计算有弥散和吸附的径向渗流问题的局部化间断Galerkin方法

在Corkburn和Shu新近发展的求解对流扩散方程的局部化间断Galerkin方法的基础上,针对有弥散和吸附的径向渗流问题中出现的推广的对流扩散方程的形式,构造了一种计算有弥散和吸附的径向渗流问题的局部化间断Galerkin有限元方法,为径向渗流问题的求解提供了一个高阶的新方法．对对流-弥散和对流-弥散-吸附两种情况进行了数值实验, 所得结果的相应部分与已知的一些精确解结果和数值结果是一致的,表明方法是可靠的．从计算速度上看,方法也是可行的．     

Three-dimensional numerical simulation of nonisotropic thermal density flow in a strongly curved open channel

The results from a 3D nonisotropic algebraic stress/flux turbulence model are presented to investigate the structure of thermal density flow and the temperature distribution in a strongly curved open channel (180° bend). The numerically simulated results show that (i) several secondary flows take place at the bend cross-section 90° of the curved open channel, the feature which is not found for the isothermal flows and thermal density flow in a straight channel, and (ii) the thermocline in a curved channel is thicker than that in a straight channel due to the secondary flows-induced strong mixing process taking place in the former. Such features may be ascribed to the complex interaction of the buoyant force, the centrifugal force and the Reynolds stresses taking place only in curved channels. The simulated results are in good agreement with available experimental data, which indicates that the developed model can be applied for predicting the motion of the nonisotropic thermal density flow in the curved open channel.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

Two dimension-curvilinear grid for open channel flow simulation

A mathematical model for two-dimensional flow simulation in an open channel is developed. The model is obtained through the use of a stretched curvilinear grid which defines points where velocity and surface elevation are simulated. Simulation is achieved by numerically integrating the Navier-Stokes mass and momentum equations using centred finite difference approximations of derivatives. The model uses an implicit discretization scheme, the Newton-Raphson iterative technique and a customized Gauss elimination solving algorithm. The computer program developed for this model was tested for uniform, non-uniform and unsteady flow conditions. The results have been found consistent with theoretical solutions and/or field measurements. Limitation and verification of the model is also outlined.     

浅水回流的混合有限分析解

混合有限分析法是一种在局部矩形单元上进行离散的数值格式,为了适应非规则边界,建立了Sigma坐标系的浅水回流数学模型。采用1)风引起的回流,2)密度驱动的回流,3)假潮,来检验数学模型和数值方法。计算结果和相应的分析解的比较表明模型和方法是可行的有效的。该技术可用于近海水域的水流和水质的数值模拟。     

Numeric modeling of thermal pollution in Plomin bay area

In order to analyze the thermal pollution of the Plomin bay induced by the used cooling water released from Plomin 1 and Plomin 2 thermal power plants, flow simulations and temperature field analysis were conducted. The measurements of the bay surface temperature field were carried out as well as the corresponding 3D water flow simulations on the realistically modeled bay. The accuracy of the simulation results was evaluated by the comparison of computed and measured surface temperatures. Furthermore, numerical meshes of different density were used in order to determine model sensitivity where the results showed a significant effect of the mesh density on the simulation results. Although the simulations obtained with a denser mesh yield more accurate results and allow for the reconstruction of heated water surface flow with better reliability, the sparser mesh provided sufficiently accurate results as well. The overall temperature field obtained with the numerical model agrees well with the measured temperature values, which demonstrates the successful application of the 3D flow numerical model on the Plomin bay thermal pollution problem.      

The effect of actuator parameters on the critical flow velocity of a fluidic amplifier

The effect of actuator parameters on the critical flow velocity of the fluidic amplifier in liquid-jet hammers has been investigated numerically and experimentally. The flow in the fluidic amplifier and actuators coupled with the rigid body movement of the impacting body has been simulated using a commercial CFD software package, Fluent. The flow is modeled by the RNG-based κ–ε turbulence model and the incompressible Navier–Stokes equations. Dynamic layering method and a user-defined function written in C programming language are used to update the mesh in the simulations. The results show that, increasing the piston diameter decreases rapidly the critical flow velocity as the piston diameter is less than a certain value. The critical flow velocity increases sharply as the piston rod diameter is greater than a certain value, and increases nearly linearly with mass of the impacting body, and is independent on stroke length of the impacting body. The findings of the numerical investigations agree well with corresponding experimental results.     

A new composite scheme for two-layer shallow water flows with shocks

This paper is devoted to solve the system of partial differential equations governing the flow of two superposed immiscible layers of shallow water flows. The system contains source terms due to bottom topography, wind stresses, and nonconservative products describing momentum exchange between the layers. The presence of these terms in the flow model forms a nonconservative system which is only conditionally hyperbolic. In addition, two-layer shallow water flows are often accompanied with moving discontinuities and shocks. Developing stable numerical methods for this class of problems presents a challenge in the field of computational hydraulics. To overcome these difficulties, a new composite scheme is proposed. The scheme consists of a time-splitting operator where in the first step the homogeneous system of the governing equations is solved using an approximate Riemann solver. In the second step a finite volume method is used to update the solution. To remove the non-physical oscillations in the vicinity of shocks a nonlinear filter is applied. The method is well-balanced, non-oscillatory and it is suitable for both low and high values of the density ratio between the two layers. Several standard test examples for two-layer shallow water flows are used to verify high accuracy and good resolution properties for smooth and discontinuous solutions.     

Numerical investigation of the effect of helix angle and leaf margin on the flow pattern and the performance of the axial flow cyclone separator

A two-stage turbulence model based on the RNG κ–ε model combined with the Reynolds stress model is developed in this paper to analyze the gas flow in an axial flow cyclone separator. Five representative simulation cases are obtained by changing the helix angle and leaf margins of the cyclone. The pressure field and velocity field of the five cases are simulated, and then the effects of helix angle and leaf margins on the internal flow field of the cyclone are analyzed. When the continuum fluid (air) flow is relatively convergent, the discrete particle phase is added into the continuous phase and the gas-solid two-phase flow is simulated. One-way coupling method is used to solve the two-phase flow and a stochastic trajectory model is implemented for simulation of the particle phase. Finally, the pressure drop and separation efficiency of one case are measured and compare quantitatively well with the numerical results, which validates the reliability and accuracy of the simulation method based on the two-stage turbulence model.     

A new spectral-homotopy analysis method for solving a nonlinear second order BVP

A modification of the homotopy analysis method (HAM) for solving nonlinear second-order boundary value problems (BVPs) is proposed. The implementation of the new approach is demonstrated by solving the Darcy–Brinkman–Forchheimer equation for steady fully developed fluid flow in a horizontal channel filled with a porous medium. The model equation is solved concurrently using the standard HAM approach and numerically using a shooting method based on the fourth order Runge–Kutta scheme. The results demonstrate that the new spectral homotopy analysis method is more efficient and converges faster than the standard homotopy analysis method.     

高精度隐式参差光滑格式的构造

参照Lax-Wendroff格式的构造方法,就双曲型方程、抛物型方程和双曲-抛物型方程,构造了一种新的IRS(implicit residual smoothing)格式。该IRS格式有二阶或三阶时间精度且大大地拓宽了解的稳定区域和CFL数。这种新的IRS格式有中心加权型和迎风偏向型两种,并用von-Neumann分析方法分析了格式的稳定范围。讨论了在透平机械中广泛应用的Dawes方法的局限性,发现该方法对稳态问题得出的解与时间步长的选取有关,对粘性问题求解时,时间步长受严格限制。最后,结合TVD(total variation diminishing)格式和四阶Runge-Kutta技术,用IRS格式和Dawes方法对二维反射激波场进行了数值模拟,数值结果支持本文的分析结论。     

Optimal routing of vehicles with communication capabilities in disasters

Major emergencies and disasters such as acts of terrorism, acts of nature, or human-caused accidents may lead to disruptions in traffic flow. Minimizing the negative effects of such disruptions is critical for a nation’s economy and security. A decision support system that is capable of gathering (real-time) information about the traffic conditions following a disaster and utilizing this information to generate alternative routes for vehicles would benefit the government, industry, and the public. For this purpose, we develop a mathematical programming model to minimize the delay for vehicles with communication capabilities following a disaster. Most commercial trucks and public buses utilize QUALCOMM as a communication tool. We also develop a prediction model for vehicles that do not have any communication capabilities. Although the problem is inherently integer we developed a linear program to reduce the computational burden caused by the large size of the problem. An algorithm is proposed to update the parameters of the linear program based on a duality analysis in order to obtain better results. A monotonic speed–density relationship is embedded in the model to capture high traffic congestion that occurs after a disaster. The model and the algorithm are tested using a simulated disaster scenario. The results indicate that the proposed model improves system performance measures such as mobility and average speed.     

Operator splitting for the numerical solution of free surface flow at low capillary numbers

Free surface flows are pervasive in engineering and biomedical applications. In many interesting cases—particularly when small length scales are involved—surface forces (capillarity) dominate the flow dynamics. In these cases, computing the flow together with the shape of the surfaces, requires specialized solution techniques. This article investigates the capabilities of an operator splitting/finite elements method at handling accurately incompressible viscous flow with free surfaces at low capillary numbers. The test case of flow in the downstream section of a slot coater is used for three reasons: (1) it is an established benchmark; (2) it represents an idealized, yet industrially relevant flow; (3) high-fidelity results obtained with monolithic algorithms are available in literature. The flow and free surface shape attained with the new operator splitting scheme agree very satisfactorily with the results obtained with monolithic solvers. Because of its inherent computational simplicity, the new operator splitting scheme is attractive for large-scale simulations, three-dimensional flows, and flows of complex fluids.     

A class of distributed optimization methods with event-triggered communication

We present a class of methods for distributed optimization with event-triggered communication. To this end, we extend Nesterov’s first order scheme to use event-triggered communication in a networked environment. We then apply this approach to generalize the proximal center algorithm (PCA) for separable convex programs by Necoara and Suykens. Our method uses dual decomposition and applies the developed event-triggered version of Nesterov’s scheme to update the dual multipliers. The approach is shown to be well suited for solving the active optimal power flow (DC-OPF) problem in parallel with event-triggered and local communication. Numerical results for the IEEE 57 bus and IEEE 118 bus test cases confirm that approximate solutions can be obtained with significantly less communication while satisfying the same accuracy estimates as solutions computed without event-triggered communication.     

Lattice hydrodynamic model of pedestrian flow considering the asymmetric effect

The original lattice hydrodynamic model of traffic flow is extended to single-file pedestrian movement at middle and high density by considering asymmetric interaction (i.e., attractive force and repulsive force). A new optimal velocity function is introduced to depict the complex behaviors of pedestrian movement. The stability condition of this model is obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the pedestrian phase transitions. The modified Korteweg-de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method, and its kink-antikink soliton solution can better describe the stop-and-go phenomenon of pedestrian flow. From the density profiles, it can be found that the asymmetric interaction is more efficient than the symmetric interaction in suppressing the pedestrian jam. The numerical results are consistent with the theoretical analysis.     

Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.     

A two-dimensional intake manifold flow simulation

A computer flow model of an intake manifold of a four cylinder engine has been developed using a computational fluid dynamic code. This code is base on the Conchas-Spray code developed at the Los Alamos National Laboratory. The flow inside the intake manifold is assumed to be two-dimensional, unsteady, compressible, and turbulent. A simple subgrid scale (SGS) turbulence model and hypothetical boundary conditions are employed in the simulation. Atmospheric pressure is specified at the inlet and the velocities are specified at the outlets of the manifold, together with the law of the wall at all the wall boundaries. Numerical results of the simulation are presented in the form of velocity, pressure, density, and temperature fields. The model is designed in such a way that different manifold geometries may be simulated with ease. A simulation of a concept manifold “the loop-manifold” is also presented.     

Recursive prediction of chaotic time series

Summary Considerable progress has been made in recent years in the analysis of time series arising from chaotic systems. In particular, a variety of schemes for the short-term prediction of such time series has been developed. However, hitherto all such algorithms have used batch processing and have not been able to continuously update their estimate of the dynamics using new observations as they are made. This severely limits their usefulness in real time signal processing applications. In this paper we present a continuous update prediction scheme for chaotic time series that overcomes this difficulty. It is based on radial basis function approximation combined with a recursive least squares estimation algorithm. We test this scheme using simulated data and comment on its relationship to adaptive transversal filters, which are widely used in conventional signal processing.     

An improved scheme for accelerating the convergence of the simulated annealing algorithm applied to real world problems

When formulated in mathematical terms, the problem of zoning a protected natural area subject to both box and spatial constraints results in a large combinatorial optimization problem belonging to the NP-hard class. These facts suggest the need to apply a heuristic approach. In this contribution a new proposal to decrease the control parameter, known as temperature, in the simulated annealing algorithm is presented. The strategy is based on that proposed by Lundy and Mees [4], and developed in order to decrease the running time of the algorithm applied to large scale problems. When applied to solving small-size simulated problems, results were indistinguishable from those obtained via an exact, enumerative method. A coarse-scale zoning of Talampaya National Park (Argentina) rendered maps remarkably similar to those produced by subject area experts using a non-quantitative consensus-seeking approach. Results are encouraging and show particular potential for the periodical update of zoning of protected natural areas. Such a capability is crucial for application in developing countries where both human and financial resources are usually scarce but still critical for updating zoning and management plans. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A three-dimensional fluid flow model for puddle formation in the single-roll rapid solidification process

The single-roll rapid solidification process (SRRSP) is considered to be a process of perspective to produce a Fe-Si-B ribbon of amorphous microstructure and near net shape products such as thin strips of stainless steel. The condition of a melt puddle between the nozzle and rotating wheel in the single-roll rapid solidification process significantly affects the quality and dimensional uniformity of the products as well as the smoothness of the operation. The purpose of this study was to develop a three-dimensional fluid flow analysis system to model the formation of puddle and flow conditions of molten metal in the puddle for the single-roll rapid solidification processes which include the planar flow casting (PFC) process and the single-roll strip casting process. The model is based on a computational fluid dynamics technique called the SOLA-VOF scheme, which possesses the capability of treating transient fluid flow problems with the evolution of free boundaries. Furthermore, the SOLA-VOF scheme is extended from two dimensions to three dimensions. The simulated results reveal how the melt puddle is formed between the nozzle and the rotating substrate and its corresponding fluid flow behavior for the PFC process as well as the single-roll strip casting process. The test results also demonstrate that two-dimensional analysis cannot properly consider the actual flow condition in the puddle.