Numerical Treatments and Applications of the 3D Transient Green Function

How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.

瞬变电磁虚拟波场层状Green函数Born近似成像方法

瞬变电磁虚拟波场Born近似成像是通过Born近似对瞬变电磁虚拟波场方程进行线性化处理,求取速度扰动量实现成像的方法.Born近似采用半空间Green函数,在背景速度变化较大时成像分辨率较低.因此,本文从虚拟波场出发,建立辐射场与散射场满足的Helmholtz方程,导出层状介质Green函数表达式,将其应用于Born近似中,得到了基于层状介质格林函数的Born近似电导率计算公式和散射场关于速度扰动量的关系式,最终利用速度扰动量实现成像.通过对理论模型的实验计算,验证了利用层状模型Green函数的Born近似成像算法,能够重建地层电阻率分布,改善Born近似虚拟波动方程逆散射反演的垂向分辨率,获得较好的成像效果.对甘肃地区的实际资料处理结果表明,层状介质Green函数的Born近似,是一个精确度较高、稳定性好、有实际应用价值的成像方法.

船舶有航速时三维时域格林函数计算方法研究

船舶工业CAE软件势流求解器的开发对势流计算方法的可靠性提出要求,本文针对船舶有航速时深水三维时域格林函数计算方法开展研究。首先引入三维时域自由面格林函数,其瞬时项的求解采用Hess&Smith方法,自由面记忆项的求解采用美国密歇根大学Beck团队的方法。其次,分区域推导出三维时域自由面格林函数记忆项及其导数的编程所用的数学展开表达式。然后,采用间接法模型求解分布源强和速度势,并采用压力直接积分法求出时域辐射力。最后,针对Wigley I船型开展了辐射力计算,并与公开的试验及计算结果进行对比,验证本文方法的可靠性。

THE BOUNDARY ELEMENT ANALYSIS PROGRAM FOR 3-D TRANSIENT DYNAMIC FIELD

推演了三维瞬态动力场的边界积分方程在拉普拉斯变换空间中的矩阵表达式，并且采用蜕变单元方法改进并处理了积分核函数中的奇异性．在计算程序ＢＥＭＴＤＹ中应用了Ｋｏｉｚｕｍｉ数值反演方法，通过３个算例的验证，结果令人满意．

Analytical prediction and field validation of transient temperature field in asphalt pavements

This work presented the development and validation of an analytical method to predict the transient temperature field in the asphalt pavement.The governing equation for heat transfer was based on heat conduction radiation and convection.An innovative time-dependent function was proposed to predict the pavement surface temperature with solar radiation and air temperature using dimensional analysis in order to simplify the complex heat exchange on the pavement surface.The parameters for the time-dependent pavement surface temperature function were obtained through the regression analysis of field measurement data.Assuming that the initial pavement temperature distribution was linear and the influence of the base course materials on the temperature of the upper asphalt layers was negligible,a close-form analytical solution of the temperature in asphalt layers was derived using Green's function.Finally,two numerical examples were presented to validate the model solutions with field temperature measurements.Analysis results show that the solution accuracy is in agreement with field data and the relative errors at a shallower depth are greater than those at a deeper one.Although the model is not sensitive to dramatic changes in climatic factors near the pavement surface,it is applicable for predicting pavement temperature field in cloudless days.

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.

Transient Thermal Analysis of a Plate Fin Heat Sink with Green＇s Function

The accurate analyses for a plate fin heat sink with the ability to control the temperature of the avionics devices within a pre-set controllable temperature range are required both in the process of circuit design and for the real-time temperature monitoring purposes. In order to provide an insight into the behavior of the temperature of a plate fin heat sink subjected non-uniform heat density on the surfaces, it is necessary to obtain accurate analytical solutions yielding explicit formulas relating the dissipated power to the temperature rise at any point of avionics devices. This paper presents a method for thermal simulation of a plate fin heat sink using an analytical solution of the three-dimensional heat equation resulting from an appropriate plate fin heat sink transient thermal model. The entire solution methodology is illustrated in detail on the particular examples of the plate fin heat sink subjected non-uniform heat density on the surfaces. The transient temperature profiles are obtained for different positions at the surface of the plate fin heat sink. The analytical results are compared with measurements made on the surface of the cold plate and it is found that they are in good agreement with an error of less than 3 K.

系泊Spar平台波浪中耦合运动的数值模拟及模型试验

为了研究恶劣环境载荷引起海洋结构物的非线性运动响应,文章基于三维时域格林函数理论,提出了采用时域物面非线性理论方法直接模拟系泊浮体时域耦合分析所需的水动力,建立了系泊浮体波浪中时域耦合运动的数学模型。该方法充分考虑了每时每刻浮体在瞬态波面下湿表面的变化,并计及平均水线面下瞬时空间位置的改变,系统研究了系泊Spar平台波浪中的耦合运动响应及系泊线张力。最后,将数值模拟结果与模型试验结果进行了比较,计算结果令人满意。

波浪中浮体运动的时域混合格林函数法

基于混合格林函数法,对浮体在波浪中的运动进行了时域模拟.通过假想的直壁控制面将流场分割成内域和外域,分别引入Rankine源和自由面格林函数并结合控制面上的连续条件,对初边值问题进行求解.利用开发的数值计算程序对圆柱形平台和S175船进行了计算分析,给出了时延函数、波浪力幅值和运动响应结果,通过与频域方法和试验数据对比,证明该方法对零航速和有航速水动力问题均适用,能有效解决外飘船型的数值发散问题,且具有更高的计算效率.

应用混合格林函数法计算波浪中浮体运动及离散参数取值的算例分析

通过假想的直壁控制面将流场分割成内域和外域,分别引入Rankine源和自由面Green函数并结合控制面上的连续条件进行耦合求解,应用混合格林函数法对浮体在波浪中的运动进行了时域计算。以wigley型船为例,针对不同的时间步长、自由面和控制面的不同区域范围、面元划分的不同密度等进行了一系列数值计算和比较,讨论了离散区域大小、网格密度等参数对计算结果的影响,并给出其合理的取值范围。在此基础上,对一艘LNG船在不同浪向入射波中的运动响应进行计算,并与试验数据对比。结果证明,该方法能有效解决外飘船型时域计算的发散问题,可以对浮体在斜浪中的运动进行时域模拟。

Domain Decomposition and Matching for Time-Domain Analysis of Motions of Ships Advancing in Head Sea

A domain decomposition and matching method in the time-domain is outlined for simulating the motions of ships advancing in waves. The flow field is decomposed into inner and outer domains by an imaginary control surface, and the Rankine source method is applied to the inner domain while the transient Green function method is used in the outer domain. Two initial boundary value problems are matched on the control surface. The corresponding numerical codes are developed, and the added masses, wave exciting forces and ship motions advancing in head sea for Series 60 ship and S175 containership, are presented and verified. A good agreement has been obtained when the numerical results are compared with the experimental data and other references. It shows that the present method is more efficient because of the panel discretization only in the inner domain during the numerical calculation, and good numerical stability is proved to avoid divergence problem regarding ships with flare.

海洋结构物时域边界积分方程的改进方法(英文)

文章基于三维时域格林函数理论,提出了一种时域边界积分方程的改进计算方法,用于预报海洋结构物在波浪中运动受到的时域波浪力。该方法通过利用物体内部构造的满足拉普拉斯方程的内部解,在时域边界积分方程中只需要计及时域格林函数记忆项本身,从而有效地避免了求解具有高震荡积分特性的时域格林函数记忆项的法向导数。对潜体和浮体作了计算,结果表明,这种方法十分有效,可以有效节省内存使用量和计算机空间。通过与相关已发表文献的结果进行比较,计算结果令人满意。

直井体积压裂不稳定试井研究-双孔双区模型

体积压裂技术的起裂模式突破了单一方向的张性起裂,具有复杂缝网的扩展形态。作为一种新兴的增产技术,其相关渗流理论与试井模型的研究正处于起步阶段。以Warren-Root模型为基础,以双区复合为特征,建立了一种可以描述体积压裂直井渗流规律的基本模型:首先将渗流分为改造区的流动与非改造区的流动,用格林函数和达西径向流描述油藏渗流过程,然后在两区分界面处进行油藏压力和流量的耦合。经过数学求解后得到了新模型下的压力及压力导数双对数特征曲线,并分析了储容比、窜流系数,以及流度比对模型曲线的影响。实例应用表明,该模型有效实现了垂直井、双重介质和径向复合储层的耦合。

船舶航行时水动力系数求解二维半理论的稳定算法

给出一种基于高速细长体理论的预报排水型船在波浪上运动水动力求解的数值方法。在该理论的定解条件中,自由面条件是三维的,而控制方程和物面条件则是二维的,所以称为二维半理论。采用二维时域自由面Green函数将定解问题转化为船体切片上的积分方程,进而求解有航速下的船舶水动力问题。重点讨论了水动力计算的稳定算法。对ITTC建议的标准WIGLEY船型作了理论预报,并与DELFT大学的实验结果和用STF切片法的理论预报结果作了比较。比较结果表明,本文提出的二维半理论的预报结果与试验结果相当接近,而计算效率和切片法相当,且大大改善了理论预报的精度。

深海系泊浮体物面非线性时域耦合动力分析

文章基于三维时域势流理论和弹性细长杆理论,研究并提出了深海系泊浮体物面非线性时域耦合动力分析方法。该方法采用时域物面非线性理论方法在瞬态位置直接时域模拟系泊浮体所需水动力,结合有限元方法计算系泊缆索的动力响应,利用异步耦合方法实现浮体和系泊缆索的时域耦合动力求解。既满足系泊浮体时域水动力耦合,又满足系泊浮体和系泊缆索动力耦合。通过对二阶非线性不规则波作用下深海系泊半潜式平台的时域耦合响应特性进行研究,将不同海况下物面非线性时域耦合静力响应和动力响应与间接时域耦合动力响应的三种方法计算结果进行比较。研究结果表明,系泊缆索动力响应明显,平台瞬态空间位置对垂荡低频运动影响较大,有必要在平台瞬时湿表面采用动力响应方法进行深海系泊浮体时域耦合响应分析。

瞬变电磁场时域格林函数解

近源时间域电磁场具有信号强、探测深度大、精度高等优点,但传统勘探电磁场理论中偶极子近似在近源会引起较大误差,导致这一优势的发挥受到了制约.开展直接时间域电磁场解析式研究,是解决这一问题的途径之一.本文提出在点电荷微元假设下,引入时域格林函数,求取瞬变电磁场时间域解析解.采用积分运算法,把电磁场阻尼波动方程的求解问题转化为求其格林函数积分形式解的问题;建立辅助路径解决奇点问题,利用复分析中的约当引理、留数定理和广义函数等理论和方法,推导计算出时间域格林函数的时空四重广义积分.得到达朗贝尔方程的直接时域格林函数精确解析式,与传统方法"比拟"出的公式具有相同的形式,验证了本文推导的时域格林函数解析公式的正确性;推导出扩散方程的直接时间域解析解.通过与时变点电荷源时间域的电磁响应近似表达式进行对比,得出本文所推导的公式计算精度较高的结论;建立了全空间回线源瞬变电磁场问题的直接时间域求解公式.为解决全场区瞬变电磁场精细探测直接时域解析问题提供了基础理论.

GMRES(m)方法在海洋结构物时域水动力分析中的应用

为了提高海洋结构物时域水动力边界元方法的计算求解效率,基于三维时域势流理论,分别对浮体的线性绕射问题和非线性辐射问题进行数值计算,同时采用基于Galerkin原理的GMRES(m)方法求解用时域水动力边界元方法离散得到的线性代数方程组,并与现有文献结果进行比较。研究结果表明,该方法适于求解时域水动力边界元分析中形成的非对称稠密线性方程组,具有较好的收敛特性。计算结果令人满意,求解效率高。

基于时域格林函数法的船舶有航速问题数值求解(英文)

为了解决船舶以恒定速度在波浪中运动的水动力问题,文章开发了基于瞬时格林函数方法的三维时域计算程序。从数值精度和计算效率的角度出发,采用了精细时程法和一些数学上的推导计算时域格林函数的波动部分及其导数。并对Wigley型船进行了数值计算,通过水动力系数与试验数据及文献结果的比较,验证了三维时域计算程序的可靠性。

多段压裂水平井不均匀产油试井模型

针对某条或多条裂缝产油量较小或不产油这一问题,运用Green函数、Newman乘积方法和叠加原理,建立多段压裂水平井不均匀产油试井模型,将裂缝内流动划分为远离井筒的变质量线性流和靠近井筒的径向流表征裂缝有限导流,利用Stehfest数值反演得到考虑井筒存储和表皮效应的实空间井底压力解,绘制典型图版,并分析不均匀产油和裂缝参数对井底压力的影响。结果表明:多段压裂水平井均匀产油和不均匀产油的压力和压力导数特征差异明显;两端裂缝产油量越大,压裂裂缝间距越大,裂缝半长越小,裂缝呈纺锤形分布时,缝间干扰越小,早期径向流越明显,在系统拟径向流之前出现一个新平台。与试井软件Saphir中的经典多级压裂水平井数值模型对比,结果证明了提出的模型的正确性。