K-S稳定性,又能保持三对角矩阵是严格对角占优的.数值试验表明:2阶和3阶边界格式分别能够保持3阶和4阶的整体精度;4阶的SFEBS格式也能够保持4阶的整体精度,同时能够减小自由流出边界上的最大误差.     

一种求解变波数Helmholtz方程的高精度紧致差分方法

【目的】进一步研究Helmholtz方程对于大波数和变波数问题的数值计算,数值求解Helmholtz方程具有重要的理论价值和现实意义。【方法】利用泰勒级数展开,并结合混合型紧致格式的思想,推导了数值求解一维和二维Helmholtz方程的六阶精度紧致差分格式。并且格式涉及到未知函数及其一阶和二阶导数值,为保证格式的整体精度,对一阶和二阶导数的计算也采用六阶紧致差分格式。【结果】格式在小波数和变波数的情况下都有六阶精度,在大波数的情况下仍然能保持三阶以上精度。【结论】数值实验验证了格式的精确性和可靠性。     

两点边值问题的一种高精度差分方法

从中心差分公式出发,利用二阶微分的四阶差分公式,对两点边值问题得到了一种四阶精度的差分格式,该方法仅涉及中心点及相邻网格点,具有四阶精度,并且由所提格式得到的线性方程组是三对角线型的,可以直接采用追赶法进行求解,数值算例的结果表明,该格式比以往的格式具有更高的精度,并且计算简便。     

椭圆界面问题的高阶差分格式

构造混合边界条件下椭圆界面问题的一个高阶数值格式.在求解区域内部及界面处采用四阶逼近,边界处采用三阶数值格式,得到一个整体四阶精度的求解格式.数值实验证明了格式的高精度及有效性.     

求解非定常不可压Navier-Stokes方程的一种高精度并行算法

采用一阶投影法,建立了一种基于MPI求解非定常不可压N-S方程的高精度并行算法.该算法在空间上可达到4阶精度,其中,对流项中的1阶导数和粘性项中的2阶导数分别采用WENO格式和4阶对称型宽格式进行离散,而Poisson方程则采用4阶精度的紧致格式进行迭代求解.通过对2维Taylor涡列和双周期双剪切边界层流动问题及3维回转体绕流问题的数值计算,验证了算法的可靠性及其并行效率.     

一种辛紧致格式FDTD方法的行为分析

针对传统时域有限差分法精度较低、长期响应较差的缺点，本文采用时间辛算法与空间紧致格式结合的方法来计算Maxwell方程．这样的改进格式在空间、时间上均达到了四阶精度．格式不产生耗散误差，色散误差很小，对长期响应问题有很好的计算结果．     

一类弱非线性波浪数值模型及其适用性分析

研究了一类含弱非线性的改进型Boussinesq水波方程,在非交错网格下,利用有限差分法建立了混合四阶Adams-Bashforth-Moulton的预报校正格式的波浪数值模型。在数值模型中,关于空间一阶导数差分格式采用四阶精度、二阶导数差分格式采用二阶精度。针对波浪的一维、二维传播变形问题进行了数值计算,并通过与相关实验结果对比分析考察了该数值模型的适用性。     

时间分数阶Allen-Cahn方程的重心插值配点法

采用Laplace变换近似Caputo型分数阶导数,将分数阶方程转换成整数阶方程;然后,在时-空方向均采用重心插值配点法离散,非线性项采用Newton迭代格式求解,并给出配点格式的相容性误差分析.数值实验表明:该配点法格式具有较高精度,能满足能量递减规律.     

基函数法在黏性可压缩流动中的研究与应用

研究基函数法在二维和三维轴对称情形下可压缩黏性流动中的应用, 并利用此法数值地计算了二维圆柱的超音速黏性绕流和三维球头的轴对称超音速黏性绕流两个算例。取一阶三角函数为基函数, 构造出导数的中心格式和迎风格式。对于可压缩N-S 方程中的对流项, 采用通量分裂法及中心格式与迎风格式相结合的技术;对于可压缩N-S方程中的黏性项, 则采用中心格式进行处理。由此, 构造出了数值求解黏性可压缩流动的一阶三角函数类型的基函数格式。两个算例的数值计算结果表明, 基函数法不仅在处理无黏可压缩流动时, 是一种高精度、高分辨率的新型计算方法, 而且在处理黏性可压缩流动问题时也一样行之有效。     

人工压缩法数值模拟非定常不可压缩热对流流场

利用人工压缩方法数值模拟了由于强热浮力不稳定性引起的非定常不可压缩热对流流场．在非定常动量、能量方程中引入了一伪时间项,连续性方程中加入与伪时间层相关的人工压缩项,使连续性方程与动量方程自动耦合,得到一沿物理时间准确推进的沿伪时间层采用ＧａｕｓｓＳｉｄｌｅ内迭代的推进迭代算法．在每一时间层进行内迭代直到连续性方程满足为止．对流项用四阶中心差分格式,时间项用三阶向后差分．利用此算法数值研究了二维ＰｏｉｓｅｕｉｌｅＢｅｎａｒｄ流场和底部加热的非定常水平射流问题,成功地模拟了流场中涡旋的生成及发展过程．结果表明,用该算法模拟非定常热对流问题具有较高的效率和准确性     

An experimental study on fine structures of supersonic laminar/turbulent flow over a backward-facing step based on NPLS

Fine structures of supersonic flow over a 5 mm high backward facing step(BFS),including expansion wave fan,reattachment shock,supersonic boundary layer were measured in a Ma=3.0 low-noise indraft wind tunnel.By varying the superficial roughness of the wall upstream from the step,supersonic laminar flow and supersonic turbulent flow could be formed over a BFS.Measurements on the spatiotemporal features of the holistic flow field and the fine structures in four typical regions were carried out using NPLS(nano-based planar laser scattering).Flow structures,including expansion wave fan,reattachment shock,supersonic boundary layer and its separation,reattachment and redevelopment are revealed by measuring the holistic structure of the transient flow field.Comparing the two time-averaged flow fields with each other,it is apparent that supersonic turbulent flow over a BFS(STF-BFS) has a larger expansion angle and a shorter recirculation region,and its redeveloped boundary layer increases at a smaller obliquity while the angle of reattachment shock is the same for the supersonic laminar flow over a BFS(SLF-BFS).With regard to time-evolution features,the K-H vortices in the SLF-BFS suffers from shearing,expansion,reattachment and three-dimensional effects while in the STF-BFS large-scale structures are affected by the incline and distortion at the reattachment point due to expansion,viscosity and reverse-pressure.Studies on local regions indicate that in the SLF-BFS,the emergence of compression waves which distinctly converge into a reattachment shock is due to the local convective Mach number and the inducement of K-H vortices in the free shear layer.Nevertheless,in the STF-BFS,compression waves and K-H vortices are barely evident,and the formation of a reattachment shock is related to the wall compressive effect.     

导弹构形横向喷流干扰流场数值模拟

利用对称TVD格式和重叠网格技术数值模拟了翼面位置不同的两种导弹构形的横向喷流干扰流场,研究了喷口附近的流场结构、涡系结构、波系结构及流动分离等流场特性及翼面位置对干扰效应及气动性能的影响,并将计算得到的干扰力放大因子和干扰力矩系数的结果与实验结果进行比较,吻合良好.     

Experimental investigation of supersonic flow over a hemisphere

The experimental investigation of supersonic flow over a hemisphere was conducted using Nanoparticle-based Planar Laser Scattering(NPLS) technique in a supersonic quiet wind tunnel at Ma=2.68.Ahead of the hemisphere,boundary layer separation with the formation of a three-dimensional separated flow was observed,which was resulted from the interaction between the three-dimensional bow shock wave and the boundary layer.The complex flow structures of supersonic flow over the hemisphere were visualized.Based on the time correlation of NPLS images,time-space evolutionary characteristics of supersonic flow over the hemisphere were studied,and the evolutionary characteristics of the spanwise and streamwise large scale vortex structures were obtained,which have the features of periodicity and similar geometry.     

Experimental investigation on upstream-injection interaction with a scramjet cavity flameholder

The study has evaluated the coherent structures and the velocity field of gaseous transverse jet upstream of a scramjet flameholder in a supersonic turbulent flow. The high spatiotemporal resolution coherent structures of the jet plume/wakes and the cavity shear layer were obtained by utilizing the nanoparticle-based planar laser scattering technique. Compared to the no upstream injection case, the cavity shear layer downstream of the jet shows significant mass exchange with mainstream. The particle image veloc- imetry velocity field and the velocity profiles demonstrated that the interaction intensity of the cavity shear layer with the upstream injection is further enhanced as the injection stagnation pressure increases.     

考虑固体颗粒的自由喷流噪声的数值研究

研究固体颗粒对喷流流场和声场的影响.选取6种不同的湍流模型，对自由喷流进行稳态计算分析，对比发现RNG k-ε模型最适合用于稳态喷流数值模拟；采用LES模型计算喷流的非稳态结果，并结合FW-H方程进行了喷流声场分析，与试验数据进行对比，验证了数值模型的正确性；在此模型的基础上，添加固体颗粒研究其对自由喷流流场和声场的影响，仿真结果表明固体颗粒的存在减小了喷流流场的超音速段长度，显著提高了喷流温度；增大了喷流下游区域噪声，减小了中上游区域噪声.      

气体离心机供料射流的三维数值模拟

通过使用有限体积法和隐式二阶迎风格式求解了三维Navier-Stokes方程组,研究了气体离心机内部供料射流。得到不同供料压强条件下供料射流流场的三维分布,数值模拟结果表明:供料射流对离心机内部流场的影响随供料压强的增大而增大;当供料压强为3 kPa时,Mach盘出现在无量纲半径0.81处。由于强旋条件下的供料射流结构较为复杂,实际供料流动情况与均匀供料假设存在较大差异,因此根据射流流场分布对环流计算边界条件进行修正,将更准确地评估离心机分离性能。     

超声速气流中氢气燃料喷流的数值模拟研究

从可压缩流动的多组分湍流Ｒｅｙｎｏｌｄｓ 平均ＮａｖｉｅｒＳｔｏｋｅｓ 方程出发,结合ＢａｌｄｗｉｎＬｏｍａｘ 的代数湍流模型,采用高精度的差分方法进行数值求解．数值研究了燃烧室（矩形管道和矩形扩张管道）内氢气燃料喷流（下壁面横向喷流和流向顺流喷射）和超声速空气主流相互作用的三维流场结构,以及燃气的对流、扩散输运过程在燃烧室内的浓度空间分布特性．     

Transitional phenomenon of particle dispersion in gas-solid two-phase flows

Without using any turbulent model, direct numerical simulation of a three-dimensional gas-solid two-phase turbulent jet was performed by finite volume method. The effects on dispersion of particles with different Stokes numbers by the transitional behavior of turbulent structures were investigated. To produce high-resolution results and reduce the computation and storage, the fractional-step projection algorithm was used to solve the governing equations of gas phase fluid. The low-storage, three-order Runge-Kutta scheme was used for time integration. The governing equations of particles were solved in the Lagrangian framework. These numerical schemes were validated by the good agreement be-tween the statistical results of flow field and the related experimental data. In the study of particle dis-persion, it was found that the effects on particle dispersion by the spanwise vortex structures were prominent. The new behaviors of particle dispersion were also observed during the evolution of the flow field, i.e. the transitional phenomenon of particle dispersion occurs for the particles with small and intermediate Stokes numbers.