Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics

In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.

Numerical Solution of Troesch’s Problem by Sinc-Collocation Method

A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the sinc-collocation method yields better results.

Sniffer Technique for Numerical Solution of Korteweg-de Vries Equation Using Genetic Algorithm

A novel heuristic technique has been developed for solving Ordinary Differential Equation (ODE) numerically under the framework of Genetic Algorithm (GA). The method incorporates a sniffer procedure that helps carry out a memetic search within the solution domain in the vicinity of the currently found best chromosome. The technique has been successfully applied to the Korteweg- de Vries (KdV) equation, a well-known nonlinear Partial Differential Equation (PDE). In the present study we consider its solution in the regime of solitary waves, or solitons that is first used to convert the PDE into an ODE. It is then shown that using the sniffer technique assisted GA procedure, numerical solution has successfully been generated quite efficiently for the one-dimensional ODE version of the KdV equation in space variable (x). The technique is quite promising for its applications to systems involving ODE equations where analytical solutions are not directly available.

Numerical Solution for a Similar Flow between Two Disks in the Presence of a Magnetic Field

Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.

NUMERICAL SOLUTION OF NAVIER-STOKES EQUATION OF UNSTEADY SEPARATED FLOWS DUE TO A SPOILER'S OSCILLATION

The finite difference method (FDM) is applied in the present paper to solve the unsteady NHS equations for incompressible fluids. ADI and SLOR methods are served for the vorticity equation and the Poisson equation for ψ respectively. The upwind scheme is used for the convective terms. The moving boundary conditions are specially treated, and the effects of outlet conditions on the flow field are abo examined. Numerical results obtained show that the spoiler's oscillation induces forming, growing and shedding of the vortices. The shedding frequency of vortices is equal to that of the spoiler's oscillation. The forced unsteady separated flows under the present investigation depend mainly on the reduced frequency. At low reduced frequency, the vortices shed from the spoiler interact weakly with each other, and move downstream at an almost uniform speed of 038 V∞. At high reduced frequency, the interaction between the adjacent vortices strengthens. They close up to and rotate around each other, and eventually, merge into one vortex.

Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J2.

转盘-静盘腔内层流流动的相似分析及其N-S方程数值解

对转盘—静盘系统进行的相似分析表明：转盘—静盘腔内层流流场主要受入口流量数、旋转雷诺数、盘腔间隙系数、密封间隙系数和入口孔径比等５个参数影响。采用ＳＩＭＰＬＥ法对转盘—静盘系统层流流场进行了计算。结果表明：盘腔间隙的大小和密封冠对旋转核的存在具有决定性影响，当入口流量数减小或旋转雷诺数增大时，旋转核趋向于生成且转速增大；证明了影响径向速度的主要是惯性力，而影响周向速度的是惯性力和粘性力共同作用。通过数值计算还得到了防止外燃气“入侵”的最小入口流量数。

非结构网格下涡轮级三维非定常N-S方程的数值解

本文在非结构网格下,采用时间上二阶精度、空间上不低于二阶的高分辨率格式求解涡轮级三维流场,得到了与实验数据大体接近的N-S方程数值解。计算表明:本文所构造的双时间步迭代格式具有稳定、高效的特征。实践显示:本文用FORTRAN与C语言混合编制的N-S方程源程序,可用于涡轮级三维非定常流场计算。

Numerical solutions of Green's integral equation for the diffraction of femtosecond laser pulses through a subwavelength aperture

In this letter, we propose a method for the numerical calculations of the femtosecond laser pulse passed through a subwavelength aperture. The time-dependent laser pulse is decomposed into a series of monochromatic simple harmonic waves. For the light field of the harmonic wave with a single frequency, the numerical calculation is made based on the solution of the Green's integral equation set of the electromagnetic waves. Such numerical solution is iterated for all the waves with different frequencies, and all the numerical solutions are transformed into the light fields in the time domain by inverse Fourier transform. The light intensity distributions transmitted the subwavelength aperture are calculated and the results show the propagation of the light field is along the direction of the medium interface.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio =0.18) with rotating inner and stationary outer spheres are simulated numerically for Reci<Re<1500 1500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775<Re<1220 and three steady stable flows with 0, 1, or 2 vortices for 1 220<Re<l500. The formation of different flows at the same Reynolds number is related with different initial conditions which can be generated by different accelerations of the inner sphere. Generation of asro-or two-vortex flow depends mainly on the acceleration, but that of one-vortex flow also depends on the perturbation breaking the equatorial symmetry. The mechanism of development of a saddle point in the meridional plane at higher Re number and its role in the formation of two-vortex flow are analy2Ed.

余弦微分求积法求解Kuramoto-Sivashinsky方程的数值解

通过用余弦微分求积法(CDQM)对空间的离散,用差分法对时间的离散及Crank-Nicolson(C-N)线性化技术构造了求解Kuramoto-Sivashinsky(K-S)方程的数值格式.通过算例以及与相关文献的比较,结果表明:该算法精确度高,适应性强,适合时间较长的非线性演化过程.

3-RSS/S并联机构位姿误差的数值分析方法

位姿精度是机构的重要性能指标,也是并联机构结构分析的难点之一。针对在3-RSS/S并联机构误差分析中采用全微分方法忽略高次项会使精度下降的问题,提出采用数值分析的方法来研究位姿误差:基于逆向运动学模型,通过不含误差的机构尺寸参数进行逆解计算,得出机构的输入参数;基于正向非线性运动学模型,以原姿态角作为迭代初值,计算出包含误差时的动平台末端姿态,进而计算出位姿误差;根据设定的误差源分布规律,基于蒙特卡洛方法随机生成机构尺寸参数的误差,计算得到位姿误差的分布规律;遍历整个工作空间,得到位姿误差在整个工作空间中的数字特征值与分布规律。通过三维建模方法验证了数值计算的正确性,通过算例验证了该方法的可行性与有效性,为3-RSS/S并联机构的精度研究奠定了基础。

Stokes'first problem for the fourth order fluid in a porous half space

In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy＇s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed.

An improved method to assess the required strength of cemented backfill in underground stopes with an open face

Backfill is increasingly used in underground mines to reduce the surface impact from the wastes produced by the mining operations. But the main objectives of backfilling are to improve ground stability and reduce ore dilution. To this end, the backfill in a stope must possess a minimum strength to remain self-standing during mining of an adjacent stope. This required strength is often estimated using a solution proposed by Mitchell and co-workers, which was based on a limit equilibrium analysis of a wedge exposed by the open face. In this paper, three dimensional numerical simulations have been performed to assess the behavior of the wedge model. A new limit equilibrium solution is proposed, based on the backfill displacements obtained from the simulations. Comparisons are made between the proposed solution and experimental and numerical modeling results. Compared with the previous solution, a better agreement is obtained between the new solution and experimental results for the required cohesion and factor of safety. For large scale(field) conditions, the results also show that the required strength obtained from the proposed solution corresponds quite well to the simulated backfill response.

用N－S方程求解跨声速涡轮叶栅流场

用时间相关Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的数值方法来预测跨声速涡轮叶栅流场。基于分裂运算技术导出了一种新的压力速度耦合算法。方程的离散化在非交错网格上进行，方程用无迭代的时间推进方式求解。湍流用带壁面函数的κ－ε模型。对一短弦长涡轮导向叶栅和一高转折涡轮叶栅作出了计算。计算与试验结果吻合良好。

High precision approximate analytical solutions to ODE using LS-SVM

The problem of solving differential equations and the properties of solutions have always been an important content of differential equation study. In practical application and scientific research,it is difficult to obtain analytical solutions for most differential equations. In recent years,with the development of computer technology,some new intelligent algorithms have been used to solve differential equations. They overcome the drawbacks of traditional methods and provide the approximate solution in closed form( i. e.,continuous and differentiable). The least squares support vector machine( LS-SVM) has nice properties in solving differential equations. In order to further improve the accuracy of approximate analytical solutions and facilitative calculation,a novel method based on numerical methods and LS-SVM methods is presented to solve linear ordinary differential equations( ODEs). In our approach,a high precision of the numerical solution is added as a constraint to the nonlinear LS-SVM regression model,and the optimal parameters of the model are adjusted to minimize an appropriate error function. Finally,the approximate solution in closed form is obtained by solving a system of linear equations. The numerical experiments demonstrate that our proposed method can improve the accuracy of approximate solutions.

Navier’s slip condition on time dependent Darcy-Forchheimer nanofluid using spectral relaxation method

In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary.

S型铺管的常用数值求解法的探讨

S型铺管法在现阶段海底管道铺设中应用广泛,国内外众多学者对其进行了研究,这些研究给工程应用提供良好的指导。本文分析和总结了国内外在研究S型铺管法时的常用数值求解方法。

三维电磁响应积分方程法数值模拟

从电磁基本理论出发，深入研究了均匀导电半空间频域三维电磁散射问题，由张量格林函数求解Ｆｒｅｄｈｏｌｍ方程，将异常体划分为一系列立方单元，并将该积分方程转化为矩阵方程，从而计算出空间任意点的电场和磁场；此外，还给出了计算实例，并与国外结果进行分析对比，证明作者运用的计算方法结果正确，算法快速．

高精度弯管流量计的理论研究和实验验证

通过求取N-S方程数值解的方法对弯管流量计进行理论研究，得出其测量准确度不仅与传感器自身的管径、曲率半径、弯径比、压力测点位置等几何结构尺寸的准确度有关，而且还与测量使用的条件有关。特别是弯管流量计与前后直管段产生的安装偏转角、直管段管径与其自身管径的一致性等环境应用条件会对弯管流量计的高精度使用产生影响。针对上述影响因素，通过对用整体数控加工的、自身带有直管段的弯管流量计进行反复实验，结果表明：在2σ准则下，弯管流量计可以达到0．5％的测量准确度水平；不同管径情况下，流量系数也具有良好的一致性。