一阶弹性波方程数值模拟中的混合吸收边界条件

Liu和Sen（2010和2012）在地震波场数值模拟中提出一种混合吸收边界条件. 该方法具有计算量小、容易实现及吸收效果好等优点. 但现有的混合吸收边界条件是针对二阶位移-应力方程设计的,存在稳定性问题. 本文首先推导了两种速度-应力单程波方程：二阶Higdon单程波方程和一阶Higdon单程波方程. 进而提出基于一阶弹性波方程的混合吸收边界条件方法. 在内部区域和边界之间引入一个过渡区域,通过单程波与双程波方程平滑过渡来消除人工边界反射. 为了改善混合吸收边界条件的吸收效果和稳定性,我们采用了能同时吸收纵、横波反射的一阶单程波方程和与变量位置有关的加权系数. 为了验证混合吸收边界条件的有效性,将其与常规分裂完全匹配层（PML）方法进行了比较. 数值模拟结果表明,与PML边界条件相比,混合吸收边界条件在耗用更小计算时间和存储量的前提下,可以获得更好的吸收效果. 另外,本文提出的两种混合吸收边界条件中,混合一阶Higdon吸收边界条件具有更好的稳定性.     

辅助微分方程完全匹配层在声波方程数值模拟中的应用

在地震波数值模拟中,为提高算法精度,需要使用高阶时间更新格式,而普通的非分裂完全匹配层（PML）吸收边界局限于低阶时间格式。辅助微分方程完全匹配层（ADE PML）是一种可以适应任意阶时间格式的非分裂完全匹配层技术,且可以直接应用复频移拉伸算子以提高PML在高角度入射时的效果。作者将ADE PML应用于声波方程四阶Runge Kutta时间格式的数值模拟中,对其吸收效能进行了检验。数值模拟表明,复频移ADE PML在高角度入射时表现优于非复频移ADE PML。另外,不同辅助变量更新格式的吸收效果存在微小差异,显格式下计算结果与解析解吻合较好。长时间能量衰减计算表明ADE PML可以稳定至2 × 10⁵时间步。     

Recent Advances in Predictability Studies in China （1999-2002）

Since the last International Union of Geodesy and Geophysics (IUGG) General Assembly (1999), the predictability studies in China have made further progress during the period of 1999-2002. Firstly, three predictability sub-problems in numerical weather and climate prediction are classified, which are concerned with the maximum predictability time, the maximum prediction error, and the maximum allowable initial error, and then they are reduced into three nonlinear optimization problems. Secondly, the concepts of the nonlinear singular vector (NSV) and conditional nonlinear optimal perturbation (CNOP) are proposed,which have been utilized to study the predictability of numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be revealedby NSV and CNOP. Thirdly, attention has also been paid to the relations between the predictability and spatial-temporal scale, and between the model predictability and the machine precision, of which the investigations disclose the importance of the spatial-temporal scale and machine precision in the study of predictability. Also the cell-to-cell mapping is adopted to analyze globally the predictability of climate,which could provide a new subject to the research workers. Furthermore, the predictability of the summer rainfall in China is investigated by using the method of correlation coefficients. The results demonstrate that the predictability of summer rainfall is different in different areas of China. Analysis of variance, which is one of the statistical methods applicable to the study of predictability, is also used to study the potential predictability of monthly mean temperature in China, of which the conclusion is that the monthly mean temperature over China is potentially predictable at a statistical significance level of 0.10. In addition,in the analysis of the predictability of the T106 objective analysis/forecasting field, the variance and the correlation coefficient are calculated to explore the distribution characteristics of the mean-square errors.Finally, the predictability of short-term climate prediction is investigated by using statistical methods or numerical simulation methods. It is demonstrated that the predictability of short-term climate in China depends not only on the region of China being investigated, but also on the time scale and the atmospheric internal dynamical process.     

有限差分格式与物理量守恒性

为了成功地开展大气数值模拟,如何构造相应的离散格式是一项十分重要的工作.本文以大气球面浅水方程为例,从不同形式的微分方程组出发,分别构造了能量守恒格式、准辛格式和多守恒格式,并作相应的数值检验和比较,从中可以清楚地看到三类格式的优劣.这三类格式构造方法不同,所保持的物理守恒性不完全相同,数值计算时所需机时也不同,这些比较结果为实际工作的不同使用需求提供了选择依据.     

Numerical Modeling of Sediment Mass Sliding and Tsunami Generation: The Case of February 7, 1963, in Corinth Gulf,Greece

Numerical modeling of a landslide process at the continental slope by taking into account slope parameters is performed for the tsunami event of February 7, 1963, reported in the Corinth Gulf, central Greece. A layered sediment structure was considered, and an initial external dynamic action at the landslide process was introduced. The results obtained were quite consistent with the observational runup data as well as with the results arrived at by conventional rigid-body and viscous-fluid models. However, this approach permits to describe in detail the formation of several wave groups and particular tsunami characteristics that are strongly dependent on the landslide model.     

Optimal precursor of the transition from Kuroshio large meander to straight path

We used the conditional nonlinear optimal perturbation(CNOP) method to explore the optimal precursor of the transition from Kuroshio large meander(LM) to straight path within a barotropic inflowoutflow model,and found that large amplitudes of the optimal precursor are mainly located in the east of Kyushu,which implies that perturbations in the region are important for the transition from LM to straight path.Furthermore,we investigated the transition processes caused by the optimal precursor,and found that these processes could be divided into three stages.In the first stage,a cyclonic eddy is advected to the formation region of the Kuroshio large meander,which enhances the LM path and causes a cyclonic eddy to shed from the Kuroshio mainstream.This process causes the LM path to change into a small meander path.Subsequently,the small meander is maintained for a period because the vorticity advection is balanced by the beta effect in the second stage.In the third stage,the small meander weakens and the straight path ultimately forms.The positive vorticity advecting downstream is responsible for this process.The exploration of the optimal precursor will conduce to improve the prediction of the transition processes from LM path to straight path,and its spatial structure can be used to guide Kuroshio targeted observation studies.     

基于探地雷达的混凝土无损检测反演成像方法

本文针对水利水电工程中的混凝土构件无损探测问题,提出了一种新的反演成像方法.传统方法主要依赖人工经验观察偏移探测数据,精度无法保证.这种方法以Maxwell方程的TM问题为数学模型,在混凝土的表面放置发射源与接收器,根据探地雷达的接收数据,采用同伦优化方法结合收敛速度较快的阻尼高斯牛顿方法作为反演算法,其成像结果更具定量化和可视性.该成像方法克服了传统雷达剖面图只能近似地反映混凝土中埋藏物及缺陷的深度、大小等缺点,不仅能够探测混凝土内部异物的位置,而且能够比较准确地确定异物的大小及属性.通过计算机模拟以及对实际资料的处理,验证了该反演成像结果直观、可靠、具有一定的应用价值.     

基于Xu-White模型横波速度预测的误差分析

在砂泥岩剖面中,基于Gassmann方程和Xu-White岩石物理模型,利用常规测井资料及实验室岩石物理数据进行横波速度估算.模型中考虑了泥质砂岩中基质性质、泥质含量、孔隙度大小和孔隙形状以及孔隙饱含流体性质对岩石速度的影响.综合分析了模型中砂、泥岩和孔隙流体弹性参数以及孔隙纵横比等输入参数的误差对预测横波速度精度的影响.数值模型试验表明,在Xu-White模型中采用变化的孔隙纵横比估算出的横波速度远远比采用固定孔隙纵横比估算出的横波速度准确.     

具有精确色散性的非线性波浪水平二维数学模型

建立具有色散性的水平二维非线性波浪方程,方程的非线性近似到了三阶。方程以波面升高和自由表面速度势表达的微分-积分型数学方程,给出方程的数值求解方法和算例,对方程积分项的处理给出了计算方法。计算结果与Boussinesq方程模型和缓坡方程模型的对应计算结果进行了对比。     

Wave Height Transformation and Set-up Between a A Submerged Permeable Breakwater and A Seawall

In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.