偏微分方程数值计算在虚拟现实中应用与研究

随着虚拟现实(Virtual Reality,VR)相关硬件的发展以及软件技术的日趋成熟,VR技术正在进入人们的日常生活。然而不可否认,VR的核心问题之一——物理真实感依然没有很好的解决。其原因大多都是由于解算模型控制方程耗费了大量的时间,从而迫使人们采用牺牲精度的方法以满足实时性的要求。而许多的物理模型的解算都归结于偏微分方程求解,因此如何准确高效快速的求解偏微分方程(PDE)和PDE方程组对于提升虚拟现实系统的物理真实感有着至关重要的作用。本文从求解典型PDE出发,建立相应的PDE求解器,并对计算结果进行验证。最后将该思想应用于计算流体力学领域,通过对流体力学中的NS方程和水力学中的浅水波方程的求解,得到计算区域的速度场或高度场,并且对结果进行验证。结果表明,该方法具有较高的可信度。     

基于MATLAB PDE的变压器二维建模和漏磁场分析

MATLAB提供了一个偏微分方程求解的工具箱(PDE),利用该工具可以实现偏微分方程类型的设定、几何模型建立、方程求解和结果图形化显示.变压器短路阻抗主要由漏磁场决定,本文通过建立变压器的二维模型,并利用MATLAB PDE工具箱进行分析计算漏磁场,并在此基础上采用能量法计算了变压器漏磁通和短路阻抗大小,得到了短路阻抗与变压器结构的关系.     

波浪与水囊潜堤相互作用的数值模拟

基于黏性流体力学理论构建波浪与水囊潜堤相互作用的计算流体力学数值模型.利用高阶差分方法求解纳维斯托克斯方程,采用有限元方法求解结构动力学方程,采用虚拟单元浸入边界法实现流体和固体求解器的高精度耦合求解.通过流体体积方法实现界面重构,与试验结果比较验证模型的有效性.对规则波与不同充盈水囊潜堤相互作用进行数值模拟,寻找合适...     

基于传递矩阵法的纵肋圆柱壳振动特性计算

基于传递矩阵法,结合振动微分方程,提出一种计算纵肋圆柱壳自由振动特性的周向传递矩阵法.该方法基于板壳理论和圆柱壳振动控制方程,推导出圆柱壳周向传递的场传递矩阵和纵肋处的点传递矩阵,结合圆柱壳边界条件,得到频率方程,利用精细时程积分法原理,可保证计算的精度.将计算结果与有限元解进行比较,验证方法的有效性,同时比较传递矩阵...     

非缓坡非均匀流场中多向不规则波传播数学模型的建立

根据线性波动的叠加原理和波浪方向谱理论,在文献[1]的非缓坡非均匀流场的规则波基本方程的基础上,推导出了非缓坡非均匀流场中的多向不规则波传播变形的偏微分方程,并使用有限差分方法建立了数学模型。该模型避开了求解波动势函数的困难,直接求解波动能量的空间分布,可采用简单的有限差分数值方法求解,对空间步长没有限制,适合非缓坡复杂地形及存在流场的情况下大面积波浪场(波高和波向)的计算。     

基于PDE解析解的潜艇艇型设计

随着CAD技术应用的日益普及,人们对几何造型方法提出了越来越高的要求,对于复杂曲面的构造和高质量曲面的设计,传统的B样条方法已经不能满足人们的需求,用偏微分方程构造曲面,是一种新颖的曲面造型方法.本文主要讨论了偏微分方程的解析解在潜艇艇型设计中的应用.仿真实验表明,PDE方法能很好的构造出潜艇的艇型.     

流体管道流固耦合14方程频域传递矩阵法

考虑流体管道的体积力以及流体的横向惯量,忽略管道和流体之间的摩擦效应,导出流体管道流固耦合的14方程模型.利用拉氏变换,把时域方程变换到频域,对频域模型进行推导,方程化为12个一元四阶常微分和2个一元二阶常微分,变换后的方程可以直接进行求解,得到简单直管的频域解析解.把管道始末端的坐标代入解析解,可得到管道始末端的关系,结合结点平衡条件,推导出多管段的频域传递矩阵法.对算例进行仿真计算和分析,并用实验结果来验证计算结果,验证模型和方法的正确性.     

考虑流固耦合的多分支管道系统振动研究

利用拉普拉斯变换,把时域14方程模型变换到频域,并化多元一阶常微分方程为一元高阶方程,对其求解,得到直管的频域解析解。然后把任一管段的初始坐标值和末端坐标值代入直管的频域解析解,得到单管的传递矩阵,结合分支点的平衡条件,便可以推导出任意N个分支管的传递矩阵。增加7(N+2)个分支管的边界条件,求解得出任意N分支管路的频域解。最后,进行仿真计算,利用英国Dundee大学Tijsseling教授的实验结果以及ANSYS仿真计算对结果进行验证,验证了文中方法的正确性;并例举了不同分支数目以及不同分支位置管路的仿真计算结果,同时对仿真结果进行了分析。     

全局布索门式刚架索参数确定方法

基于门式刚架和预应力钢结构的研究成果,对全局布索预应力门式刚架进行了分析.根据结构的变形特征和受力机理,提出拉索参数确定准则,并依据该准则及简化计算模型,推导了结构在预应力及竖向荷载下的内力及变形的求解方程;最后,采用SAP2000建立典型算例,验证了理论求解方程,分析了理论解与数值模拟间的误差.为门式刚架全局快速布索的初步设计奠定了理论基础.     

潜艇流场数值模拟及不确定度分析

为了分析计算流体力学预测结果的可信度问题,采用雷诺平均N-S方程,结合SSTκ-ω湍流模型,对验证研究用的美国DARPA潜艇模型SUBOFF光体湍流场进行数值计算,预报了艇体压力系数,计算流体力学预报值与实验基准数据有较好地吻合,并对雷诺平均N-S方程法进行了验证与确认,不确定度为1.52%.本文相关计算网格数20万左右,单机运行时间大约在2 h后得到收敛值,充分显示了计算流体力学方法在潜艇初步设计中预测水动力性能的高效性、可用性与可信性.     

基于虚拟现实技术的船舶运动仿真

虚拟现实技术是目前国内外最热门的仿真技术之一,由于其有着高效、安全和低成本等特点越来越受到各国的重视。介绍了在虚拟环境下的船舶运动仿真的可行性方法。首先用二维半切片法给出了船舶运动的方程,接着用3DMax软件建立船舶的模型,最后在OpenGL环境中建立场景进行船舶的运动仿真。仿真场景有着较好的感观效果,给人以真实性,同时系统有着较好的可控性。对船舶运动仿真的进一步研究有着重要的作用。     

船舶对称响应的非线性水弹性微分分析法

本文给出了一个预报波浪诱导的船舶垂向运动和结构总体动响应的非线性时域水弹性力学微分分析法，这一理论是控制论的分析方法应用于船体与流体非线性相互作用研究领域的尝试，其流固耦合系统的非线性时域水动作用过程（含记忆效应）由一阶非齐次偏微分方程组来描述，理论预报与Ｓ１７５弹性材料船模型实验比较，结果令人满意。     

An approximate method for the surge response of the tension leg platform

The solution for the Duffing equation in anonlinear vibration problem is studied in this paper. Clearly,in the case of the perturb parameter being a larger value, thetraditional perturbation method is no longer valid but theHomotopy Perturbation Method （HPM） is applicable usually.HPM is used to solve the weak and strong nonlineardifferential equations for finding the perturbed frequency ofthe response. The obtained frequencies via HPM and theapproximate method have good accordance for weak andstrong nonlinear differential equations. Additionally, thecalculated responses by use of the approximate method arecompared with the responses obtained from the Numericalmethod in the time history of the response and phase plane.The results represent ~ood accordance between them.     

利用AGM求解粘弹性地基刚性梁的非线性控制微分方程（英文）

In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji’s method(AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations.Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method(Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration(A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure.Therefore, AGM can be considered as a significant progress in nonlinear sciences.     

舰船动力装置虚拟训练技术研究

针对传统实装训练受装备数量、机型、训练场地、环境的限制及实装结构复杂、造价昂贵、开发周期长的特点,提出了一种现代化的训练手段-虚拟训练方法作为其有效的替代手段,利用现代CAD技术、虚拟现实技术、网络技术开发出一套舰艇动力装置虚拟训练系统,不仅满足了训练任务的需要,而且节约了经费、缩短了开发周期。     

虚拟现实技术在水运工程中的应用与展望

近年来,虚拟现实技术发展较快,已经广泛应用在水运工程设计、施工和运营工作中,主要包括视景仿真、虚拟仿真、辅助设计、远程虚拟监控和虚拟操作训练5个方面。随着水运工程全寿命理论的提出、虚拟现实技术和智能化技术的发展,水运工程全寿命虚拟现实系统、分布式视景仿真系统和智能虚拟港口系统将是今后的发展方向。     

Construction of wave-free potentials and multipoles in a two-layer fluid having free-surface boundary condition with higher-order derivatives

There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation (or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.     

基于虚拟现实技术的船舶辅锅炉控制系统研究

结合实船上燃油辅锅炉的实际情况和具体操作要求，通过建立三维模型、人机交互、Web 3D网页浏览技术等米构建船舶辅锅炉虚拟操控系统，达到以虚拟操作代替实际操作，节省开支、实现远程培训、以及人机交互的目的，克服了船舶辅锅炉控制系统实际训练中不可避免的资源消耗、维护费用高等难题。     

Determination of attainable regions in ship maneuvers: an application of differential inclusions to the modeling of ship dynamics

A commonly used mathematical tool in vehicle dynamics simulation is the ordinary differential equation. However, in some situations, these equations may not be sufficient to solve problems. For robust flight, surface ship or submarine control design, safety assessment, missile and aircraft guidance, the influence of disturbances, and differential games of pursuit–evasion, more versatile tools are needed. The differential inclusion (DI) is a generalization of a differential equation that can be extremely useful. The solution of a DI is not just a model trajectory or a set of trajectories obtained by a randomization of the original problem. The solution is a reachable set, and it is a deterministic object. A differential inclusion solver and its application to vessel movement are described. Compared to previous publications on the DI solver, the new feature is an implementation of the fuzzy sets technique to improve the resulting images. It is pointed out that the reachable sets cannot be assessed properly while treating the uncertain variables as random. The application of the DI solver can give a proper view of the regions in the state space where all the possible model trajectories belong.     

具有高阶导数自由表面边界条件的两层流体无波势和多级的构建（英文）

There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace's equation(or Helmholtz equation) arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace's equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.