物理计算的保真与代数动力学算法——Ⅲ.辛代数动力学算法

在常微分方程的代数动力学精确解的基础上,对Hamilton系统,设计出保持局域辛几何结构的各阶代数动力学算法-辛代数动力学算法.讨论了辛代数动力学算法与辛几何算法和Runge-Kutta算法的关系.对N阶辛代数动力学算法,估计了相空间轨道、运动学变量的代数关系和代数-几何不变量以及动力学守恒量的精度.在6个模型的计算实验中,比较了辛代数动力学算法与辛几何算法,发现四阶辛代数动力学算法比四阶辛几何算法在精度和轨道相位失真两方面都有所改进.

CFD prediction of local scour hole around bridge piers

In order to predict the local scour hole and its evaluation around a cylindrical bridge pier, the computational fluid dynamics （CFD） and theories of sediment movement and transport were employed to carry out numerical simulations. In the numerical method, the time-averaged Reynolds Navier-Stokes equations and the standard k-e model were first used to simulate the three-dimensional flow field around a bridge pier fixed on river bed. The transient shear stress on river bed was treated as a crucial hydrodynamic mechanism when handling sediment incipience and transport. Then, river-bed volumetric sediment transport was calculated, followed by the modification of the river bed altitude and configuration. Boundary adaptive mesh technique was employed to modify the grid system with changed river-bed boundary. The evolution of local scour around a cylindrical bridge pier was presented. The numerical results represent the flow pattern and mechanism during the pier scouring, with a good prediction of the maximum scour hole depth compared with test results.

Riser VIV and its numerical simulation

This paper summarizes some of the typical riser vortex-induced vibration （VIV） problems in subsea oil and gas developments, and presents the corresponding computational fluid dynamics （CFD） time domain simula- tion results to address these problems. First, the CFD time domain simulation approach was applied to analyze the wake field behind a stationary cylinder and a vibrating cylinder. Then a vertical riser VIV response under uniform current was studied. The VIV response time histories revealed some valuable clues that could lead to explanation of the higher harmonics. After that, a vertical riser VIV response under shear current was investigated. A 3 000 ft （1 ft=-0.304 8 m） water depth top tensioned riser was sized, and its VIV responses under uniform and shear current were studied. Then this paper continues to discuss one catenary flexible riser VIV response during normal lay. Last, the time domain simulation approach was applied to a partially submerged flexible jumper, to study the jumper VIV behavior, and dynamic motion envelopes. It was demonstrated that the time domain simulation ap- proach is able to disclose details of the flow field, vortex shedding pattern, and riser dynamic behavior, and han- dle different tvoes of risers under different Woe of currents.

A Fuzzy-based Adaptive Genetic Algorithm and Its Case Study in Chemical Engineering

Considering that the performance of a genetic algorithm （GA） is affected by many factors and their rela-tionships are complex and hard to be described,a novel fuzzy-based adaptive genetic algorithm （FAGA） combined a new artificial immune system with fuzzy system theory is proposed due to the fact fuzzy theory can describe high complex problems.In FAGA,immune theory is used to improve the performance of selection operation.And,crossover probability and mutation probability are adjusted dynamically by fuzzy inferences,which are developed according to the heuristic fuzzy relationship between algorithm performances and control parameters.The experi-ments show that FAGA can efficiently overcome shortcomings of GA,i.e.,premature and slow,and obtain better results than two typical fuzzy GAs.Finally,FAGA was used for the parameters estimation of reaction kinetics model and the satisfactory result was obtained.

Time Collocation Method for Structural Dynamic Problems

In order to achieve highly accurate and efficient numerical calculations of structural dynamics, time collocation method is presented. For a given time interval, the numerical solution of the method is approximated by a polynomial. The polynomial coefficients are evaluated by solving algebraic equation. Once the polynomial coefficients are evaluated, the numerical solutions at any time in the interval can be easily calculated. New formulae are derived for the polynomial coefficients,which are more practical and succinct than those previously given. Two structural dynamic equations are calculated by the proposed method. The numerical solutions are compared with the traditional fourth-order Runge-Kutta method. The results show that the method proposed is highly accurate and computationally efficient. In addition, an important advantage of the method is the simplicity in software programming.

Dynamic mathematical model and numerical calculation method on spontaneous combustion of loose coal

Through the experiment of coal spontaneous combustion and relationship particle size with oxidation character of loose coal, some calculation formula of characteristic parameters is got in the process of coal spontaneous combustion. According to these theories of porous medium hydrodynamics, mass transfer and heat transfer, mathematical models of air leak field, oxygen concentration field and temperature field are set up. Through experimental and theoretical analysis, 3 D dynamic mathematical model of coal spontaneous combustion is set up. The method of ascertaining boundary condition of model is analyzed, and finite difference method is adopted to solve 2 D mathematical model.

Crosswind stability of high-speed trains in special cuts

Analysis of the aerodynamic performance of high-speed trains in special cuts would provide references for the critical overturning velocity and complement the operation safety management under strong winds.This work was conducted to investigate the flow structure around trains under different cut depths,slope angles using computational fluid dynamics(CFD).The high-speed train was considered with bogies and inter-carriage gaps.And the accuracy of the numerical method was validated by combining with the experimental data of wind tunnel tests.Then,the variations of aerodynamic forces and surface pressure distribution of the train were mainly analyzed.The results show that the surroundings of cuts along the railway line have a great effect on the crosswind stability of trains.With the slope angle and depth of the cut increasing,the coefficients of aerodynamic forces tend to reduce.An angle of 75°is chosen as the optimum one for the follow-up research.Under different depth conditions,the reasonable cut depth for high-speed trains to run safely is 3 m lower than that of the conventional cut whose slope ratio is 1:1.5.Furthermore,the windward slope angle is more important than the leeward one for the train aerodynamic performance.Due to the shield of appropriate cuts,the train body is in a minor positive pressure environment.Thus,designing a suitable cut can contribute to improving the operation safety of high-speed trains.

Separation Processes of Granular Materials by Sizes at the Sieve Classifiers

A mathematical model of the kinetics of thin-layer separation of granular materials by size stacked sieve classifiers based on the theory of Markov processes is constructed. The probability of screening in a cell in the shape and size of the holes and particle sieve material shared with the influence of the relative speed of their movement was determined. Residues on whole meal with sieves were identified by a kinetic model and numerical calculations, the efficacy of separation.

Numerical method of static aeroelastic correction and jig-shape design for large airliners

In this paper,a coupled CFD-CSD method based on N-S equations is described for static aeroelastic correction and jig-shape design of large airliners.The wing structural flexibility matrix is analyzed by a finite element method with a double-beam model.The viscous multi-block structured grid is used in aerodynamic calculations.Flexibility matrix interpolation is fulfilled by use of a surface spline method.The load distributions on wing surface are evaluated by solving N-S equations with a parallel algorithm.A flexibility approach is employed to calculate the structural deformations.By successive iterations between steady aerodynamic forces and structural deformations,a coupled CFD-CSD method is achieved for the static aeroelastic correction and jig-shape design of a large airliner.The present method is applied to the static aeroelastic analysis and jig-shape design for a typical large airliner with engine nacelle and winglet.The numerical results indicate that calculations of static aeroelastic correction should employ tightly coupled CFD-CSD iterations,and that on a given cruise shape only one round of iterative design is needed to obtain the jig-shape meeting design requirements.

Numerical aerodynamic analysis of bluff bodies at a high Reynolds number with three-dimensional CFD modeling

This paper focuses on numerical simulations of bluff body aerodynamics with three-dimensional CFD(computational fluid dynamics) modeling,where a computational scheme for fluid-structure interactions is implemented.The choice of an appropriate turbulence model for the computational modeling of bluff body aerodynamics using both two-dimensional and three-dimensional CFD numerical simulations is also considered.An efficient mesh control method which employs the mesh deformation technique is proposed to achieve better simulation results.Several long-span deck sections are chosen as examples which were stationary and pitching at a high Reynolds number.With the proposed CFD method and turbulence models,the force coefficients and flutter derivatives thus obtained are compared with the experimental measurement results and computed values completely from commercial software.Finally,a discussion on the effects of oscillation amplitude on the flutter instability of a bluff body is carried out with extended numerical simulations.These numerical analysis results demonstrate that the proposed three-dimensional CFD method,with proper turbulence modeling,has good accuracy and significant benefits for aerodynamic analysis and computational FSI studies of bluff bodies.

Numerical study on the gas-kinetic high-order schemes for solving Boltzmann model equation

The high-order compact finite difference technique is introduced to solve the Boltzmann model equation, and the gas-kinetic high-order schemes are developed to simulate the different kinetic model equations such as the BGK model, the Shakhov model and the Ellipsoidal Statistical (ES) model in this paper. The methods are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the inner flows of normal shock wave for different Mach numbers, and the two-dimensional flows past a circular cylinder and a NACA 002 airfoil to verify the reliability of the present high-order algorithm and simulate gas transport phenomena covering various flow regimes. The computed results are found in good agreement both with the theoretical prediction from continuum to rarefied gas dynamics, the related DSMC solutions, and with the experimental results. The numerical effect of the schemes with the different precision and the different types of Boltzmann collision models on the computational efficiency and computed results is investigated and analyzed. The numerical experience indicates that an approach developing and applying the gas-kinetic high-order algorithm is feasible for directly solving the Boltzmann model equation.

Mechanistic study and kinetic properties of the CF_3CHO+Cl reaction

Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQCISD/3//MP2/cc-pVDZ level and the kinetic calculations were done using variational transition state theory with interpolated single-point energy (VTST-ISPE) approach. The calculated results show that the reaction proceeds primarily via the H-abstraction channel, while the Cl-addition channel is unfavorable due to the higher barriers. The improved canonical variational transition-state theory (ICVT) with the small-curvature tunneling correction (SCT) was used to calculate the rate constants. The theoretical rate constants at room temperature are in general agreement with the experimental values. A three-parameter rate constant expression was fitted over a wide temperature range of 200-2000 K.

Dynamic analysis of a fractional order system

In this paper, we investigate the dynamical behavior of a fractional order phytoplankton- zooplankton system. In this paper, stability analysis of the phytoplankton zooplankton model （PZM） is studied by using the fractional Routh-Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PZM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PZM.