二维GEL耦合方法的研究及对爆炸容器的数值模拟

 将以Euler方法为基础的MF PPM（Piecewise-Parabolic Method）程序和以Lagrange方法为基础的DEFEL（2-D Finite Elements Code,二维流体弹塑性动力有限元）程序,根据压力和法向速度连续准则进行耦合,发展了基于Level Set的GEL（Ghost-Fluid Euler-Lagrange）方法。该方法在处理大变形流场与小变形结构以及复杂流动与多物体相互作用等问题具有优越性。通过二维算例的计算结果与文献比较,检验了GEL方法和耦合程序的正确性,并对球形和椭球封头的爆炸容器进行了数值模拟,通过与实验结果的比较分析,表明本研究程序可以比较好地处理内爆引起的壳体流固耦合问题。     

Difference Discrete Variational Principle,Euler—Lagrange Cohomology and Symplectic,Multisymplectic Structures II：Euler—Lagrange Cohomology

In this second paper of a series of papers,we explore the difference discrete versions for the Euler-Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multiparameter differential approach.In terms of the difference discrete Euler-Lagrange cohomological concepts,we show that the symplectic or multisymplectic geometry and their difference discrete structure-preserving properties can always be established not only in the solution spaces of the discrete Euler-Lagrange or canonical equations erived by the difference discrete variational principle but also in the function space in each case if and only if the relevant closed Euler-Lagrange cohomological conditions are satisfied.     

Difference Discrete Variational Principles,Euler—Lagrange Cohomology and Symplectic,Multisymplectic Structures Ⅲ：Application to Symplectic and Multisymplectic Algorithms

In the previous papers I and II,we have studied the difference discrete variational principle and the Euler-Lagrange cohomology in the framework of multi-parameter differential approach.We have gotten the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and field theory as well as the difference discrete versions for the Euler-Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the lagrangian and Hamiltonian formalisms.In this paper,we apply the difference discrete variational principle and Euler-Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms.We will show that either Hamiltonian schemes of Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler-Lagrange cohomological conditions are satisfied.     

On Symplectic and Multisymplectic Structures and Their Discrete Versions in Lagrangian Formalism

We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively.We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire grometric object and the noncommutative differential calculus on regular lattice.In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations,the Euler-Lagrange cohomological concepts and content in the configuration space are employed.     

Euler-Lagrange Forms and Cohomology Groups on Jet Bundles

Using the language of jet bundles, we generalize the definitions of Euler-Lagrange one-form and the associated cohomology which were introduced by Guo et al. [Commun. Theor. Phys. 37 (2002) 1]. Continuous and discrete Lagrange mechanics and field theory are presented. Higher order Euler-Lagrange cohomology groups are also introduced.     

Hamiltonian Formulation of Singular Lagrangians on Time Scales

The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed.     

Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm

We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists the discrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existence in finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodic perturbation. The numerical results are satisfactory.     

在合成的梯度折射率介质中的光线追迹

本文介绍由光程的幂级数展开成欧拉-拉格朗日(Euler-Lagrange)方程的解,引入一个对一种合成的梯度折射率介质的光线追迹算法。     

弯管和文丘里管组合燃烧器的颗粒分布特性

本文给出一种弯管和文丘里管组合结构的新型浓淡煤粉燃烧器,并分别对弯管、文丘里管和这种弯管和文丘里管组合结构燃烧器内的气固两相流动进行了数值模拟。采用Euler-Lagrange方法和离散相模型（DPM）研究气固两相流动,气相湍流采用分离涡（DES）模拟方法,固相湍流采用离散随机游动（DRW）模型。结果表明,这三种结构对...     

有限温度自洽半经典方程及其虚时迭代解

利用Skyrme力和半经典近似,推导了有限温度自洽半经典(FTSCSC)方程,即通常所说的Euler-Lagrange方程。利用虚时迭代方程对此方程作数值求解,以确定热核的核子密度,并研究其部分静态性质。 关键词：     

流化床内单个颗粒传热特性的模拟

单个颗粒的传热过程对于燃煤流化床锅炉中煤的着火和随后的燃烧过程具有重要的影响。本文建立了一个基于Euler-Lagrange方法的数学模型对其进行了数值研究。该模型对流体相的运动和传热规律以Euler。方法描述,对固体颗粒相则以近年来发展起来的离散单元方法(DEM)在颗粒层次上进行描述。研究结果表明颗粒与床层之间有很高的传热系数。另外,对单个颗粒温度变化过程的模拟研究表明,颗粒经过较短的时间便能接近床层的温度,且不同颗粒具有类似的温度变化特性。     

事件空间中力学系统的微分变分原理

研究事件空间中力学系统的微分变分原理.基于D'Alembert原理，建立了事件空间中力学系统的D'Alembert-Lagrange原理、Jourdain原理、Gauss原理和万有D'Alembert原理，给出了这些原理的Euler-Lagrange参数形式、Nielsen参数形式和Appell参数形式，并导出了万有D'Alembert原理的Mangeron-Deleanu参数形式. 关键词： 分析力学 事件空间 微分变分原理     

Kirchhoff弹性杆动力学建模的分析力学方法

以杆的横截面为研究对象，讨论了其自由度，给出了截面虚位移定义，并定义变分和偏微分运算对独立坐标服从交换关系. 给出了曲面约束的基本假设，讨论了约束对截面自由度的影响以及加在虚位移上的限制方程. 从D'Alembert原理出发结合虚功原理，建立了弹性杆动力学的D'Alembert-Lagrange原理，当杆的材料服从线性本构关系时，化作Euler-Lagrange形式、Nielsen形式和Appell形式. 由此导出了Kirchhoff方程以及Lagrange方程、Nielsen方程和Appell方程，得到 关键词： 超细长弹性杆 分析力学方法 Kirchhoff动力学比拟 变分原理     

串联弹前级装药对后级随进弹爆炸作用的研究

 为获得串联战斗部随进弹在受到前级装药爆炸作用时,质量对其所受最大过载及动能衰减的影响规律,采用非线性动力学软件AUTODYN,基于Euler-Lagrange耦合算法,对前级装药的爆炸过程中,不同弹径、不同质量的随进弹穿越爆轰场进行了数值模拟。得出了随进弹在前级爆炸作用下所受最大过载和动能衰减的变化规律。基于数值模拟结果建立了随进弹剩余速度与质量的无量纲关系式,计算结果得到了实验验证。     

The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass

This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.     

On General Volume-Preserving Mechanical Systems via Cohomology

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold(Μ,ω) via the highest Euler-Lagrange cohomology. It is shown that for every volume-preserving fiow there are some 2-forms that play a similar role to the Hamiltonian in the Hamilton mechanics and the ordinary canonical equations with Hamiltonian H are included as a special case with a 2-form Hω/(n - 1).     

超声速气流中液体横向射流雾化过程数值模拟

为了更加深入了解超燃冲压发动机燃烧室中的燃料雾化机理,对来流Mach数为1.94的超声速气流中液体横向射流的雾化过程进行了数值模拟研究.计算采用Euler-Lagrange方法,液滴二次破碎模型采用K-H/R-T模型.计算结果表明:考虑液滴二次破碎时,采用雾化锥模型获得的射流穿透深度以及液滴速度分布与实验结果符合得很好;初始液滴直径对射流穿透深度和液滴分布的影响很小;随着初始雾化锥角的增加,相同横截面上的射流穿透深度逐渐减小.当不考虑液滴二次破碎时,液滴穿透深度及分布与所选的初始液滴直径有很大关系.      

On General Volume-Preserving Mechanical Systems via Cohomology

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M,ω) via the highest Euler-Lagrange cohomology.It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in the Hamilton mechanics and the ordinary canonical equations with Hamiltonian H are included as a special case with a 2-form Hω/(n-1).     

Hamilton formalism and Noether symmetry for mechanico—electrical systems with fractional derivatives

This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives.The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established.The definition and the criteria for the fractional generalized Noether quasisymmetry are presented.Furthermore,the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations.An example is presented to illustrate the application of the results.