Atmospheric stability effect on subgrid-scale physics for large-eddy simulation

Field measurements in the atmospheric boundary layer were carried out to identify the effect of atmospheric stability on subgrid-scale physics for large-eddy simulation. The basic instrumentation setup consisted of 12 three-dimensional sonic anemometers arranged in two parallel horizontal arrays (seven sensors in the lower array and five sensors in the upper array). Data from this setup are used to compute the subgrid-scale (SGS) heat fluxes and SGS dissipation of the temperature variance under stable and unstable stability conditions. The relative contribution of the SGS vertical flux to the total turbulent flux increases when going from unstable to stable conditions. The relative importance of negative SGS dissipation (backscatter) events becomes larger under stable conditions. The model coefficients for two well-known SGS models (eddy-viscosity and non-linear) are computed. Model coefficients are found to depend strongly on stability. Under both stable and unstable conditions, large negative SGS dissipation is associated with the onset of ejection events while large positive SGS dissipation tends to occur during the onset of sweep events. These findings are also supported by conditionally sampled 2D velocity and temperature fields obtained using the 12 anemometers placed in a vertical array.     

伪谱法弹性波场数值模拟中的边界条件

边界条件问题长期以来一直是困扰地震波数值模拟研究者的一个难题,许多人都提出了有效的方法,但是该问题仍然需要研究.本文针对伪谱法地震波场数值模拟的特殊要求,即所有网格点相互耦合,且傅立叶变换的周期性使得方程在网格边界上很难得到一个吸收的替代方程,研究衰减边界条件中衰减系数的变化对边界反射波衰减效果的影响.数值实验结果说明,随着衰减系数的增大,振幅衰减加快,用很少的过渡带网格就可以使边界上的反射波能量很小.但是如果衰减率过大,就会在传播区和过渡带产生干扰波场.因此,在衰减系数的选择上应采取折中办法,即在取某一较小的衰减系数的前提下,设置较少的过渡带网格数使边界的能量反射最少.     

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with M being a positive integer for regular grids are discussed and illustrated by constructing the second order (M = 1) and the fourth order (M = 2) recursion formulas.     

矿井瞬变电磁法三维时域有限差分数值模拟

给出了矿井全空间瞬变电磁场的时域有限差分法(FDTD)算法,并推导了Mur吸收边界条件.利用Mur吸收边界条件,选用均匀全空间电偶极源作为初始激发源,模拟了均匀介质中巷道底板岩层内部和层状介质中三维低阻异常体的全空间响应特性,分析了瞬变电磁场在均匀介质中1.9μs和27.6μs两时刻的传播规律及在层状介质中1.2μs和0.023 ms两时刻的传播规律.结果表明:巷道对电场的影响在初期并不明显,在20μs后才表现出来;瞬变场能较好地分辨低阻层,对高阻层的穿透能力强,并且对低阻体反映灵敏;吸收边界条件只有在场域较大、网格节点较多时才能产生明显的效果.所研究成果为矿井瞬变电磁法资料的解释提供了理论依据.     

数值模拟在地球动力学中的研究进展

本文主要针对有限单元法,对近10几年来数值模拟在地球动力学中的应用和发展作了回顾,分为构造应力场模拟;地幔热对流模拟;板块碰撞模拟;岩石圈流变学模拟;以及地震机制与预测模拟等部分.简单阐述了当前地球动力学数值模拟的发展趋势并论述了其面临的主要问题.     

An explicit method for numerical simulation of wave equations: 3D wave motion

In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order (M=1) recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.     

井间地震波动方程正演数值模拟及其应用

井间地震正演模拟是在给定地层参数及边界条件的情况下求波动方程数值解的过程.本文详细推导了井间二维声波方程四阶差分方程;根据假设的包含楔形体和丘状体的理论地层模型,对其波场进行了模拟计算分析;据胜利油田垦71区块两口井的实际声波测井资料建立了精细速度模型,对其正演模拟的合成记录波场进行分析,并把合成记录反射波成像与实际的过井三维地震剖面进行了对比,验证了所设计观测系统的合理性.     

浅层地震勘探中有限元数值模拟方法的应用研究

针对目前广泛用于解决工程地质问题的浅层地震勘探特点,通过对浅层小尺度介质进行地震波数值模拟,揭示地震波在不同浅层介质模型中的波场特征和传播规律.为浅层地震勘探野外数据采集前合理选择观测系统提供指导性的方案,并能对地震勘探成果解释的合理性给予客观评价.在分析各种数值模拟方法特点的基础上,选择具有精度高、易模拟复杂结构的有...     

基于电场矢量波动方程的三维可控源电磁法有限单元法数值模拟

从可控源电磁法的基本原理出发,推导了基于电场矢量波动方程的三维边值问题,利用广义变分原理,把边值问题转换为变分问题,并引入散度条件,避免了伪解的出现,使有限元计算在理论上更加完备.在准静态近似条件下,把水平电偶极子在空中和大地的远区电场闭合表达式作为有限元计算中的区域外边界条件,解决了边界条件加载的困难;把应用于地震模拟中的伪delta函数引入到可控源电磁法中的三维有限元模拟中,消除了源点的奇异性,提高了方程组的稳定性.通过对均匀大地和层状介质模型的模拟,检验了程序的正确性,并对典型的地质体模型进行了数值模拟,分析了其变化规律.     

波场模拟中的数值频散分析与校正策略

波动方程有限差分法正演模拟,对认识地震波传播规律、进行地震属性研究、地震资料地质解释、储层评价等,均具有重要的理论和实际意义.但有限差分法本身固有存在着数值频散问题,数值频散在正演模拟中是一种严重的干扰,会降低波场模拟的精度与分辨率.针对TI介质波场模拟的交错网格有限差分方法,本文从空间网格离散、时间网格离散和算子近似等三个方面对其产生的数值频散进行了分析,并结合其他学者的研究成果给出了TI介质波场模拟中压制数值频散的方法与策略：在已知介质频散关系时,对差分算子可实施算子校正;通过提高差分方程的阶数来提高波场模拟精度;采用流体力学中守恒式方程的通量校正传输方法来压制波场模拟中的数值频散;在实际正演模拟时,采用交错网格高阶有限差分方程,不仅在空间上采用高阶差分,而且在时间上也要采用高阶差分,否则只在单一方向上（空间或时间）提高方程的阶数对压制数值频散也不会取得理想的效果.     

Field isotope investigations and numerical simulation of lake hydrodynamics

A three‐dimensional, numerical free‐surface‐flow simulation model is developed to investigate hydrodynamics of a lake and the predictive capabilities of the numerical model are validated by comparing them with field results obtained from Lake Naini, Uttar Pradesh, using environmental isotope (δ¹⁸O, δD and ³H) techniques. This has been carried out in order to understand the hydrodynamics of a lake (i.e. circulations, mixing and transport of water within the lake). Copyright © 2002 John Wiley & Sons, Ltd.     

Theoretical/numerical model for the transport of non-uniform suspended sediment in open channels

In this paper, we address the transport of multi-disperse suspended sediment mixtures in open channels, via the use of the two-fluid model. To that end, we extend previously developed frameworks for the dilute and non-dilute transport of suspended sediment. Within the scope of the Reynolds-averaged Navier-Stokes (RANS) equations, these modeling frameworks comprise mass and momentum equations for both phases (water and sediment). Here, we calculate the distribution of total volumetric concentration of sediment using two approaches: (1) by considering the mixture as represented by a single size; we call this approach Partial two-fluid model for uniform sediments (PTFMU); and (2) by combining the volumetric concentration of the sediment corresponding to several particle size classes; we call this approach Partial two-fluid model for non-uniform sediments (PTFMNU). In the second approach, we propose a methodology for the computation of the overall velocity of the disperse phase as a function of the velocities of each size class. k-ε type closures to account for the turbulence in the carrier phase (water) are applied. We also consider the coupling between the two phases through the drag force. Velocities of the carrier and disperse phases, and concentrations for each sediment class size are numerically solved by integrating the differential equations over control volumes. In order to validate our models, we compare numerical results to experimental data of Einstein and Chien [H.A. Einstein, N. Chien, Effects of heavy sediment concentration near the bed on velocity and sediment distribution, MRD sediment series report, University of California, Berkley, 1955] and Taggart et al. [W.C. Taggart, C.A. Yermoli, S. Montes, A. Ippen, Effects of sediment size and gradation on concentration profiles for turbulent flow, Massachusetts Institute of Technology, 1972]. Results of mean velocity of the carrier phase are in close agreement with the experimental data. For the prediction of sediment concentrations, we observe that there is a difference in the results using the two approaches mentioned above. We additionally obtain values of the Schmidt number needed to improve the agreement between predictions of the distribution of suspended sediment and the experimental data, and discuss the effect of sediment size and increasing sediment concentration on the values of the Schmidt number.     

3D DEMAP 数值模拟与观测实验

为推动电磁剖面(EMAP)技术向找矿勘探领域发展, 本文针对密集阵列剖面(DEMAP)测量方式, 利用三维积分方程法对层状介质中赋存三维地质异常体的电性结构进行了数值模拟, 并在青海野马泉铁锌矿集区西部进行了大地电磁(MT)与DEMAP的野外对比观测实验.数值模拟结果显示, DEMAP观测方式获得的结果受偏移距影响, 造成的视电阻率和相位误差与偏移距大小和地下电性结构的复杂性密切相关, 但在整体上, 统计误差≤10%.通过对野马泉矿集区的实验结果分析可得, DEMAP与MT的视电阻率断面和相位断面具有较好的一致性.本文从理论和实验上都表明DEMAP观测技术是一种有潜力的、经济、快速、有效的找矿手段.     

基于LS-RSGFD方法优化的横向各向同性(TI)介质一阶qP波高精度数值模拟

为克服各向异性介质弹性波数值模拟中存在着计算量大和波场分离困难等局限,研究了声学近似的VTI介质和TTI介质一阶qP波数值模拟方法.首先对VTI介质弹性波方程进行声学近似,推导了VTI介质一阶qP波方程;然后基于精确的TTI介质频散关系,引入一个包含各向异性控制参数σ的新辅助波场,推导了稳定的TTI介质二阶耦合qP波波动方程,并通过引入波场的伪速度分量,推导了等价的一阶应力-速度形式.结合旋转交错网格有限差分(RSGFD)和基于最小二乘优化的有限差分(LS-FD)两种各具优势的方法,研究了最小二乘旋转交错网格有限差分(LS-RSGFD)方法,并用其数值求解VTI和TTI介质一阶qP波方程,然后通过构造其LS-RSGFD格式,实现了高精度的各向异性介质qP波波场数值模拟.数值模拟结果表明:TI介质一阶qP波方程能够准确地模拟各向异性介质中qP波的运动学特征,引入控制参数σ能够有效地减弱不稳定性问题,保证非均匀TTI介质中qP波场的稳定传播;利用优化的LS-RSGFD方法可以得到高精度的合成地震记录,同时还可以相对地提高计算效率.     

VTI介质纯P波混合法正演模拟及稳定性分析

各向异性介质纯P波方程完全不受横波的干扰,在一定程度上可以减缓由于介质各向异性引起的数值不稳定,本文推导了具有垂直对称轴的横向各向同性(VTI)介质纯P波一阶速度-应力方程.由于纯P波方程存在一个分数形式的伪微分算子,无法直接采用有限差分法求解.针对该问题,本文采用伪谱法和高阶有限差分法联合求解波动方程,重点分析了混合法求解纯P波一阶速度-应力方程的稳定性问题,并给出了混合法求解纯P波方程的稳定性条件.数值模拟结果表明纯P波方程伪谱法和高阶有限差分混合法能够进行复杂介质的正演模拟,在强变速度、变密度的地球介质中仍然具有较好的稳定性.     

地温场数值模拟软件包

为了实现多年来我国地热数据的挽救和共享,我们开发了“大地热流数据库”,该库的开发使用了Microsoft Visual C++6.0 和Visual Basic 6.0作为编成语言.该库是“中国岩石圈三维结构数据库”的子库之一.该库具备对原始数据的查询、增加、删除和编辑和地温场的数值模拟,针对岩石圈范围内的地质体,比如对地下一维、二维和三维温度场的有限元数值模拟,以方便地热工作者解决一些常见的地热问题.     

太湖风生流的三维数值模拟

建立了太湖三维风生流数值模型,并用差分法求解;垂直方向上采用了坐标变换技术,把任一节点的水深转换成无量纲水深,从而有效地消除了因风力作用造成的自由水面波动和湖底不规则的影响;水平面上采用锯齿网格处理,对于四周以闭边界为主的湖泊水域,显得比较合理。计算结果表明,湖泊风生流沿垂直、水平方向都有较大变化,流向上下、水平也并不一致,这是湖泊水流区别于其它水域水流之所在。计算模拟显示所建模型的有效性和可操作性。     

数值模拟方法在应力场演化及地震科学中的研究进展

本文对数值模拟方法(主要针对有限单元法)在应力场演化及地震科学中的应用和发展做了回顾与总结,主要包括构造应力场模拟、地震活动性模拟、地震危险性模拟等部分,并对数值模拟方法的发展趋势、方法的优势及其所存在的主要问题做了探讨.     

大型结构地震反应值模拟中的波动输入

解耦的时域有限元数值模拟技术在考虑土－结构相互作用的大型结构地震反应分析中的应用日趋成熟。为完善其中的波动输入技术，本提出 了一种波动输入时步数值模拟的简便方法，替换对自由场的频域计算，从而使结构反应分析可以完全通过时步数值模拟实现。同时，通过数值实现，对这一实施方案的有效性进行了检验。     

有限元算法在声波方程数值模拟中的频散分析

针对有限元算法在地震波数值模拟中的数值频散问题,利用集中质量矩阵双线性插值有限元算法,推导了二维声波方程的频散函数.在此基础上采用定量分析方法,对比分析了网格纵横长度比变化时的入射方向、空间采样间隔、地震波频率以及地层速度对数值频散的影响.数值算例和模型正演结果表明：当采用集中质量矩阵双线性插值有限元算法时,为了有效地压制数值频散,在所使用震源子波的峰值频率对应的波长内,采样点数目应不少于20个;减小网格长度的纵横比可以有效地抑制入射角(波传播方向与z轴的夹角)较小的地震波的数值频散;地震波频率越高,传播速度越慢,频散越严重,尤其是当相速度与其所对应的频率比值小于2倍空间采样间隔时,不仅会出现严重的数值频散,还会出现假频现象.