4t阶欧拉方构造方法研究

在 4t幻方构造研究的基础上 ,提出 4t阶欧拉方构造的图表法 ,阐明用图表法构造欧拉方的思路 ,介绍 4、8、1

4t阶欧拉方的一种构作方法

提出了4t阶欧拉方的一种构作方法，阐明了4t阶欧拉方构作的基本思路，介绍了24阶段拉方构件的过程及构作结果。

n=t^3阶正交拉丁方的构造方法

在三重正交拉丁立方构造研究的基础上 ,发现了一种适用于 n=t3 阶正交拉丁方构造的方法。并利用其方法构造 n=8,2 7,64,1 2 5 ,343,5 1 2 ,…等阶的正交拉丁方。阐明了 n=t3阶正交拉丁方构造的特点 ,介绍了 n=t3 阶正交拉丁方的构造方法及 n=8,2

8t阶幻方及正交拉丁方的构造方法

一种４ｔ阶幻方及正交拉丁方的构造方法被首次发现。文中验证了４ｔ阶幻方及正交拉丁方构造方法的可行性，阐明了８ｔ阶幻方及正交拉丁方构造的思路，介绍了１６阶幻方及正交拉丁方的构造过程。构造验证表明，该法是简便的，可构造任意８ｔ阶幻方及正交拉丁方。

幻方世界

过去在大多数人看来,一些数构成的一个具有特殊操作特性的正方形——数方(幻方)似乎具有神奇的性质或力量。幻方的最早记录是在我国公元前200年左右。

13阶三重正交拉丁立方及其构造

介绍了奇 n阶三重正交拉丁立方的构造方法 ,并利用所述的方法构造出 1 3阶三重正交拉丁立方。对 1 3阶三重拉丁立方的性质进行了分析 ,讨论了 1

奇n阶幻立方和正交拉丁立方的构造

在奇 n阶幻方构造研究的基础上 ,发现了奇 n阶幻立方和正交拉丁立方的构造方法。阐明了奇 n阶幻方、幻立方及正交拉丁立方构造的基本思路。介绍了奇

HIGH RESOLUTION POSITIVITY-PRESERVING DIFFERENCE SCHEMES FOR TWO DIMENSIONAL EULER EQUATIONS

A class of high resolution positivity preserving Boltzmann type difference schemes for one and two dimensional Euler equations is studied. First, the relation between Boltzmann and Euler equations is analyzed. By using a kind of special interpolation, the high resolution Boltzmann type difference scheme is constructed. Finally, numerical tests show that the schemes are effective and useful.

Rotation of the Earth as a Triaxial Rigid Body

The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.

A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids

We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.

Some Kind of Equations Involving Euler＇s Function

For any given positive integer n ≥ 1, the Euler function φ（n） is defined to be the number of positive integers not exceeding n which are relatively prime to n. w（n） is defined to be the number of different prime divisors of n. Some kind of equations involving Euler＇s function is studied in the paper.

CFD simulation of an industrial hydrocyclone with Eulerian-Eulerian approach: A case study

In the present study, a three-dimensional computational fluid dynamics simulation together with experimental field measurements was applied to optimize the performance of an industrial hydrocyclone at Sarcheshmeh copper complex. In the simulation, the Eulerian–Eulerian approach was used for solid and liquid phases, the latter being water. In this approach, nine continuous phases were considered for the solid particles with different sizes and one continuous phase for water. The continuity and momentum equations with inclusion of buoyancy and drag forces were solved by the finite volume method. The k–e RNG turbulence model was used for modeling of turbulency. There was a good agreement between the simulation results and the experimental data. After validation of the model accuracy, the effect of inlet solid percentage, pulp inlet velocity, rod inserting in the middle of the hydrocyclone and apex diameter on hydrocyclone performance was investigated. The results showed that by decreasing the inlet solid percentage and increasing the pulp inlet velocity, the efficiency of hydrocyclone increased. Decreasing the apex diameter caused an increase in the hydrocyclone efficiency.

Analysis of mathematical model for micromechanical vibratory wheel gyroscope

By the sketch of structure of MVWG,the working laws of this kind of gyroscope we re explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.

Coupling of 3D Eulerian and Lagrangian Spray Approaches in Industrial Combustion Engine Simulations

The Lagrangian DDM （discrete droplet model） is state-of-the-art for CFD （computational fluid dynamics） simulations of mixture formation and combustion in industrial engines. A commonly known drawback of the DDM approach is the attenuated validity in the dense spray, where the bulk liquid disintegrates into droplets. There the assumption of single droplets surrounded by a homogenous gas field is not reasonable. In this region, the Eulerian-Eulerian multi-phase approach performs better because instead of parcels the spray is represented by the volume fractions of one bulk liquid and several droplet size class phases. A further drawback of the DDM approach is that increasing the spatial resolution of the computational grid leads to a reduced statistical convergence, since the number of spray parcels per computational cell becomes smaller. It is desirable to combine the benefits of both spray approaches in coupled CFD simulations. Therefore, the dense spray region is simulated separately with the Eulerian spray approach on a highly resolved mesh covering only the region close to the nozzle orifice. The entire engine domain with combustion and emission models is simulated with the Eulerian-Lagrangian spray approach for the dilute spray region. The two simulations are coupled through exchange of boundary conditions and model source terms. An on-line coupling interface manages the data transfer between the two simulation clients, i.e., Eulerian spray and engine client. The aim of this work is to extend the coupled spray approach in terms of exchanging combustion related heat and species sources, and consequently creating the link between Eulerian spray and combustion models. The results show mixture formation and combustion in real-case engine simulations, and demonstrate the feasibility of spray model combination in engineering applications.

Introduction and evaluation of a novel hybrid brattice for improved dust control in underground mining faces: A computational study

A proper control and management of dust dispersion is essential to ensure safe and productive underground working environment. Brattice installation to direct the flow from main shaft to the mining face was found to be the most effective method to disperse dust particle away from the mining face. However,it limits the movement and disturbs the flexibility of the mining fleets and operators at the tunnel. This study proposes a hybrid brattice system- a combination of a physical brattice together with suitable and flexible directed and located air curtains- to mitigate dust dispersion from the mining face and reduce dust concentration to a safe level for the working operators. A validated three-dimensional computational fluid dynamic model utilizing Eulerian–Lagrangian approach is employed to track the dispersion of dust particle. Several possible hybrid brattice scenarios are evaluated with the objective to improve dust management in underground mine. The results suggest that implementation of hybrid brattice is beneficial for the mining operation: up to three times lower dust concentration is achieved as compared to that of the physical brattice without air curtain.

Role of oxides in the formation of hole defects in friction stir welded joint of 2519-T87 aluminum alloy

The role of oxides in the formation of hole defects in friction stir welded joint of 2519-T87 aluminum alloy has been investigated by using optical microscope, scanning electron microscope, electron backscatter diffraction and electron probe microanalyzer to examine the distribution of oxides and the features of hole defects, and using ABAQUS 3D thermo-mechanical coupling finite element model based on arbitrary Lagrangian-Eulerian method to simulate the material flow behavior. Oxides exist at the edge of tunnel hole and in the micropores in the joint. Based on distribution of oxygen and material flow behavior, it is believed that the oxides on the surface of the alloy tend to flow down into the bulk along the flow direction of plastic material during friction stir welding, aggregate in the weak region of material flow at the intersection of the shoulder affected zone and the stir pin-tip affected zone, and consequently prevent the material from contacting and diffusing. Due to the insufficient material flow and therefore the small plastic deformation,the pressure is not high enough to compress the accumulated oxides, resulting in hole defects.

Computational Modeling of Tangentially Fired Boiler (I) Models, Flow Field and Temperature Profiles

In this work, an Eulerian/Lagrangian approach has been employed to investigate numerically the flow characteristics, heat transfer and combustion in a tangentially fired furnace. The RNG (Re-normalization group) k-ε model and a new method for cell face velocity interpolation based on a non-staggered grid system are employed. To avoid pseudo-diffusion that is significant in modeling tangentially fired furnaces, attempts are made at improving the differential volume scheme. Some new developments on turbulent diffusion of particles are also taken into account. Thus, computational accuracy is improved substantially.

A New Approach to Estimating the T-Year Return-Period Wave Height

The paper introduces a new approach to estimating the T-year return-period wave height (TRPW), i.e. the wave height expected to occur in T-year, from two sets of observed extreme data and on the basis of the maximum entropy principle. The main points of the approach are as follows. 1) A maximum entropy probability density function (PDF) for the extreme wave height H is derived from a Euler equation subject to some necessary and rational constraints. 2) The parameters in the function are expressed in terms of the mth moment of H. 3) This PDF is convenient to theoretical and practical applications as it is simple and its four parameters are easy to be determined from observed extreme data. An example is given for estimating the TRPW in 50 and 100 years by the present approach and by some currently used methods using observed data at two hydrographic stations.The comparison of the estimated results shows that the present approach is quite similar to the Pearson-Ⅲ and Gumbel methods.

Automatic DEXP method derived from Euler’s Homogeneity equation

The depth from extreme points(DEXP)method can be used for estimating source depths and providing a rough image as a starting model for inversion.However,the application of the DEXP method is limited by the lack of prior information regarding the structural index.Herein,we describe an automatic DEXP method derived from Euler’s Homogeneity equation,and we call it the Euler–DEXP method.We prove that its scaling field is independent of structural indices,and the scaling exponent is a constant for any potential field or its derivative.Therefore,we can simultaneously estimate source depths with diff erent geometries in one DEXP image.The implementation of the Euler–DEXP method is fully automatic.The structural index can be subsequently determined by utilizing the estimated depth.This method has been tested using synthetic cases with single and multiple sources.All estimated solutions are in accordance with theoretical source parameters.We demonstrate the practicability of the Euler–DEXP method with the gravity field data of the Hastings Salt Dome.The results ultimately represent a better understanding of the geometry and depth of the salt dome.

Dynamic Adaptive Finite Element Analysis of Acoustic Wave Propagation Due to Underwater Explosion for Fluid-structure Interaction Problems

In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes：a） calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b） fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c） adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.