Properties of High-Order Finite Difference Schemes and Idealized Numerical Testing

Construction of high-order difference schemes based on Taylor series expansion has long been a hot topic in computational mathematics, while its application in comprehensive weather models is still very rare. Here, the properties of high-order finite difference schemes are studied based on idealized numerical testing, for the purpose of their application in the Global/Regional Assimilation and Prediction System(GRAPES) model. It is found that the pros and cons due to grid staggering choices diminish with higher-order schemes based on linearized analysis of the one-dimensional gravity wave equation. The improvement of higher-order difference schemes is still obvious for the mesh with smooth varied grid distance. The results of discontinuous square wave testing also exhibits the superiority of high-order schemes. For a model grid with severe non-uniformity and non-orthogonality, the advantage of high-order difference schemes is inapparent, as shown by the results of two-dimensional idealized advection tests under a terrain-following coordinate. In addition, the increase in computational expense caused by high-order schemes can be avoided by the precondition technique used in the GRAPES model. In general, a high-order finite difference scheme is a preferable choice for the tropical regional GRAPES model with a quasi-uniform and quasi-orthogonal grid mesh.     

完全非线性波浪破碎模型沿岸流数值模拟

探讨一种基于完全非线性Boussinesq方程的波浪破碎模型在沿岸流计算中的应用问题。针对控制方程中的完全非线性项对沿岸流成长过程的影响进行了深入讨论。数学模型计算结果表明,完全非线性项有使平均流局部化的作用;通过数模实验还发现,垂向高阶涡度项可以有效抑制破波区外回流;运用Visser的实验室沿岸流实测资料从沿岸流速度、波高和平均水位几方面对所提模型进行了验证,并给出了紊动参数的计算结果。     

结合边界条件的截断高阶隐式有限差分方法(英文)

有限差分方法广泛应用于求解许多科技领域所涉及的偏微分方程,高阶显式有限差分方法通常用来提高求解精度,已经提出的高阶隐式有限差分方法和截断高阶显式有限差分方法可用来进一步提高模拟精度而不增加计算量。本文首先计算了针对常规网格上的一阶导数和二阶导数、交错网格上的一阶导数的有限差分系数,发现高阶隐式有限差分系数中存在一些小的系数。频散分析结果表明:忽略这些小的差分系数能够近似维持有限差分的精度,但是显著减小了计算量。然后,引入镜像对称边界条件来提高隐式有限差分方法的精度和稳定性,采用混合吸收边界条件来减小来自模型边界所不需要的反射。最后,给出了针对均匀和非均匀介质模型的弹性波模拟例子,表明了本文方法的优点。     

基于最小平方和残差的高阶模糊联合聚类算法

目前,多数高阶联合聚类算法属于硬划分方法,不考虑聚簇重叠问题。为了更有效地分析具有重叠聚簇结构的数据,提出了一种基于最小平方和残差的高阶模糊联合聚类算法(MSR-HFCC),该算法将聚类问题转化为最小化模糊平方和残差的优化问题,推导出求解优化问题的隶属度迭代更新公式,设计出聚类过程的迭代算法。实验结果表明,MSR-HFCC算法聚类效果优于目前已有的5种硬划分高阶联合聚类算法。     

煤层水压致裂后煤岩应力解析

水压致裂后煤岩应力分布规律对水压致裂防冲效果起关键性作用。采用理论研究方法得出高压注水压致裂后及卸水后水区和气区的孔隙、瓦斯压力和煤体应力解析解。结果表明,致裂后水区孔隙压力沿径向变化不大,与注水压力接近;气区瓦斯压力沿径向呈递减趋势;在水区外围一定范围内形成瓦斯压力升高区;水区煤体环向应力将会减小,直到变为拉应力;气区煤体径向应力沿径向递减。卸水后水区孔隙压力、煤体径向应力沿径向呈递增趋势;气区煤体径向应力沿径向呈递增趋势,趋近于原始煤体应力;气区煤体环向应力沿径向呈递减趋势;气区孔隙压力沿径向呈递减趋势。这为煤层水压致裂预防冲击地压提供理论基础。     

精密单点定位的高阶电离层误差改正研究

描述了高阶电离层误差对精密单点定位(precise point positioning,PPP)的影响公式,并通过实验分析了该误差对PPP静动态定位的影响。数值结果表明,改正电离层高阶项误差可以mm级提高PPP静动态定位精度和缩短动态定位的收敛时间。     

下扬子区二叠系烃源岩评价与生源环境

基于下扬子区海域-陆域钻井岩心和露头岩样, 通过有机岩石学和有机地球化学方法, 应用有效指标参数, 从不同维度综合分析下扬子区上二叠统大隆组、龙潭组和下二叠统孤峰组、栖霞组4套烃源岩在纵向及平面上的有机地球化学特征、生烃潜力和生源环境。根据测试数据及前人研究资料, 栖霞组和大隆组烃源岩的有机质丰度为中等-好级别, 龙潭组烃源岩的有机质丰度为一般-中等级别, 孤峰组烃源岩有机质丰度达到很好级别。下二叠统烃源岩有机质丰度在平面展布上表现出海域优于陆域的特点, 上二叠统则反之。根据干酪根碳同位素特征, 栖霞组烃源岩有机质类型最好, 为Ⅰ~Ⅱ型; 其他3套烃源岩均为Ⅱ~Ⅲ型母质类型。4套烃源岩成熟度参数镜质体反射率主频分布范围为1.3%~2.0%, 均达到高热演化阶段, 在平面展布上表现出明显的非均一性。二叠系4套烃源岩生物来源以低等水生生物为主, 有机质均在贫氧的弱还原-弱氧化条件下保存, 其中大隆组沉积的水体动荡频繁和生物变化较明显。综合认为, 下扬子区二叠系烃源岩有机质丰度高, 类型较好, 具有形成大型油气田的良好物质基础, 尤其是以往被忽略的孤峰组烃源岩评价等级被提高, 是一套潜在的优质烃源岩, 其对该区进一步的油气勘探具有重要的指导意义。     

近红外反射光谱学在岩石矿物研究中的应用Ⅱ.快速测定地质样品中有机质

利用偏最小二乘法回归的多变量校正方式,建立了应用近红外反射光谱学方法无损快速测定各种地质样品中有机质的模型.设计了多重散射光校正、标准正常变量转换及导数光谱,扣除额外基线和重叠信号的影响,分离出与有机质含量有关的光谱信息.大多数地质样品的有机质近红外反射光谱估算结果与化学法符合.     

Hyporheic exchange mechanism driven by flood wave

To study the hyporheic exchange driven by a single peak flood-induced water level fluctuation (i.e., flood wave), a method combining numerical simulation with theoretical derivation was proposed based on the Inbuk Stream, Korea, where flooding occurs frequently. The hyporheic exchanges induced by different flood waves were investigated by varying amplitude (A), duration (T), wave type parameter (r), and rising duration (t_p), which were adopted from the real-time stream stage fluctuations. Additionally, the idea of constant upstream flood volume (CUFV) condition for flood waves was put forward, and the effects of “Botan” (T/A) and peak number (N) on hyporheic exchange were studied. The results showed that the hyporheic exchange flux (q) was controlled by the water level h (sine-type) and its change rate v (cosine-type), and was proportional to the polynomial of them q ∝ (ω∙ h + v), where ω is the angular frequency of the flood wave. Based on this mechanism, the influence principles on hyporheic exchanges of the typical flood wave parameters (A, T, r and t_p) as well as T/A and N under CUFV condition were clarified. The main characteristic variables of hyporheic exchange, which were maximum aquifer storage and residence time, were positively correlated. They also had positive relations to the integral of the flood wave over time, which increased when the wave became higher, wider, rounder and less skewed. However, when CUFV condition was imposed, the residence time was positively correlated with T/A, whereas the maximum aquifer storage was negatively correlated with T/A. With the increase in N, water exchanged more frequently and some water returned to the stream early, leading to the slight decrease in maximum aquifer storage and residence time. These findings enriched the theory of hyporheic exchange driven by surface water fluctuation and be of great significance to enhance pollutant degradation in the hyporheic zone downstream of reservoirs.     

A High-Order Spatiotemporal Precision-Matching Taylor–Li Scheme for Time-Dependent Problems

Based on the Taylor series method and Li's spatial differential method, a high-order hybrid Taylor–Li scheme is proposed.The results of a linear advection equation indicate that, using the initial values of the square-wave type, a result with thirdorder accuracy occurs. However, using initial values associated with the Gaussian function type, a result with very high precision appears. The study demonstrates that, when the order of the time integral is more than three, the corresponding optimal spatial difference order could be higher than six. The results indicate that the reason for why there is no improvement related to an order of spatial difference above six is the use of a time integral scheme that is not high enough. The author also proposes a recursive differential method to improve the Taylor–Li scheme's computation speed. A more rapid and highprecision program than direct computation of the high-order space differential item is employed, and the computation speed is dramatically boosted. Based on a multiple-precision library, the ultrahigh-order Taylor–Li scheme can be used to solve the advection equation and Burgers' equation.