求解流动和传热问题的一种新的全隐算法-CLEAR(下)

本文上篇阐述了CLEAR算法的推导过程和计算步骤,本文下篇通过五个二维不可压缩流动和传热的算例,对CLEAR算法和SIMPLER算法进行了比较,比较的内容为,在相同的收敛条件下, CLEAR算法和SIMPLER算法收敛所需的迭代次数的比值和对应的CPU时间的比值,以及这两个比值和时步倍率的关系,从而进一步研究了CLEAR算法的健壮性。计算结果表明,CLEAR算法可以在很大程度上加速迭代收敛,就所比较的算例而言,其可以节省迭代次数31％-85％,节省CPU时间17％-78％,而且该算法的健壮性可以通过引入第二松弛因子而得以提高。     

CAMPLE一种求解不可压流动的协调算法

本文提出了一种两次求解质量守恒方程、速度与压力协调的求解不可压缩流体流动与传热问题的算法。它采用与SIMPLER求解压力相似的方式,将不含亚松弛因子的离散动量方程转化为假拟速度与压力差的函数,代入到离散质量守恒方程中得到压力方程,以解决压力没有控制方程的问题。通过两次计算假拟速度和求解质量守恒方程,获得同时满足质量守恒与动量守恒的速度和压力,克服了以往的SIMPLE类算法中每一迭代步中速度和压力均不满足动量方程的缺点。有限几个算例表明,新算法的速度松弛因子对收敛速度的影响远小于SIMPLER算法,在松弛因子接近于1时,收敛速度略低于SIMPLER算法,但松弛因子低于0.8时,收敛时间与迭代次数则远小于SIMPLER,算法。     

求解流动与传热问题的一种高效稳定的分离式算法-IDEAL

本文提出了一种求解流动与传热问题的高效稳定的分离式算法-IDEAL(Inner Doubly-iterative EfficientAlgorithm for Linked-equations).在IDEAL算法中每个迭代层次上对压力方程进行两次内迭代计算,第一次内迭代过程用于克服SIMPLE算法的第一个假设,第二次内迭代过程用于克服SIMPLE算法的第二个假设.这样在每个迭代层次上充分满足了速度和压力之间的耦合,从而大大提高了计算的收敛速度和计算过程的稳定性.本文通过2个三维不可压缩流动和传热的算例对IDEAL算法与其它三个被广泛使用的算法(SIMPLER、SIMPLEC和PISO)进行了比较.通过分析比较得出IDEAL算法在收敛性和健壮性上均优于SIMPLER、SIMPLEC和PISO算法.在这2个算例中IDEAL算法几乎可以在任意的松弛因子下获得收敛的解,并且IDEAL算法所需最短计算时间较SIMPLER算法减少12.9%～52.6%;较SIMPLEC算法减少48.3%～79.1%;较PISO算法减少10.7%～46.5%.     

一个计算椭圆型流动的隐式数值方法

一、引言 目前常用的求解椭圆型流动问题的方法是S.V.Patankar和D.B.Spalding 1972年提出的SIMPLE算法与后来改进的SIMPLER算法。SIMPLE算法的核心是在交错网格上利用连续方程和动量方程构造了一个近似的压力校正方程来计算压力场并校正速度。由于压力校正方程引入了过多的近似,SIMPLE算法的收敛性和     

CLEAR与SIMPLE系列的三种算法的收敛性和健壮性比较

通过六个典型流动换热问题对CLEAR、SIMPLE、SIMPLEC和SIMPLER四种算法进行收敛性和健壮性比较.在相同的数值处理方法下,收敛所用CPU时间多少用来判断算法的收敛特性;能得到收敛解的时步倍率范围大小用来比较算法的健壮性.比较结果表明,对于开口系统SIMPLEC算法综合效果较好,而闭口系统CLEAR算法综合占优.     

压力修正算法对刮削层等离子体输运方程数值求解性能的影响

基于C++撰写测试程序,研究SIMPLE(Semi-Implicit Method for Pressure Linked Equations)、 SIMPLEC(SIMPLE Consistent)、 SIMPLER(SIMPLE Revised)、 SIMPLEX(SIMPLE Extrapolation)以及PISO(Pressure-Implicit with Splitting of Operators)等压力修正算法对刮削层等离子体Braginskii输运方程数值求解性能的影响。测试程序采用SOLPS(Scrape-Off Layer Plasma Simulation)的等离子体模型方程,数值计算针对简化平板模型开展。结果表明：5种压力修正算法均能使程序收敛至正确的结果,其中PISO算法的收敛速度最快,SIMPLE、 SIMPLEC、 SIMPLER、 SIMPLEX的收敛速度无明显差异。     

基于单目视觉的航天器间相对位姿测量算法

对航天器间相对位姿的光学测量问题进行了研究,提出了一种新的单目视觉测量算法——相似迭代算法。该算法根据三角形相似原理提出了一种新的深度迭代机制,并通过引入深度变量,将求解2D-3D问题转化为迭代求解3D-3D问题。对数值仿真与两种现有的测量算法进行了比较。仿真结果表明,该算法具有精度高、抗噪声能力强和实时性较好等优点,可以应用于航天器间相对位姿测量等任务。     

一种变频相移干涉测量的相位提取算法

相位提取的精度直接影响相移干涉测量的精度。在变频相移干涉测量中,相移量由干涉腔长和波长变化量决定,必须对测试系统进行相位标定,但常因相位标定不精确而引入相移误差,影响相位提取的精度。运用一种基于迭代的相位求解算法,该算法无需对测试系统进行相位标定,可以在被测相位和相移量均未知的情况下,通过交替迭代法求解出被测相位。通过仿真比较了传统四步相移和基于迭代的相位求解算法的相位提取精度,结果表明,基于迭代的相位求解算法的相位提取精度优于传统四步相移算法的精度。     

Krylov子空间法在SIMPLER算法中的求解性能分析

本文开发了Krylov子空间法中的Bi-CGSTAB、GMRES(m)、CGS、TFQMR及QMR方法的计算程序,并将其实施于SIMPLER算法作为其内迭代方法,针对CFD/NHT领域的问题,研究了它们的求解特性;发现:Bi-CGSTAB方法有着高效的收敛速度和良好的稳定性;N-S方程求解中不同方程不同m值的协调选取是GMRES(m)方法在CFD/NHT领域推广应用的关键;CGS和QMR方法易于中断;TFQMR方法收敛速度慢于其他方法,但能适用于更广泛问题的求解.     

基于r-ADMM算法的轴向超分辨荧光显微技术研究

多角度全内反射荧光显微镜层析成像技术是实现轴向超分辨的主要技术之一,其关键算法是基于交替方向乘子算法对逆问题模型求解。为进一步提高交替方向乘子算法的迭代速度及收敛性,提出将一种基于松弛因子的改进型交替方向乘子算法应用于逆问题的求解中,其核心思想是对拉格朗日函数的分解迭代过程进行过松弛求解。基于该算法,搭建了多角度全内反射荧光显微镜成像系统,采集不同照明角度对应的不同穿透深度的图像堆栈,利用改进型算法重构细胞微管的深度信息,给出了系统的轴向分辨率,并与传统交替方向乘子算法进行了收敛速度的对比,给出了改进型算法达到最优收敛的松弛因子的取值范围,最后通过对线粒体样品进行长时程拍摄,重构了其三维信息,并观测了其融合和裂变的连续过程。实验结果表明,改进型交替方向乘子算法可以实现40 nm的轴向分辨率,并能在保证图像重构质量的同时,使迭代过程的收敛速度提升20%以上。     

一种保持二阶精度的反距离加权空间插值算法

针对传统反距离加权（IDW）插值精度较低的缺陷,发展一种高精度插值算法.该插值算法采用迭代亏量校正技术（IDeC）对一次反距离加权插值结果进行修正,通过有限次迭代,理论上将计算精度提高至二阶.在基于结构化网格、非结构化网格的数值验证中,该插值算法的计算精度均保持在二阶左右.应用该算法针对二维圆形和三维球形界面重构时,算法提高了重构界面的光滑度,且计算精度保持为二阶.双层网格插值实验中,算法将速度和压力的绝对误差降低45%以上,得到的压力等值线更接近于初始场.     

解不可压缩流体力学问题的降阶法——Ⅱ.空间Vh的基函数和误差估计

本文对于一大类数值求解二维Navier-Stokes方程边值问题的有限元格式给出了零散度空间V^h的一组简单基函数,讨论了速度的数值误差对压力的数值解的影响,并提出一个改进算法。     

An efficient method for the incompressible Navier–Stokes equations on irregular domains with no-slip boundary conditions,high order up to the boundary

Common efficient schemes for the incompressible Navier–Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries (which destroy uniform convergence to the solution). In this paper we recast the incompressible (constant density) Navier–Stokes equations (with the velocity prescribed at the boundary) as an equivalent system, for the primary variables velocity and pressure. equation for the pressure. The key difference from the usual approaches occurs at the boundaries, where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time. This avoids the common difficulty of an, apparently, over-determined Poisson problem. Since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity, the recast equations are ideal for numerical marching methods. The new system can be discretized using a variety of methods, including semi-implicit treatments of viscosity, and in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy in the L^∞ norm, for both the velocity and the pressure. The scheme has a natural extension to 3-D.     

Analytical and semi-analytical solutions to flows of two immiscible Maxwell fluids between moving plates

Unsteady flows of two immiscible Maxwell fluids in a rectangular channel bounded by two moving parallel plates are studied. The fluid motion is generated by a time-dependent pressure gradient and by the translational motions of the channel walls in their planes. Analytical solutions for velocity and shear stress fields have been obtained by using the Laplace transform coupled with the finite sine-Fourier transform. These analytical solutions are new in the literature and the method developed in this paper can be generalized to unsteady flows of n-layers of immiscible fluids. By using the Laplace transform and classical method for ordinary differential equations, the second form of the Laplace transforms of velocity and shear stress are determined. For the numerical Laplace inversion, two accuracy numerical algorithms, namely the Talbot algorithm and the improved Talbot algorithm are used.     

Improvement of the pressure algorithm of the stand-alone PDF method to treat unsteady three-dimensional turbulent reacting flows

This paper deals with the particle-mesh probability density function (PDF) method. It shows how an existing but less precise pressure algorithm for the stand-alone method can be improved. The present algorithm is able to handle the general case of an unsteady three-dimensional turbulent reacting flow. The transport equation of the joint PDF of velocity and composition is solved with a particle method. Open boundary conditions are realized and for statistical reasons a simple but effective particle splitting procedure is applied.

Based on a simple configuration, the properties of the presented improved pressure algorithm are analysed. It is shown which numerical condition must be taken care of so that the algorithm is able to correct the particle positions such that the normalization condition is fulfilled as accurately as specified.

To verify the algorithm the combustion of a methane–air mixture enclosed in an open simulation volume is calculated. It is shown that the simple particle splitting algorithm works very effectively in the studied case. The behaviour of the improved pressure algorithm is examined by different calculations. To analyse the convergence of the algorithm, the particle number per cell and the grid spacing are varied. To demonstrate the accuracy, a statistically stationary inflow/outflow configuration is used and the numerical solution is compared to an analytical one. For a less symmetric test case, the previous unsteady combustion problem is simulated, including an additional mean velocity in one direction.

The presented improved pressure algorithm provides the opportunity to calculate unsteady three-dimensional turbulent reacting flows with a stand-alone method, and offers an alternative to the complex hybrid finite-volume/particle PDF method.     

A coupled pressure-based computational method for incompressible/compressible flows

Pressure-based flow solvers couple continuity and linearized truncated momentum equations to derive a Poisson type pressure correction equation and use the well known SIMPLE algorithm. Momentum equations and the pressure correction equation are typically solved sequentially. In many cases this method results in slow and often difficult convergence. The current paper proposes a novel computational algorithm, solving for pressure and velocity simultaneously within a pressure-correction coupled solution approach using finite volume method on structured and unstructured meshes. The method can be applied to both incompressible and subsonic compressible flows. For subsonic compressible flows, the energy equation is also coupled with flow field and the density of fluid is obtained by equation of state. The procedure eliminates the pressure correction step, the most expensive component of the SIMPLE-like algorithms. The proposed coupled continuity-momentum-energy equation method can be used to simulate steady state or transient flow problems. The method has been tested on several CFD benchmark cases with excellent results showing dramatically improved numerical convergence and significant reduction in computational time.     

水平线列阵方位—相速度联合的卡尔曼滤波方法*

传统的水下被动测向方法通过波束形成估计目标角度,水平线列阵波束形成中的参考声速应使用声传播的相速度,在被动测向中,由于声源距离未知,因此在对目标角度估计时选取的参考声速与接收阵处的相速度往往存在偏差,从而影响测向精度。本文提出了一种水平线列阵方位-相速度联合的纯方位扩展卡尔曼滤波方法,该方法引入相速度作为估计状态量以此校准参考声速,提高测向精度,进而改善了由于测向误差较大引起的纯方位扩展卡尔曼滤波算法跟踪结果发散的问题。浅海传播条件下的数值仿真结果表明,改进方法较常规纯方位扩展卡尔曼滤波算法具有更高的跟踪精度及稳健的跟踪性能。     

Measurement of pressure distribution from PIV experiments

In this study, a non-staggered grid SIMPLER pressure solution algorithm, which is able to produce correct pressure distribution directly if correct velocities are given, is proposed to solve the pressure distribution for PIV experiments. The cell face pseudo velocity required in the pressure equation is approximated by a simple linear average of the adjacent nodal pseudo velocities so that the velocity and pressure are collocated without causing the checkerboard pressure distribution problem. In addition, the proposed pressure solution algorithm has the features that upwind effects of the convective terms are considered, boundary conditions are not required, and the pressure distribution obtained can be used to correct the velocity field so that the continuity equation is satisfied. These features make the present algorithm a superior method to calculate the pressure distribution for PIV experiments. The pressure field solved is realistic and accurate. The proposed pressure equation solver is first calibrated with a two-dimensional cavity flow. It is found that the results are almost identical to the exact solution of the test flow. The algorithm is then applied to analyze a uniform flow past two side-by-side circular cylinders in a soap film channel. With the velocity and pressure distributions successfully measured, the structures of the complex shedding flow patterns are clearly manifested.     

一种基于矢量水听器阵的归一化加权Capon波束形成方法

矢量水听器同时拾取声场的标量信息声压和矢量信息振速。本文在分析了各向同性噪声场下矢量水听器阵Capon波束形成方位谱的基础上，提出了一种归一化加权Capon波束形成的改进算法，并给出了方位谱的表达式。本方法不需要特征分解，并且得到的是通常意义上的功率谱(可用于估计信号的能量)。仿真计算表明，此方法的性能优于Capon法，可大大提高方位估计的精度。