再入体头部粘性流场高分辨率格式数值模拟

TVD格式是目前数值研究以激波为主要特征之一的超声速、高超声速流场的最先进的算法之一。本文用二阶迎风TVD格式,对三种烧蚀外形的轴对称粘性流场和10°钝锥有攻角三维粘性流场进行了数值模拟,得到了高质量的头部脱体激波和与实验结果及直线推进法计算一致的物面压力分布,表明了TVD格式在再入体粘性绕流计算中的独特优势。     

振荡机翼跨音速非定常粘性绕流的数值计算

以非定常Ｎ－Ｓ方程为主管方程，采用ＬＵ－ＮＮＤ混合差分格式，Ｃ和Ｃ－Ｈ型贴体运动网格，Ｂ－Ｌ双层代数紊流模型，求解绕振荡翼型和三维机翼的跨音速非定常粘性流场，分别计算了ＮＡＣＡ００１２翼型和Ｍ６机翼作俯仰振荡时跨音速非定常粘性绕流流场。研究了非定常绕流的气动特性，部分计算结果和风洞实验值作了比较。     

高精度格式WCNS-E-5计算物面热流

采用加权紧致非线性格式WCNS-E-5,四阶精度的二阶导数差分近似以及四阶精度的边界格式构造了高精度算法,对高超声速粘性流动的物面热流进行数值研究.首先考察了壁面网格雷诺数对驻点热流的影响,然后开展了边界格式对热流计算结果影响的研究,最后对大攻角钝锥绕流进行了数值模拟.研究结果表明:WCNS-E-5能降低边界层内网格分辨率,全场高精度的WCNS-E-5计算得到的流场图像清晰、真实、分辨率高,热流值准确、可靠.     

钝锥绕流流动稳定性分析与转捩预报

研究了超音速钝锥绕流的稳定性和转捩点预报的数值计算方法,首先采用Euler方程求解钝锥绕流基本流场,用所得到的物面压力分布作为粘性边界层的外缘压力分布,给出了基本流场的初值;然后应用反迭代法与边界层渐近匹配的方法求解了钝锥边界层的稳定性方程,得到了钝锥边界层转捩数据.该方法可提高计算精度,节约计算时间.     

多重散射展开方法应用于电子-氢原子弹性散射角分布的计算

本文将文献[1]中提出的方法应用于电子-氢原子弹性散射角分布的计算。对所得结果作了讨论,并与实验数据作了比较,符合程度比较好。     

一个高压比离心叶轮的CFD结果确认

本文采用NUMECA的FINE/Turbo软件包数值分析了一个高压比离心叶轮的三维定常粘性流场。选用二阶精度的中心格式和Spalart-Allmaras的一方程湍流模型。通过与现有实验结果(包括性能曲线、外环壁静压和截面马赫数分布等)的比较对计算结果就行了详细的确认,同时讨论了网格密度和间隙尺度、以及不同的数据处理方法对计算结果确认的影响。     

多重散射展开方法应用于正电子-氢原子的弹性散射角分布的计算

将文献[1]提出的多重散射展开方法用来计算正电子-氢原子的弹性散射角分布。对结果作了讨论,并与其他作者的结果作了比较。结果表明,多重散射展开方法的数值计算相当简单,而精确度又与其它较为复杂的方法相当。     

柱二维内电磁脉冲的自洽计算方法(Ⅲ)

本文是[1]、[2]两篇的续篇,也是这一工作的最后一篇。其主要内容是用拉格朗日方法求解初级电子数方程组,同时给出用PIC方法、欧拉方法和该方法的数值计算结果。并把这些计算结果同非自洽方法的计算结果作了比较。当场强比较高(E>10⁵V/m)时,自洽方法自身的计算结果比较接近。当场强比较低(E≤10⁵V/m)时,两类方法的计算结果符合较好。     

一个带人工粘性的中心差分格式及其在跨音速涡轮叶栅绕流计算中的应用

为了把时间相关法应用到跨音速涡轮叶栅绕流问题的工程计算中去,本文提出了一种带人工粘性的中心差分格式。逐步减小人工粘性,解的精度有相当程度的提高。试算表明当人工粘性系数降低到0.02左右时,计算结果与理论解和实验结果相当吻合,完全能满足工程设计和计算的要求。     

平面定常超音速绕流问题的新的数值解法

用特征线法解平面定常超音速绕流问题虽然有效,但当激波很弱、几乎与特征线平行时则很难处理。用有限差分法计算此问题也比较复杂。本文把作者在文章中^[1]提出的新的数值解法,发展并应用到平面定常超音速绕流的问题。仍然采用了许为厚教授提出的新拉格朗日变量^[2],这使边界条件的提法大为简化。此新的数值解法按变量指标之和,一排排地往下计算,方法简单,可以处理各种形状物体的超音速绕流。本文对向上弯曲的抛物形固壁绕流向题的实例进行了具体计算。算出了激波的形状。当激波没有形成以前,相应的普朗特一迈耶气流是有准确分析解的,把数值解与准确解进行了l比较结果是满意的。     

On the kinetic theory of vehicular traffic flow: Chapman–Enskog expansion versus Grad’s moment method

Based on a Boltzmann-like traffic equation for aggressive drivers we construct in this paper a second-order continuum traffic model which is similar to the Navier–Stokes equations for viscous fluids by applying two well-known methods of gas-kinetic theory, namely the Chapman–Enskog method and the method of moments of Grad. The viscosity coefficient appearing in our macroscopic traffic model is not introduced in an ad hoc way–as in other second-order traffic flow models–but comes into play through the derivation of a first-order constitutive relation for the traffic pressure. Numerical simulation shows that our Navier–Stokes-like traffic model satisfies the anisotropy condition and produces numerical results which are consistent with our daily experiences in real traffic.     

A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207–209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.     

采用高分辨率高精度格式求解跨音压气机转子内三维粘性流场

采用一种新型的ＬＵ隐式算法及４－５阶高分辨率ＴＶＤ格式求解了叶轮机械内的三维Ｎ－Ｓ方程和ｑ－ｗ湍流模型。应用几何法与ＰＤＦ方法混合的网格生成程序,得到了ＲＯＴＲＯ３７跨音速压气机转子内的Ｈ型网格,并将数值模拟的结果同ＬＤＶ实验值进行了比较。     

Algorithms for accurate relativistic particle injection

In particle-in-cell plasma codes, the second-order leap-frog method is used to push the velocity and position of each particle in the main loop. Once a velocity distribution has been inverted for injection, time-centering of the position and velocity is necessary to maintain second-order accuracy. We have set up non-relativistic time-centering algorithms for particle injection in our PIC code. We further developed relativistic time-centering methods for injection and we added methods to calculate higher order accurate position. Also, the algorithms are expanded to find the position and velocity at any specific time from those at the initial discrete time, which can be used not only in the leap-frog method but also any other algorithms.     

Numerical prediction of interfacial instabilities: Sharp interface method (SIM)

We introduce a sharp interface method (SIM) for the direct numerical simulation of unstable fluid–fluid interfaces. The method is based on the level set approach and the structured adaptive mesh refinement technology, endowed with a corridor of irregular, cut-cell grids that resolve the interfacial region to third-order spatial accuracy. Key in that regard are avoidance of numerical mixing, and a least-squares interpolation method that is supported by irregular datasets distinctly on each side of the interface. Results on test problems show our method to be free of the spurious current problem of the continuous surface force method and to converge, on grid refinement, at near-theoretical rates. Simulations of unstable Rayleigh–Taylor and viscous Kelvin–Helmholtz flows are found to converge at near-theoretical rates to the exact results over a wide range of conditions. Further, we show predictions of neutral-stability maps of the viscous Kelvin–Helmholtz flows (Yih instability), as well as self-selection of the most unstable wave-number in multimode simulations of Rayleigh–Taylor instability. All these results were obtained with a simple seeding of random infinitesimal disturbances of interface-shape, as opposed to seeding by a complete eigenmode. For other than elementary flows the latter would normally not be available, and extremely difficult to obtain if at all. Sample comparisons with our code adapted to mimic typical diffuse interface treatments were not satisfactory for shear-dominated flows. On the other hand the sharp dynamics of our method would appear to be compatible and possibly advantageous to any interfacial flow algorithm in which the interface is represented as a discrete Heaviside function.     

A numerical algorithm for viscous incompressible interfacial flows

We present a new algorithm to numerically simulate two-dimensional viscous incompressible flows with moving interfaces. The motion is updated in time by using the backward difference formula through an iterative procedure. At each iteration, the pseudo-spectral technique is applied in the horizontal direction. The resulting semi-discretized equations constitute a boundary value problem in the vertical coordinate which is solved by decoupling growing and decaying solutions. Numerical tests justify that this method achieves fully second-order accuracy in both the temporal variable and vertical coordinate. As an application of this algorithm, we study the motion of Stokes waves in the presence of viscosity. Our numerical results are consistent with the recently published asymptotic solution for Stokes waves in slightly viscous fluids.     

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334–2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.     

Implementation of LDA + Gutzwiller with Newton's method

In order to calculate the electronic structure of correlated materials, we propose implementation of the LDA+Gutzwiller method with Newton's method. The self-consistence process, efficiency and convergence of calculation are improved dramatically by using Newton's method with golden section search and other improvement approaches.We compare the calculated results by applying the previous linear mix method and Newton's method. We have applied our code to study the electronic structure of several typical strong correlated materials, including SrVO_3, LaCoO_3, and La_2O_3Fe_2Se_2. Our results fit quite well with the previous studies.     

多粒子GHZ纠缠实验中Fisher信息的保真度方法获取

保真度与Fisher信息在量子精密测量和量子纠缠判定中充当着非常重要的角色。本文从概率统计和量子力学的角度出发,阐明了两者之间的区别与联系,给出了保真度方法获取Fisher信息的数学表达式;基于量子测量中常见的宇称测量模型,我们对多粒子Greenberger-Horne-Zeilinger (GHZ)纠缠产生实验中Fisher信息的获取开展了保真度方法研究,通过对实验数据的蒙特卡洛模拟,二阶或高阶曲线拟合获取了系统的Fisher信息,并将其与理论计算结果进行对比,结果表明保真度方法可以有效地获取量子系统的Fisher信息,当体系粒子数目较少时,宜采用二阶拟合方法获取系统的Fisher信息,而当粒子数目较多时,需考虑高阶拟合项的影响。此外,我们还将多光子GHZ纠缠实验中Fisher信息的保真度获取结果与海林格距离方法的获取结果进行对比,发现二者是一致的,这也进一步验证了保真度方法获取Fisher信息的有效性。本文的研究也为开展与Fisher信息相关的量子拓扑学和量子相变的研究提供了新的途径。     

一维非定常炸轰的特征线方法数值模拟

本文用特征线方法计算了一维非定常炸轰的发展和传播问题。为模拟炸药的化学反应,采用了一种冲击波引爆的唯象模型。以PBX-9404高级炸药为例给出了计算的POP图与实验结果的比较以及不同时刻波后流场的分布。