二维定常不可压缩粘性流动N-S方程的数值流形方法

将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解.将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合.数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法.     

一种用边界元方法求解二维不可压缩粘性流动的方法

本文用边界元方法求解了二维不可压缩粘性流动的涡量——速度方程,利用求解区域边界上的速度法向导数和速度值直接得到了涡量的边界条件,克服了利用涡量方程求解二维不可压缩粘性流动时涡量边界条件(主要是壁面边界条件)难以给定的困难,算例表明:这种方法比较简单且计算结果基本上是令人满意的。     

配置点谱方法-人工压缩法(SCM-ACM)求解不可压缩流体流动

开发了配置点谱方法SCM（spectral collocation method）与人工压缩法ACM（artificial compressibility method）相结合的方法SCM-ACM,用于求解不可压缩粘性流动问题。选取典型的方腔顶盖驱动流为研究测试对象,首先建立人工压缩格式的控制方程,其次采用SCM离散控制方程的空间偏微分项,推导出矩阵形式的代数方程,最后测试了SCM-ACM代码的有效性。结果显示,SCM-ACM能够有效求解不可压缩流动问题,并继承了谱方法的指数收敛特性,且具有ACM求解过程简单及易于实施的特点。     

基于局部DQ-RBF不可压缩N-S方程的数值求解

以RBF作为DQ方法的基函数,将迎风机制引入DQ-RBF中,建立了二维不可压缩黏性N-S方程数值求解模型,采用Levenberg-Marquardt算法求解非线性方程组.求解时分析了形状参数对求解精度的影响,改进了边界速度的处理方法.对平板Couette流及有限宽台阶绕流流动问题进行了数值求解.比较了本文方法和FLUE...     

高阶紧致格式求解二维粘性不可压缩复杂流场

提出了一种求解二维不可压缩复杂流场的高精度算法．控制方程为原始变量、压力Ｐｏｉｓｓｏｎ方程提法．在任意曲线坐标下，采用四阶紧致格式求解Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组，时间推进采用交替方向隐式（ＡＤＩ）格式，在非交错网格上用松弛法求解压力Ｐｏｉｓｓｏｎ方程．对于复杂的流场，采用了区域分解方法，并在每一时间步对各子域实施松弛迭代使之能精确地反映非定常流场．利用该算法计算了二维受驱空腔流动，弯管流动和垂直平板的突然起动问题．计算结果与实验结果和其他研究者的计算结果相比较吻合良好．对于平板起动流动，成功地模拟了流场中旋涡的生成以及Ｋａｒｍａｎ涡街的形成     

无粘可压缩流动的改进高精度方法

为更准确捕捉复杂流场的流动细节,通过对WENO格式的光滑因子进行改进,发展了一种新的五阶WENO格式。对三阶ENO格式进行加权可以得到五阶WENO格式,但是不同的加权处理,WENO格式在极值处保持加权基本无振荡的效果不同,本文构造了二阶精度的局部光滑因子,及不含一阶二阶导数的高阶全局光滑因子,从而实现WENO格式在极值处有五阶精度。基于改进五阶WENO格式,对一维对流方程、一维和二维可压缩无粘问题进行算例验证,并与传统WENO-JS格式和WENO-Z格式进行比较。计算结果表明,改进五阶WENO格式有较高的精度和收敛速度,有较低的数值耗散,能有效捕捉间断、激波和涡等复杂流动。     

一种可压缩与不可压缩气体流动的统一算法及其应用

本文采用伪时间变化率项及其"预处理"矩阵,并结合LU-SGS离散格式,发展了可压缩与不可压缩气体流动求解的统一算法.该方法有效地消除了采用可压缩方法求解低速流动时容易产生的"刚性"问题,减小了由于压力项在低速情况下产生的舍入误差.同时,在求解低速与高速并存的流场流动时,无需进行预处理矩阵的转换,实现了可压缩与不可压缩气体流动的统一理论求解.作为算法有效性的验证,本文分别计算了低速、高速、高低速混合流动的典型算例.计算值的验证结果比较表明,对求解马赫数大范围变化情况下的流场,具有很好的收敛性与稳定性,而且收敛速度基本不受流动速度的影响.这个算法程序为今后发展用于燃烧反应流动和密度梯度驱动流动的分析建立了方法基础.     

微喷管流动粒子仿真与Navier-Stokes数值模拟比较研究

运用DSMC（Direct Simulation Monte—Carlo）方法从分子运动论层次对大膨胀比、喉部转角为尖角的微喷管流动现象进行模拟,考察来流总压对喷管性能的影响,并与Navier—Stokes方程运算结果、实验结果进行比较。研究表明：在模拟微型喷管的流动现象时,DSMC方法比N—S方程更加适用。     

不可压缩流场多体运动问题的两种数值解法

不可压缩流场中多体运动的数值模拟是计算流体动力学的前沿课题,目前可以求解此问题的两种高精度方法是重叠网格法和移动网格法。本文详细讨论了两种方法的理论基础,典型算法的实现过程,并采用两种方法对单圆柱和多圆柱运动问题进行了数值试验。通过分析比较,本文认为重叠网格法计算效率高于移动网格法,重叠网格法比移动网格法更适合于求解物体大位移运动问题,尤其当计算区域几何形状复杂时重叠网格法的优势更加明显。     

两种浸入式边界方法的比较

介绍两类不同的浸入式边界方法及其对它的改进. 然后采用均匀矩形交错网格和压力校正投影法,对不可压流场中的二维圆柱绕流进行了数值求解并对比了两类方法的精度.计算分析表明,连续显力法具有构造简单,适用性强的优点. 但离散隐力法在物面边界精度上要优于前者. 改进后,在二阶精度的离散格式下物面边界精度较低的显示力源法的精度有一定提高,同时发现,加密网格以提高数值精度的方法对于连续显力法并不总是有效.而同样格式下,离散隐力法具有更高精度,其中预测-校正离散隐力法可以在此基础上获得更小的计算误差和更快的收敛速度. 数值解与文献已有的数值和实验结果吻合得很好,表明边界算法及其程序是可靠和有效的.      

A PRESSURE-CORRECTION METHOD FOR THE SOLUTION OF INCOMPRESSIBLE VISCOUS FLOWS ON UNSTRUCTURED GRIDS

An unstructured grid, finite volume method is presented for the solution of two-dimensional viscous, incompressible flow. The method is based on the pressure-correction concept implemented on a semi-staggered grid. The computational procedure can handle cells of arbitrary shape, although solutions presented herein have been obtained only with meshes of triangular and quadrilateral cells. The discretization of the momentum equations is effected on dual cells surrounding the vertices of primary cells, while the pressure-correction equation applies to the primary-cell centroids and represents the conservation of mass across the primary cells. A special interpolation scheme s used to suppress pressure and velocity oscillations in cases where the semi-staggered arrangement does not ensure a sufficiently strong coupling between pressure and velocity to avoid such oscillations. Computational results presented for several viscous flows are shown to be in good agreement with analytical and experimental data reported in the open literature.     

A COMPARATIVE STUDY OF TIME-STEPPING TECHNIQUES FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS: FROM FULLY IMPLICIT NON-LINEAR SCHEMES TO SEMI-IMPLICIT PROJECTION METHODS

We present a numerical comparison of some time-stepping schemes for the discretization and solution of the non-stationary incompressible Navier– Stokes equations. The spatial discretization is by non-conforming quadrilateral finite elements which satisfy the LBB condition. The major focus is on the differences in accuracy and efficiency between the backward Euler, Crank–Nicolson and fractional-step Θ schemes used in discretizing the momentum equations. Further, the differences between fully coupled solvers and operator-splitting techniques (projection methods) and the influence of the treatment of the nonlinear advection term are considered. The combination of both discrete projection schemesand non-conforming finite elementsallows the comparison of schemes which are representative for many methods used in practice. On Cartesian grids this approach encompasses some well-known staggered grid finite difference discretizations too. The results which are obtained for several typical flow problems are thought to be representative and should be helpful for a fair rating of solution schemes, particularly in long-time simulations.     

用BGK格式计算不可压缩流场

简要介绍BGK方法的基本思想,数值方法及其对不可压缩流场数值计算的推广。然后详细介绍将BGK方法应用于平面方框流的结果,将其结果与Ghia的结果进行了详细的比较。本方法还用来模拟后台阶流动,所得结果与相应的实验数据进行比较。以上比较表明本方法的有效性,同时也确定在计算不可压缩流体时参数的正确选择。     

NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE FLOW BY A NEW FORMULATION

A new mathematical formulation, called the pseudovorticity–velocity formulation, of the three-dimensional incompressible Navier–Stokes equations is presented as an alternative to the vorticity–velocity approach. For the model lid-driven cavity flow problem in two and three dimensions, combined with an explicit mixed spectral /finite different numerical scheme the proposed formulation is found to be efficient and very accurate as compared with the results available in the literature. In particular, the simulation results demonstrate an attractive feature of the present formulation compared with the vorticity–velocity approach, namely that the divergence-free condition of the velocity field can always be achieved on a non-staggered mesh.     

AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS

An approximate projection scheme based on the pressure correction method is proposed to solve the Navier–Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward-facing step.     

THE OSCILLATION MODE OF INCOMPRESSIBLE CAVITY FLOW

采用二维大涡模拟方法进行了空腔水流场的数值计算, 考察空腔前缘动量损失厚度及来流速度等因素如何影响空腔流的振荡, 同时考察了空腔长深比与空腔流振荡模式的关系. 用空腔水流场的粒子图像测速测量结果验证了数值计算的可信性.结果表明, 空腔水流是否发生振荡取决于壁面摩擦速度.瞬时涡结构和空腔阻力系数2个方面的特征显示空腔水流场有2种典型的振荡模式, 剪切层模式与尾流模式, 确定振荡模式的关键因素是空腔长深比.     

NUMERICAL SIMULATION FOR NAVIER-STOKES EQUATIONS BY PROJECTION/CHARACTERISTIC-BASED OPERATOR-SPLITTING FINITE ELEMENT METHOD

提出了一种求解非定常不可压缩纳维-斯托克斯方程（N-S方程）的新型有限元法：基于投影法的特征线算子分裂有限元法.在每一个时间层上将N-S方程分裂成扩散项、对流项、压力修正项.对流项采用多步显式格式,且在每一个对流子时间步内采用更加精确的显式特征线-伽辽金法进行时间离散,空间离散采用标准伽辽金法.应用此算法对平面泊肃叶流、方腔流和圆柱绕流进行数值模拟,所得结果与基准解符合良好.尤其对于Re=10000的方腔流,给出了方腔中分离涡发展和运动的计算结果,并发现在该雷诺数下存在周期解,表明该算法能较好地模拟流体流动中的小尺度物理量以及流场中分离涡的运动.     

振荡管流换热的理论解

本文从流体在管内振荡的运动方程和流体及管壁的能量方程出发,经过变量转换对常微分方程组进行求解,得到了计及管壁影响的振荡流体轴向换热的一般理论解。由这解,可以导出各种特殊条件下的表达式,包括已有的各种解析解。本解经数字化而制成各种图线,它们与已有的实验数据基本吻合。     

UNIFIED COMPUTATION OF FLOW WITH COMPRESSIBLE AND INCOMPRESSIBLE FLUID BASED ON ROE''''S SCHEME

A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm. The primitive variables are pressure, velocities and temperature. The time integration scheme is used in conjunction with a finite volume discretization. The preconditioning is coupled with a high order implicit upwind scheme based on the definition of a Roe's type matrix. Computational capabilities are demonstrated through computations of high Mach number, middle Mach number, very low Mach number, and incompressible flow. It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe's scheme.