UNSTEADY/STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

多重三棱柱网格法计算不可压Navier-Stokes方程

描述了三棱柱半结构网格的细化及多重三棱柱网格的生成方法 ,采用有限体积法在三棱柱网格上离散求解雷诺平均三维不可压Navier Stokes方程。并将该方法应用于简化车身模型的外流气动特性计算中 ,其数值计算结果和实验结果具有合理的一致性。

使用Navier－Stokes方程叶栅粘性反问题的数值解

本文发展了一种解叶栅粘性流动反问题的新的数值方法。使用非正交曲线坐标与相应的非正交速度分量下的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，计算直接在物理平面上实现。本方法规定叶面的压力系数分布反求叶型，ＭａｃＣｏｒｍａｒｋ显式时间推进算法和Ｂａｌｄｗｉｎ－Ｌｏｍａｘ湍流模型被使用，计算中叶片表面将随时间步有规律地移动直至迭代达到收敛。

三维Navier-Stokes方程的有限元分析

流体力学中,由于所建立的控制方程一般是非线性的,很难用解析法或数值法求解.Navier-Stokes方程是流体力学中一类很重要的数学物理方程,要得到它的解析解甚至是数值解都很困难.推导了三维Navier-Stokes方程的有限元公式,并用ANSYS8.0软件对动脉血管中血液流动进行了数值模拟分析.

与密度相关的Navier-Stokes方程的数值模拟

利用有限差分理论,研究了二维与密度相关的非定常不可压缩常粘性的Navier-Stokes方程的数值理论,模拟了流场动态形式,得到相关的流场图.

基于线性化Navier-Stokes方程二维水槽内单涡到双涡的数值模拟

建立了Navier-Stokes方程的预估-校正有限差分方法,在此基础上求得了二维水槽内部单涡到双涡的数值解,所得结果与前人的数值结果和解析解吻合很好.数值模拟结果表明,自由振动运动中自由面波高因粘性作用会发生衰减,且Reynolds数越大衰减越缓慢.在短时间内倾斜加速度激励下对于不同Reynolds数会出现一定周期的单涡.经过长时间的倾斜激励,水槽内涡场由单涡变化成双涡,而且只在较低的Reynolds数条件下出现双涡.

求解二维Navier-Stokes方程的修正NLG方法的一个数值实现

考虑修正NLG(一种变模形式非线性Galerkin)方法求解二维Navier-Stokes方程的 全离散形式,通过一个例子的数值实现,按几种不同形式作了计算,数值算例表明了在不损失精 度的情况下,修正NLG方法于CPU耗时方面有明显的节省。

定常NAVIER-STOKES方程的一类非协调元解法

本文考虑了Navier-Stokes方程的一个新的变分形式应用于一类非协调元的情形,并给出了在本文所定义意义下的最优误差估计。

应用Darcy-Stokes方程求解缝洞型介质的渗透率

在对碳酸盐岩储层渗透率进行定量计算和预测时,目前主要采用多重介质模型对该类油气层进行数值模拟,但存在大洞穴、大裂缝不适合作为连续介质处理,大洞穴的等效渗透率难以确定等问题,因此,使用了一种更精细的求取缝洞型介质渗透率的方法:在微观尺度上,用Stokes方程模拟流体在缝洞中的流动特性,用Darcy定律模拟岩石基质中流体的渗流特性,在它们的界面利用Beavers-Joseph-Saff man边界条件,建立了Darcy-Stokes方程。在此基础上,构建了3个二维缝洞型介质的概念模型,应用区域分解算法计算了概念模型的渗透率,并用解析方法进行了验证,结果表明,该计算方法与解析方法相吻合。最后讨论了孔洞形状、裂缝张开度对渗透率的影响,计算结果表明,裂缝张开度是影响缝洞型介质渗透率的最重要的因素。

Numerical Simulation on Hydraulic Performances of Quarter Circular Breakwater

Quarter circular breakwater （QCB） is a new-type breakwater developed from senti-circular breakwater （SCB）. The superstructure of QCB is composed of a quarter circular front wall, a horizontal base slab and a vertical rear wall. The width of QCB＇ s base slab is about half that of SCB, which makes QCB suitable to be used on relatively finn soil foundation. The numerical wave flume based on the Reynolds averaged Navier-Stokes equations for impressible viscosity fluid is adopted in this paper to simulate the hydraulic performances of QCB. Since the geometry of both breakwaters is similar and SCB has been studied in depth, the hydraulic performances of QCB are given in comparison with those of SCB.

A NUMERICAL AND ANALYTICAL STUDY ON A TAIL-FLAPPING MODEL FOR FISH FAST C-START

The force production physics and the flow control mechanism of fish fast C-start are studied numerically and theoretically by using a tail-flapping model.The problem is simplified to a 2-D foil that rotates rapidly to and fro on one side about its fixed leading edge in water medium.The study involves the simulation of the flow by solving the two-dimensional unsteady incompressible Navier- Stokes equations and employing a theoretical analytic modeling approach.Firstly,reasonable thrust magnitude and its time history are obtained and checked by fitting predicted results coming from these two approaches.Next,the flow fields and vortex structures are given,and the propulsive mechanism is interpreted.The results show that the induction of vortex distributions near the trailing edge of the tail are important in the time-averaged thrust generation,though the added inertial effect plays an important role in producing an instant large thrust especially in the first stage.Furthermore,dynamic and energetic effects of some kinematic controlling factors are discussed.For enhancing the time- averaged thrust but keeping a favorable ratio of it to time-averaged input power within the limitations of muscle ability,it is recommended to have a larger deflection amplitude in a limited time interval and with no time delay between the to-and-fro strokes.

Numerical Simulation of Irregular Wave Overtopping Against A Smooth Sea Dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model, a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes. Simulations of fully nonlinear standing wave and regular wave＇s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules. To model stationary ergodic stochastic processes, several cases with different random seeds are computed for each specified irregular wave spectrum. It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas, other numerical results and experimental data.

Numerical Model of Internal Solitary Wave Evolution on ImpermeableVariable Seabed in A Stratified Two-Layer Fluid System

In the present study a numerical model developed by Lynett and Liu （2002） is modified to include density difference in a stratified two-layer fluid in a three-dimensional internal wave domain. The internal solitary wave （ISW） in the model is assumed to be weakly nonlinear and weakly dispersive, and the viscosity effects at all boundaries are ignored. The governing equations based on the Navier-Stokes and Euler equations are solved for internal solitary wave propagation over variable seabed topography. Theoretical formulations are established, from which analytical solutions are obtained, in addition to numerical results. Wave profiles from previous experimental studies are compared with the numerical results from the present analytical solutions. Numerical models developed on the basis of the present analytical solutions are better than those developed by Lynett and Liu （2002）. The results of numerical modeling agree well with the experimental data.

Vibration analysis of hydropower house based on fluid-structure coupling numerical method

By using the shear stress transport （SST） model to predict the effect ot random now motion in a fluid zone, and using the Newmark method to solve the oscillation equations in a solid zone, a coupling model of the .powerhouse and its tube water was developed. The effects of fluid-structure interaction are considered through the kinematic and dynamic conditions applied to the fluid-structure interfaces （FSI）. Numerical simulation of turbulent flow through the whole flow passage of the powerhouse and concrete structure vibration analysis in the time domain were carried out with the model. Considering the effect of coupling the turbulence and the powerhouse structure, the time history response of both turbulent flows through the whole flow passage and powerhouse structure vibration were generated. Concrete structure vibration analysis shows that the displacement, velocity, and acceleration of the dynamo floor respond dramatically to pressure fluctuations in the flow passage. Furthermore, the spectrum analysis suggests that pressure fluctuation originating from the static and dynamic disturbances of hydraulic turbine blades in the flow passage is one of the most important vibration sources.

Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method

A two-dimensional （2D） numerical model is developed for the wave sim- ulation and propagation in a wave flume. The fluid flow is assumed to be viscous and incompressible, and the Navier-Stokes and continuity equations are used as the governing equations. The standard k-e model is used to model the turbulent flow. The Navier- Stokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell （SMAC） method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of the numerical flume. Some standard tests, such as the lid-driven cavity, the constant unidirectional velocity field, the shearing flow, and the dam-break on the dry bed, are performed to valid the model. To demonstrate the capability and accuracy of the present method, the results of generated waves are compared with available wave theories. Finally, the clustering technique （CT） is used for the mesh generation, and the best condition is suggested.

Numerical Simulation of Solitary Wave Forces on A Vertical Cylinder on A Slope Beach

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves.Based on the Reynolds-averaged Navier-Stokes equations and the k-ε turbulence model,wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations.The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy.Then,the wave forces and characteristics around the cylinder are studied,including the velocity field,wave surface elevation and pressure.The effects of relative wave height,Keulegan-Carpenter(KC)number and cylinder locations on the wave forces are also discussed.The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number.Before the wave force peaks,the growth rate of the wave force shows an increasing trend as the cylinder moves onshore.The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region.As the cylinder moves onshore,the wave force on the cylinder initially increases and then decreases.For the cases considered here,the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline.Furthermore,the fluid velocity peaks when the maximum wave force appears at the same location.

Numerical Simulation of Tidal Current in a Bay

Based on the multilevel model, numerical calculations of tidal current affected by the M-2 tide in the Tokyo Bay have been carried out. The results of calculation are compared with the data observed in the Tokyo Bay and the result calculated by an approximate formula as the Tokyo Bay is regarded as a rectangular bay, and good agreement is found. It is proved that the mathematical model and the calculation method are correct and useable.

NUMERICAL SIMULATION OF THREE DIMENSIONAL INTERACTING TURBULENCE FLOW FIELD OVER PROJECTILE WITH LATERAL JETS

In order to study complicated interacting flow field over projectile with lateral jets. External interacting turbulence flow over projectile with lateral jets was numerically simulated firstly in supersonic speed and zero attack angle. The three dimensional Reynolds averaged Navier Stokes equations and implicit finite volume TVD scheme were applied. In order to avoid zonal method, ’O’ type grid of single zone including projectile base was produced by algebraic arithmetic. Body fitted grid was generated for the lateral nozzle exit successfully so that the nozzle exit can be simulated more accurately. The high Reynolds number two equation κ ε turbulence models were used. The main features of the complex flow are captured. The two kinds of flow field over projectile with and without lateral jets are compared from shock structure, pressure of body and base, etc . It shows that lateral jets not only can provide push force, but also change aerodynamics characteristic of projectile significantly. The results are very important for the study of projectile with lateral rocket boosters.

An Analytical Solution to Neumann-Type Mixed Boundary Poiseuille Microfluidic Flow in Rectangular Channel Cross-Sections (Slip/No-Slip) including a Numerical Technique to Derive It

In most microfluidic applications, pressure-driven Poiseuille flow in a contained cross-section with no-slip boundary conditions is the underlying fluid-mechanical model. Solutions for this problem exist for many known cross-sections. We have recently demonstrated a simple method to solve the relevant Poisson equation using a finite difference scheme in a spreadsheet analysis tool such as Microsoft Excel. The numerical solutions obtained from such a spreadsheet are close-to-exact to the analytical solutions with errors on the order of only a few percent. However, there are numerous applications in microfluidics for which the no-slip boundary condition is not valid. Examples include drag-reducing air-retaining surfaces as well as open-channel flow. For these scenarios few to no analytical models exist. In this paper, we derive an analytical model for mixed boundary conditions (slip/no-slip) in two dimensions in a rectangular channel cross-section. We also demonstrate that the equivalent numerical solution can be derived conveniently by adaption of the spreadsheet. In general, mixed boundary-type flow scenarios are especially difficult to solve analytically whereas numerical solutions can be derived using Microsoft Excel within seconds.