An improved depth-averaged nonhydrostatic shallow water model with quadratic pressure approximation

Phase-resolved information is necessary for many coastal wave problems, for example, for the wave conditions in the vicinity of harbor structures. Two-dimensional (2D) depth-averaging shallow water models are commonly used to obtain a phase-resolved solution near the coast. These models are in general more computationally effective compared with computational fluid dynamics software and will be even more capable if equipped with a parallelized code. In the current article, a 2D wave model solving the depth-averaged continuity equation and the Euler equations is implemented in the open-source hydrodynamic code REEF3D. The model is based on a nonhydrostatic extension and a quadratic vertical pressure profile assumption, which provides a better approximation of the frequency dispersion. It is the first model of its kind to employ high-order discretization schemes and to be fully parallelized following the domain decomposition strategy. Wave generation and absorption are achieved with a relaxation method. The simulations of nonlinear long wave propagations and transformations over nonconstant bathymetries are presented. The results are compared with benchmark wave propagation cases. A large-scale wave propagation simulation over realistic irregular topography is shown to demonstrate the model's capability of solving operational large-scale problems.     

梯级溃坝洪水洪峰增强机制

我国在多条河流上修建了大量梯级水库, 梯级坝溃决诱发洪水大大超过单坝溃决洪水洪峰, 因此亟需加深对梯级坝溃决洪水洪峰增强机制的认识. 本文建立了梯级坝溃决洪水演进过程的一维浅水动力学模型, 发展了一套能捕捉激波、干湿边界和保平衡结构的数值求解方法, 通过大量算例, 系统研究了梯级坝溃决洪水演进过程的质量转化和能量转化机制. 研究结果表明, 梯级溃决中, 上游溃决诱发的洪水大大增大下游水库的质量和动量, 形成一个带动量的水塔, 同时在尾部残留一个动量较大的射流, 不断补充下游坝体溃决后水塔的质量和动量, 持续维持洪峰高度. 根据该射流-水塔机制, 建立了梯级坝溃决洪水演进过程对应的射流-水塔单坝溃决洪水过程等效模型, 该等效模型基本反映了梯级坝溃决诱发洪水的洪峰过程, 并成功预测了多个坝间距为百公里量级的梯级坝溃决洪水洪峰高程和流量, 可望为流域防洪和梯级坝设计提供理论依据.      

流变岩体中让压支护作用下隧道力学行为研究

高地应力深埋软岩隧道大变形问题已成为隧道工程建设领域的突出难题. 根据高地应力深埋软岩隧道的变形特征, 基于"围岩能量吸收、变形释放"的让压支护是解决软岩隧道大变形问题的有效方法. 针对流变岩体中深埋圆形隧道在让压支护作用下的力学响应问题, 通过引入分数阶微积分理论, 采用Abel黏壶元件建立了改进的分数阶Burgers蠕变模型来表征围岩的时效变形. 此外, 通过在让压支护不同变形阶段引入刚度修正系数, 克服了传统支护未能考虑围岩变形释放的问题. 据此, 本文推导了在考虑支护延迟安装影响下, 不同变形阶段围岩与让压支护相互作用的解析解. 为了验证理论研究的正确性, 对一算例进行了不同解答及工程结果的比对, 吻合较好. 最后, 参数研究结果表明: 围岩与让压支护间的相互作用受蠕变本构模型分数阶阶数影响较大. 隧道的位移或支护压力与让压位移、支护刚度修正系数间存在线性比例关系, 但由于刚度修正系数仅保持在较小的变化范围内, 隧道的位移或支护压力变化并不显著.      

受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路.      

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

Improved Reversible Zinc Storage Achieved in a Constitutionally Crystalline-Stable Mn(VO3)2 Nanobelts Cathode

Rechargeable zinc-ion batteries (ZIBs) are potential for grid-scale applications owing to their safety, low price, and available sources. The development of ZIBs cathode with high specific capacity, wide operating voltage window and stable cyclability is urgently needed in next-generation commercial batteries. Herein, we report a structurally crystalline-stable Mn(VO₃)₂ nanobelts cathode for ZIBs prepared via a facile hydrothermal method. The as-synthesized Mn(VO₃)₂ exhibited high specific capacity of 350 mAh g⁻¹ at 0.1 A g⁻¹, and maintained a capacity retention of 92 % after 10,000 cycles at 2 A g⁻¹. It also showed good rate performance and obtained a reversible capacity of up to 200 mAh g⁻¹ after 600 cycles at 0.2 A g⁻¹ under −20 °C. The electrochemical tests suggest that Mn(VO₃)₂ nanobelts impart fast Zn²⁺ ions migration, and the introduction of manganese atoms help make the structures more indestructible, leading to a good rate performance and prolonged cycle lifespan.     

An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

The global weak solution for the shallow water wave model of moderate amplitude

In this paper, we firstly establish the existence theorem of the global weak solutions of the Cauchy problem for the shallow water wave model of moderate amplitude, then following the idea in Xin and Zhang’s work (see Xin and Zhang, 2002), we prove the uniqueness of global weak solutions using the localization analysis in the transport equation theory. Finally, several travelling wave solutions are derived.     

考虑底部隆起的浅埋隧道围岩压力计算分析

针对浅埋隧道开挖后底部隆起变形现象,应用极限分析上限法构造了考虑底部隆起变形的围岩压力计算模型,结合线性Mohr-Coulomb准则等推导出极限围岩压力的理论表达式。通过约束条件将围岩压力的计算转化为数学中的最优化问题,编制程序进行了优化计算。将计算结果与工程实测数据及文献计算结果进行了对比,验证了当前方法的可靠性。同时,指出在运用极限分析法处理浅埋隧道围岩压力问题过程中应将隧道底部一同考虑,对隧道底部支护会对整个围岩压力产生影响,有助于隧道结构的整体稳定。研究可以为浅埋隧道的开挖、支护提供一定的理论指导.     

本征正交分解技术在屋盖风压场重建与预测中的应用

给出利用本征正交分解(POD)对屋盖风压场进行重建和预测的研究结果.对一个双坡屋盖用同步多点压力扫描系统进行了风洞试验,根据POD技术采用前若干阶本征模态重建屋盖风压场.采用两种方案预测未布置测压点位置的风压时间序列.第一种方案中利用插值技术获得没有测压点位置的本征模态值.第二种方案对参考屋盖和需预测的新屋盖分别进行试验,结合由参考屋盖试验萃取的本征模态和由新屋盖试验的风压数据计算的主坐标,预测出新屋盖未知区域的风压时间序列.文中对风压场重建和预测的效果作了分析,而且比较了根据测量的风压数据和预测的风压数据所计算的屋盖风致响应.