全球非静力半隐式半拉格朗日模式及其极区离散处理

全球有限区同化预报系统GRAPES(Global Regional Assimilation and Prediction System)中的全球模式是新研发的新一代全球非静力数值预报模式, 该模式将作为中国气象局下一代全球中期数值预报的业务模式. 模式动力框架的特点包括采用全可压方程组、非静力/静力可选、半隐式半拉格朗日大时间步长、利用预条件求解复杂的三维亥姆赫兹(Helmholtz)椭圆型方程等. 针对极地奇异性的特点, 介绍了GRAPES全球模式在极地的离散处理方案, 包括采用水平风分量v放在极地的Arakawa C网格, 引入极地滤波解决极地数值计算的稳定性, 近极地Helmholtz方程的订正, 及为提高球坐标系下拉格朗日上游点计算精度的处理等. 平衡流理想场试验表明, 模式对极地半拉格朗日上游点及极地的处理是正确的; Held 和 Suarez试验表明模式可保证长期时间积分的守恒特性.     

完整锚杆低应变动力响应问题的半解析解及分析

建立完整锚杆低应变瞬态动力响应的数学力学模型并推导出相应的半解析解，研究分析了不同参数对锚杆顶端瞬态动力响应的影响，并将瞬态激振条件下得到的理论曲线与反射波法测得的实际曲线进行了拟合对比，结果表明两者吻合很好。     

二维SH波方程的半解析解及其数值模拟

本文以波动理论为基础, 半解析化求解地震勘探中常用的SH波方程. 获得的主要结果包括: 给出了二维均匀介质中SH波方程的解析解; 利用Cagniard-de Hoop方法详细推导了二维双层介质中SH波方程的解析解, 获得了透射波的解析解表达式. 同时, 基于SH波方程的解析表达式, 给出了包含各种波(如直达波、反射波、首波以及透射波)的解析解和波形图. 对于比较复杂的积分型解析解, 利用数值积分方法给出了数值结果, 并与优化的近似解析离散化方法(ONADM)和4阶Lax-Wendroff修正方法(LWC)的数值结果进行了比较, 以验证解析解的正确性. 本文的研究成果有望在检验波动方程数值新方法的有效性、波传播理论分析等方面得到应用.     

刚构桥随机地震动响应的简明解析解及等效地震力计算

顺桥向随机地震动作用下,大跨度刚构桥墩梁固结处墩顶产生动弯矩会引起桥跨产生动弯矩,从而会引起桥跨结构水平及竖向耦合振动。针对现行刚构桥随机地震动响应无解析解的问题,提出了一种分析其顺桥向随机地震激励下水平及竖向耦合震动响应分析的简明解析解。首先,建立刚构桥顺桥向激励下水平和竖向耦合振动的地震动方程,利用实模态振型分解法将结构地震动化为以实模态广义坐标表示的系列单自由度地震动方程的线性组合;其次,基于虚拟激励法获得刚构桥实模态广义坐标和结构位移的频域解,并基于二次式分解法获得了上述响应量的0～2谱矩和方差的简明解析解;再次,基于动力学等效原则获得了刚构桥等效地震力的计算式;最后,通过算例验证了所提解析解的正确性,并研究了刚构桥响应量与实模态振型的关系。研究表明：刚构桥地震动分析时需要考虑多个振型的影响,且竖向振动不能忽略。本文所提方法可用于其他复杂桥梁基于复杂平稳随机激励下响应量的分析。     

饱和地基中空沟近场隔振的现场试验与二维半解析边界元分析

动力机器运行和车辆行驶等会产生振动污染,危及邻近建筑物安全和干扰精密仪器设备正常运行等。这些振动污染可通过在地基中设置空沟的方式来降低或消除。针对饱和地基上明置动力机器基础的环境振动影响及空沟近场隔振问题,进行了饱和地基上空沟近场隔振的现场试验,并对试验结果进行了无量纲化分析;基于饱和土半解析边界元法,分别推导了动力机器基础环境振动影响和空沟近场隔振的边界元方程;在此基础上,详细研究了空沟对动力机器基础振动影响的隔振效果,分析了空沟深度、宽度和距振源距离对其隔振效果的影响。结果表明:空沟能够有效的降低动力机器基础的环境振动影响;空沟宽度对其隔振效果影响相对较小,而空沟深度对其隔振效果影响较大,为获得较好的隔振效果,空沟深度建议取1倍Rayleigh波波长;空沟距振源距离对其隔振效果也有较大影响,距离越远则隔振效果也越好,当被保护建筑距振源较远时,建议空沟在被保护建筑附近设置。此外,在某些特殊情况下,空沟隔振系统会由于共振现象而出现隔振效果劣化的现象,在工程设计中应予以注意。     

均匀半空间导体的并矢格林函数解析式

导出了低频时谐电磁场中均匀半空间导体的并矢格林函数解析式,它由初等函数和修正贝塞尔函数的有限形状所表示．该解析式可用Kelvin函数的近似多项式计算,可显著提高并矢格林函数的计算速度．用"电磁分析方法验证模型"的第15号问题作为验证模型,结果表明,计算值和测量值吻合良好．     

均匀半空间导体的并矢格林函数解析式

导出了低频时谐电磁场中均匀半空间导体的并矢格林函数解析式,它由初等函数和修正贝塞尔函数的有限形状所表示．该解析式可用Kelvin函数的近似多项式计算,可显著提高并矢格林函数的计算速度．用"电磁分析方法验证模型"的第15号问题作为验证模型,结果表明,计算值和测量值吻合良好．     

半球形凹陷饱和土半空间对入射平面SV波三维散射问题的解析解

以Biot饱和多孔介质动力学理论为基础,利用Fourier-Bessel级展开法,给出了饱和多孔介质半空间中半球形凹陷地形对入射平面SV波散射问题的解析解.利用这一解析解数值计算地表位移幅值,分析入射角、入射波频率对地表位移幅值的影响,并与现存的单相介质情况下三维半球形凹陷问题解析解进行对比得出如下结论：(1)本文两相介质模型与单相介质模型有很大区别;(2)入射角、入射频率对场地表面位移分量有重要影响;(3)随着入射角、入射频率的增大,地表位移分布变得更复杂,且放大效应比单相介质模拟结果更加显著.     

基于半解析法有效和快速估计GRACE全球重力场的精度

首先基于半解析法建立了新的GRACE卫星K波段测量系统星间测速、GPS接收机轨道位置和加速度计非保守力误差联合影响累计大地水准面的误差模型;其次,基于各关键载荷精度指标的匹配关系,论证了误差模型的可靠性;最后,基于美国喷气动力实验室（JPL）公布的2006年的GRACE Level 1B实测误差数据,有效和快速地估计了120阶全球重力场的精度,在120阶处累计大地水准面的精度为18.368 cm,其结果和德国地学研究中心（GFZ）公布的EIGEN-GRACE02S全球重力场模型符合较好. 本文的研究为将来国际卫星重力测量计划（如GRACE Follow-On, 360阶）中高阶全球重力场模型精度的有效和快速估计提供了理论基础和计算保证.     

幂函数剪切模量成层土非线性地震反应的半解析算法

运用文献[1]所建议的动态应力一应变关系及其推广的Masing加卸载准则,考虑土料在地震等产生的不规则加载条件下的非线性滞回特征,将增量法与相应场地地震线性反应解析解[2]相结合,提出了该动力非线性方程的半解析时域算法,基于改进的一维剪切梁模型,对剪切模量是其深度的某一幂函数的成层非均质土层,建立了求解土体地震反应的非线性分析技术。针对文献[2]中的土层剖面,做了计算、分析和讨论。     

Development of a new semi-analytical model for cross-borehole flow experiments in fractured media

Analysis of borehole flow logs is a valuable technique for identifying the presence of fractures in the subsurface and estimating properties such as fracture connectivity, transmissivity and storativity. However, such estimation requires the development of analytical and/or numerical modeling tools that are well adapted to the complexity of the problem. In this paper, we present a new semi-analytical formulation for cross-borehole flow in fractured media that links transient vertical-flow velocities measured in one or a series of observation wells during hydraulic forcing to the transmissivity and storativity of the fractures intersected by these wells. In comparison with existing models, our approach presents major improvements in terms of computational expense and potential adaptation to a variety of fracture and experimental configurations. After derivation of the formulation, we demonstrate its application in the context of sensitivity analysis for a relatively simple two-fracture synthetic problem, as well as for field-data analysis to investigate fracture connectivity and estimate fracture hydraulic properties. These applications provide important insights regarding (i) the strong sensitivity of fracture property estimates to the overall connectivity of the system; and (ii) the non-uniqueness of the corresponding inverse problem for realistic fracture configurations.     

Existence of the solutions and the attractors for the large-scale atmospheric equations

The atmosphere is a kind of fluid surrounding therotating earth, and its state can be described by thevelocity vector v, the temperature T, the density ρ, andthe pressure p at each point. Its evolution process isessentially governed by the Navier-Stockes equationand the temperature equation. Due to the specialty andthe complexity of the atmospheric problem, althoughsome modified and simplified work have made onthese fluid mechanics and temperature equations, theyare still a very complex forc…     

耦合PML边界条件的三维大地电磁二次场有限差分法

本文将大地电磁场分解为一次场和二次场,应用交错网格有限差分法模拟计算大地电磁二次场,并引入各向异性最佳匹配层（PML）吸收边界条件作为二次场边界条件,实现了耦合PML吸收边界条件的三维大地电磁二次场有限差分正演模拟.为了确保正演的稳定性和效率,QMR求解器和磁感应矢量散度校正技术被用于PML吸收边界条件下系数矩阵的快速求解.三维模型正演响应表明,基于二次场的三维大地电磁有限差分算法具有较高的计算精度和可靠性.通过计算分析不同PML吸收因子条件的大地电磁正演结果,显示在适当的吸收因子下,PML吸收边界条件可较大幅度的减小外边界距离,从而有效的压缩模型求解空间,最终提高三维大地电磁正演模拟的效率.

     

High-order finite volume WENO schemes for the shallow water equations with dry states

The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.     

漾濞MS6.4地震长周期强地震动的有限差分初步模拟

根据我国川滇地区的地质地貌特征、前人地质资料和2021年漾濞M_S6.4地震的震源参数初步反演结果,建立三维速度结构模型,采用三维有限差分法对漾濞地震的长周期地震动进行研究.对实际地震烈度和模拟烈度进行对比,同时在区域附近布置了36个观测点,给出其中6个观测点的三分量速度时程,并给出所有观测点阻尼比为5%的速度反应谱,结果表明:(1)模拟的速度峰值已超过25 cm/s,与实际漾濞地区附近的烈度为8度吻合;(2)受断层滑动分布影响,速度水平分量在西北方向分布范围更广,衰减速度明显慢于东南方向,并且在极震区,东北—西南方向的地震动衰减也较慢.方向性效应对峰值大小及其分布范围的影响显著;(3)观测点速度反应谱的特征周期分布在1~3 s范围内,可能会因为共振效应对区域附近的大型建筑物产生较为严重的破坏.需要对漾濞地震进行进一步研究,以期对漾濞地震的长周期地震动有更为细致的认识.     

Statistical properties of an enstrophy conserving finite element discretisation for the stochastic quasi-geostrophic equation

ABSTRACT

A framework of variational principles for stochastic fluid dynamics was presented by Holm, and these stochastic equations were also derived by Cotter, Gottwald and Holm. We present a conforming finite element discretisation for the stochastic quasi-geostrophic equation that was derived from this framework. The discretisation preserves the first two moments of potential vorticity, i.e. the mean potential vorticity and the enstrophy. Following the work of Dubinkina and Frank, who investigated the statistical mechanics of discretisations of the deterministic quasi-geostrophic equation, we investigate the statistical mechanics of our discretisation of the stochastic quasi-geostrophic equation. We compare the statistical properties of our discretisation with the Gibbs distribution under assumption of these conserved quantities, finding that there is an agreement between the statistics under a wide range of set-ups.     

A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain

An unstructured Godunov-type finite volume model is developed for the numerical simulation of geometrically challenging two-dimensional shallow water flows with wetting and drying over convoluted topography. In the framework of sloping bottom model, a modified formulation of shallow water equations is used to preserve mass conservation during flooding and recession. The key ingredient of the model is the use of this combination of the sloping bottom model and the modified shallow water equations to provide a robust technique for wet/dry fronts tracking and, together with centered discretization of the bed slope source term, to exactly preserve the static flow on irregular topographies. The variable reconstruction technique ensures nonnegative reconstructed water depth and reasonable reconstructed velocity, and the friction terms are solved by semi-implicit scheme that does not invert the direction of velocity components. The robustness and accuracy of the proposed model are assessed by comparing numerical and reference results of extensive test cases. Moreover, the results of a dam-break flooding over real topography are presented to show the capability of the model on field-scale application.     

Application of the iterative solution method with Schur complement reduction to mixed finite elements based in a tetrahedral discretization

The iterative solution method for mixed finite element methods is applied to a 3-D domain partitioned with tetrahedral elements. For the particular discretization technique of first partitioning the domain with hexahedral cells, and then subsequently partitioning cells with five tetrahedral elements, a Schur complement decomposition is devised wherein the actual number of equations solved is reduced by 80%. Although this Schur complement reduction requires a fair amount of computational overhead, its application within the iterative solution method can reduce overall solution time by about 44%, depending on closure criterion and other factors.     

An explicit finite element－finite difference method for analyzing the effect of visco－elastic local topography on the earthquake motion

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时域有限差分法在地质雷达二维正演模拟中的应用

本文从地质雷达正演原理着手,分析了差分格式中半空间步长与半时间步长的实现方法,同时通过分析数值频散的产生,进而推导出了理想频散关系和超吸收边界条件．最后文中还对比了有无边界条件的雷达正演模拟效果和精度．