An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

Numerical Investigation on Vortex-Induced Rotations of A Triangular Cylinder Using An Immersed Boundary Method

A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).

Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation

This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.

Development of quadrilateral spline thin plate elements using the B-net method

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L=8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Тc=3.6403（2）. A convincing finite-size scaling analysis of the model yields ν=0.9995（21）, β/ν=0.12400（17）, γ/v=1.75223（22）, γ^1/ν=1.7555（22）, α/ν=0.00077（420） （scaling） and α/ν=0.0010（42） （hyperscaling）. The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.

THE EFFECT OF AN ELASTIC TRIANGULAR INCLUSION ON A CRACK

The interaction between an elastic triangular inclusion and a crack is investigated. The problem is formulated using the boundary integral equations for traction boundary value problems derived by Chau and Wang as basic equations. By using the continuity condition of traction and displacement on interface as supplement equations, a set of equations for solving the interaction problem between an inclusion and a crack are obtained, which are solved by using a new boundary element method. The results in terms of stress intensity factors (SIFs) are calculated for a variety of crack_inclusion arrangements and the elastic constants of the matrix and the inclusion. The results are valuable for studying new composite materials.

Finite Element Analysis of Magnetohydrodynamic Mixed Convection in a Lid-Driven Trapezoidal Enclosure Having Heated Triangular Block

A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (Rot = 0° - 90°) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed U0. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ Pr ≤ 2), Reynolds number (60 ≤ Re ≤ 120), Rayleigh number (Ra = 103) and Hartmann number (Ha = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of Nuav of hot bottom wall and θav in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.

The Numerical Integration of Discrete Functions on a Triangular Element

With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.

基于TFN-AHP熵权的铁钻工工业设计方案评价

针对铁钻工工业设计方案评价综合性强、存在一定主观性、评价影响因素多的问题,提出一种基于三角模糊数层次分析法和熵权法主、客观方法相结合的铁钻工方案评价模型。该模型在层次分析法框架下,根据专家意见构建铁钻工工业设计方案评价指标体系,划分4项1级指标和12项2级指标,以模糊决策矩阵为评价信息载体,引入三角模糊数优化传统层次分析法不能准确表征带有模糊不确定性特征的评价信息的问题,并使用客观方法熵权法组合赋权确定综合权重。将此评价模型运用于实际铁钻工设计项目方案评价,将评价结果与相关传统评价法进行对比,并将筛选出来的方案进行深入优化设计,证明了评价模型的有效性。研究结果能够有效辅助企业进行铁钻工工业设计方案决策。

Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation

This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.

Finite Element Analysis of Magnetohydrodynamic Natural Convection within Semi-Circular Top Enclosure with Triangular Obstacles

The phenomena of magneto-hydrodynamic natural convection in a two-dimensional semicircular top enclosure with triangular obstacle in the rectangular cavity were studied numerically. The governing differential equations are solved by using the most important method which is finite element method (weighted-residual method). The top wall is placed at cold Tc and bottom wall is heated Th. Here the sidewalls of the cavity assumed adiabatic. Also all the wall are occupied to be no-slip condition. A heated triangular obstacle is located at the center of the cavity. The study accomplished for Prandtl number Pr = 0.71;the Rayleigh number Ra = 103, 105, 5 × 105, 106 and for Hartmann number Ha = 0, 20, 50, 100. The results represent the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.

基于改进DEMATEL-ISM的钢桁梁桥施工风险影响因素研究

为提高钢桁梁桥施工过程中的安全管理,对钢桁梁桥施工中的风险因素进行分析,提出了一种基于改进DEMATEL-ISM的评价方法,首先引入三角模糊数对DEMATEL法中的直接影响矩阵进行改进,从而去模糊化以减少专家评价的主观性,再通过DEMATEL法分析各影响因素的影响度、被影响度、中心度与原因度并加以排序,对得到的主要影响因素进行初步分析,利用ISM法对筛选出的影响因素进行层次划分,得到直接层影响因素、过渡层影响因素与本质影响因素,并针对分析得到的5个本质影响因素提出深入的预防预警措施,可为钢桁梁桥施工方向的安全管理提供针对性措施,为事故预防提供一定的参考依据。

Triangular Curved Surface Construction of A Series ofArbitrary Disordered Points in Space

Constructing Bernstein-Bezier triangular interpolating curve surface interpolating a series of arbitrary disordered data points is of considerable importance for the design and modeling of surfaces with a variety of continuity information. In this article. a kind of simple and reliable algorithm that can process complex field triangular grid generating is presented, and a group of formulae for determining triangular curved surface with wholly C1 continuity are given. It can process arbitrary non-convex boundary and can be used to construct surfaces inner holes.

Assel轧管机辗轧角测量方法及其工程应用

针对Assel轧管机辗轧角对钢管成型质量影响大,但无准确测量方法,依靠经验调整的问题,介绍了一种测量Assel轧管机辗轧角的方法。该方法通过倾角测量仪分别测出3个轧辊相对于水平面的倾角,其中上辊的实际辗轧角等于测量角度,下辊的实际辗轧角则利用三棱锥计算空间角度法计算得到,具有操作简单、测量快速、结果准确的优点。经过在国内某Assel轧管机上应用,验证了该方法具有可行性。

复杂环境条件下大跨钢桁梁顶推施工安全风险分析与控制

复杂环境条件下大跨连续钢桁梁顶推施工工序繁多,工艺复杂,风险源众多。以北方某跨黄河大型桥梁工程为依托,充分考虑大跨钢桁梁结构特点及周边复杂环境条件,采用层次分析法对顶推施工全过程的风险源进行识别并建立层次分析模型,采用三角模糊数法对顶推施工各级风险源权重进行计算,运用模糊综合评判法确定顶推施工风险等级,实现了复杂环境条件下大跨连续钢桁梁顶推施工定量化风险评估及分析,避免了评估专家的主观性,解决了单纯理论计算的客观性问题,根据风险分析结果提出针对性的施工风险管控措施,为钢桁梁顶推施工安全提供了保障。

土壤表面与运动目标复合电磁散射的矩量法研究

为了满足土壤表面上方雷达目标检测、识别和分类等的需要,采用空间域合成法生成高度起伏遵守Alpha-stable分布的土壤表面,选用Topp模型模拟土壤的介电常数,运用矩量法研究了锥形波入射条件下土壤与其上方运动的三角形截面柱的复合电磁散射问题,通过数值计算得到了复合散射系数随散射角的变化曲线,分析了等边三角形和不规则三角形截面柱在土壤表面上方横向平移、纵向平移、转动以及电磁波入射角对复合散射系数的影响。数值计算结果表明:复合散射系数随散射角振荡地变化,等边三角形截面柱的纵向平移和转动对复合散射系数有较大的影响,而横向平移对复合散射系数的影响很小;不规则三角形截面柱的横向平移和纵向平移对复合散射系数产生的影响很小,转动对复合散射系数的影响较大。有关结果可为民用、军用领域工程问题提供理论依据和实践方法。

仿生平面三角形单元积分声场的波函数构造

波叠加法在求解声源外部辐射声场时,需要对所有离散单元进行数值积分计算导致计算效率较低,而等效源法由于过度简化单元始终存在较大的积分近似误差.针对以上缺陷,利用Helmholtz方程在球坐标系下的解构造了一种与单元积分等效且无需积分的波函数.受仿生复合材料三角形缝合结构启发,以适用范围最广的平面三角形单元为例,构造了波函数的一般形式和内推形式.最后,通过数值仿真对比了两种波函数与直接积分的计算声场的精度和效率.结果表明,两种波函数与直接积分的计算误差低于0.5%,且内推波函数的计算效率约为直接积分的6倍.

不含4-圈和三角化6-圈的环面图森林分解

假设G是一个有限简单图.令V(G)和E(G)分别表示图G的点集合和边集合.若能将G的点集合V(G)划分为2个不交的子集合V_(1)和V_(2),使得由V_(1)和V_(2)导出的子图满足G[V_(1)]是森林且G[V_(2)]是最大度至多为d的森林,则称G有一个(F,F_(d))-分解.运用反证法,通过对极小反例的结构分析,找到可约构形,再通过权转移讨论证明:不含4-圈和三角化6-圈的环面图有(F,F_(3))-分解.

冻结土壤表面等边三角形截面柱运动目标复合电磁散射特性研究

针对高寒地区冻结土壤表面运动目标雷达回波特性的研究需求,采用介电常数混合模型模拟冻结土壤的介电常数,应用空间域合成法模拟表面起伏遵守alpha-stable分布的冻结土壤表面,运用矩量法研究了入射波为锥形波时在冻结土壤表面上横向翻滚的等边三角形截面柱运动目标的复合散射问题,仿真了复合散射系数随散射角变化的曲线。数值计算结果表明,在三角形截面柱作复杂翻滚运动时,目标自身旋转对复合散射系数的影响最大,目标重心纵向振荡对复合散射系数的影响较大,而水平移动对复合散射系数的影响较小,同时考虑冻结土壤特性对复合散射特性的影响,入射波频率影响较大且入射波频率与复合散射系数呈负相关,土壤温度对复合散射系数影响较小且土壤温度与复合散射系数呈正相关,土壤质地对复合散射系数影响显著,取决于不同土壤质地自身电特性。理论上进一步推广了目标与特殊地物背景复合电磁散射计算方法,复合散射特性在诸多实践中又可提供必要的理论依据和可靠的数据支撑。