Stability of High-Order Staggered-Grid Schemes for 3D Elastic Wave Equation in Heterogeneous Media

In this paper, we firstly derive the stability conditions of high-order staggered-grid schemes for the three-dimensional (3D) elastic wave equation in heterogeneous media based on the energy method. Moreover, the plane wave analysis yields a sufficient and necessary stability condition by the von Neumann criterion in homogeneous case. Numerical computations for 3D wave simulation with point source excitation are given.

Implementation of the Semi-Lagrangian Advection Scheme on a Quasi-Uniform Overset Grid on a Sphere

The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset （Yin-Yang） grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-oriented latitude-longitude grid components （called Yin and Yang respectively） that overlapp each other, and this effectively avoids the coordinate singularity and the grid convergence near the poles. In this overset grid, the way of transferring data between the Yin and Yang components is the key to maintaining the accuracy and robustness in numerical solutions. A numerical interpolation for boundary data exchange, which maintains the accuracy of the original advection scheme and is computationally efficient, is given in this paper. A standard test of the solid-body advection proposed by Williamson is carried out on the Yin-Yang grid. Numerical results show that the quasi-uniform Yin-Yang grid can get around the problems near the poles, and the numerical accuracy in the original semi-Lagrangian scheme is effectively maintained in the Yin-Yang grid.

Application of a Shape-Preserving Advection Scheme to the Moisture Equation in an E-grid Regional Forecast Model

This paper presents a methodology which is very useful to design shape-preserving advection finite difference scheme on general E-grid horizontal arrangement of variables through introducing a two-step shape-preserving positive definite advection scheme in the moisture equation of the LASG-REM (LASG regional E-grid eta-coordinate forecast model). By trial-forecasting six local heavy raincases, the efficiency of the shape-preserving advection scheme in practical application has been examined. The LASG-REM with the shape-preserving advection scheme has a good forecasting ability for local precipitation.

A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

This paper presents a simple approach for improving the performance of the weighted essentially nonoscillatory(WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifthorder WENO-JS(WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202–228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable.The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On nonuniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime,the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.

Comparison and Modification: TVD Schemes for Scalar Transport on An Unstructured Grid

In most TVD schemes, the r-factors were proposed according to the cell-centered（CC） finite volume method（FVM） framework for the numerical approximation to the convective term. However, it is questionable whether those r-factors would be appropriate and effective for the vertex-centered（VC） FVM. In the paper, we collected five kinds of r-factor formulae and found out that only three of those, respectively by Bruner（1996）, Darwish and Moukalled（2003） and Cassuli and Zanolli（2005） can be formally extended to a context of the VC FVM. Numerical tests indicate that the TVD schemes and r-factors, after being extended and introduced to a context of the VC FVM, maintained their similar characteristics as in a context of the CC FVM. However, when the gradient-based r-factors and the SUPERBEE scheme were applied simultaneously, non-physical oscillations near the sharp step would appear. In the transient case, the oscillations were weaker in a context of the VC FVM than those in a context of the CC FVM, while the effect was reversed in the steady case. To eliminate disadvantages in the gradient-based r-factor formula, a new modification method by limiting values on the virtual node, namely Фu in the paper, was validated by the tests to effectively dissipate spurious oscillations.

Implementation of a Conservative Two-step Shape-Preserving Advection Scheme on a Spherical Icosahedral Hexagonal Geodesic Grid

An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.

Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids

A high-order upwind scheme has been developed to capture the vortex wake of a helicopter rotor in the hover based on chimera grids. In this paper, an improved fifth-order weighted essentially non-oscillatory （WENO） scheme is adopted to interpolate the higher-order left and right states across a cell interface with the Roe Riemann solver updating inviscid flux, and is compared with the monotone upwind scheme for scalar conservation laws （MUSCL）. For profitably capturing the wake and enforcing the period boundary condition, the computation regions of flows are discretized by using the struc- tured chimera grids composed of a fine rotor grid and a cylindrical background grid. In the background grid, the mesh cells located in the wake regions are refined after the so- lution reaches the approximate convergence. Considering the interpolation characteristic of the WENO scheme, three layers of the hole boundary and the interpolation boundary are searched. The performance of the schemes is investigated in a transonic flow and a subsonic flow around the hovering rotor. The results reveal that the present approach has great capabilities in capturing the vortex wake with high resolution, and the WENO scheme has much lower numerical dissipation in comparison with the MUSCL scheme.

Computational uncertainty and optimal grid size and time step of the Lax-Friedrichs scheme for the 1D advection equation

本文对于应用Lax-Friedrichs格式数值求解一维平流方程,研究数值求解过程中产生的截断误差与舍入误差,以及两种误差逐层向高时间层传播的累积,得到新的数值解总误差上界的理论近似公式,以及最优格距和最优时间步长的理论公式.通过数值算例验证了所得公式的可靠性。然后,发现了两种不同机器精度下最优时间步长之比满足的一个仅与机器精度有关的普适关系.最后,理论验证了在网格比固定的情况下,此问题满足数值计算的不确定性原理,以及在机器有限精度下最优时间步长的必然存在。

Difference between grid connections of large-scale wind power and conventional synchronous generation

In China, regions with abundant wind energy resources are generally located at the end of power grids. The power grid architecture in these regions is typically not sufficiently strong, and the energy structure is relatively simple. Thus, connecting large-capacity wind power units complicates the peak load regulation and stable operation of the power grids in these regions. Most wind turbines use power electronic converter technology, which affects the safety and stability of the power grid differently compared with conventional synchronous generators. Furthermore, fluctuations in wind power cause fluctuations in the output of wind farms, making it difficult to create and implement suitable power generation plans for wind farms. The generation technology and grid connection scheme for wind power and conventional thermal power generation differ considerably. Moreover, the active and reactive power control abilities of wind turbines are weaker than those of thermal power units, necessitating additional equipment to control wind turbines. Hence, to address the aforementioned issues with large-scale wind power generation, this study analyzes the differences between the grid connection and collection strategies for wind power bases and thermal power plants. Based on this analysis, the differences in the power control modes of wind power and thermal power are further investigated. Finally, the stability of different control modes is analyzed through simulation. The findings can be beneficial for the planning and development of large-scale wind power generation farms.

An Application of Finite Volume WENO Schemeto Numerical Modeling of Tidal Current

A depth-averaged 2-D numerical model for unsteady tidal flow in estuaries is established by use of the finite volume WENO scheme which maintains both uniform high order accuracy and an essentially non-oscillatory shock transition on unstructured triangular grid. The third order TVD Range-Kutta method is used for time discretization. The model has been firstly tested against four cases： 1） tidal forcing, 2） seiche oscillation, 3） wind setup in a closed bay, and 4） onedimensional dam-break water flow. The results obtained in the present study compare well with those obtained from the corresponding analytic solutions idealized for the above four cases. The model is then applied to the simulation of tidal circulation in the Yangpu Bay, and detailed model calibration and verification have been conducted with measured tidal current in the spring tide, middle tide, and neap tide. The overall performance of the model is in qualitative agreement with the data observed in 2005, and it can be used to calculate the flow in estuaries and coastal waters.

An Accurate Multimoment Constrained Finite Volume Transport Model on Yin-Yang Grids

A global transport model is proposed in which a multimoment constrained finite volume （MCV） scheme is applied to a Yin-Yang overset grid. The MCV scheme defines 16 degrees of freedom （DOFs） within each element to build a 2D cubic reconstruction polynomial. The time evolution equations for DOFs are derived from constraint conditions on moments of line-integrated averages （LIA）, point values （PV）, and values of first-order derivatives （DV）. The Yin-Yang grid eliminates polar singularities and results in a quasi-uniform mesh. A limiting projection is designed to remove nonphysical oscillations around discontinuities. Our model was tested against widely used benchmarks; the competitive results reveal that the model is accurate and promising for developing general circulation models.

Finite-difference modeling with variable grid-size and adaptive time-step in porous media

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

Basic function scheme of polynomial type

A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.

轮辐式索承网格屋盖钢结构单道胎架施工技术

泰安体育场作为山东省泰安市的新地标,其钢结构屋盖采用轮辐式索承网格结构,通过68榀径向索和1道中央环索形成张拉结构体系,最大悬挑跨度为45 m。通过数值分析对施工过程进行了精细化稳定性分析,针对不规则构件吊装的工程技术难点,进行了吊装方案的设计与优化;考虑到成本控制与施工周期,极具创新性地采用了径向单道胎架作为屋盖施工过程中的临时支撑,结合工程实际情况设计了胎架转换结构,并对单道胎架整体在多种可能的荷载组合作用下进行验算与校核。通过对体育场屋盖施工全过程的模拟以及对安装过程中的重难点进行优化分析,为现场施工的安全顺利开展提供了技术保障,可为其他类似采用单道胎架施工方法的工程提供施工方案设计的新思路。

融合方面语义和网格标记的多语言意见元组抽取

面向方面的细粒度意见抽取(Aspect-oriented Fine-grained Opinion Extraction,AFOE)任务的目的是以意见对的形式抽取文本评论中的方面和意见词或者再抽取情感极性,形成意见三元组。以往的研究通常以管道方式抽取意见元素,容易出现错误传播的问题,而且大多数只关注方面词和意见词的单个子任务抽取,忽略了不同意见元素之间的相互影响和指示信息,导致意见挖掘任务不完整。此外,面向中文的意见元素抽取任务的研究较少。针对以上问题,文中提出了融合方面语义和网格标记的多语言意见元组抽取模型。首先,使用向内LSTM(Inward-LSTM)和向外LSTM(Outward-LSTM)编码方面词及其对应的上下文信息建立方面和候选意见词的关联,再结合全局信息生成特定方面语义特征的上下文表示,有利于提高下游意见元素抽取的性能。其次,使用网格标记方案的推理策略,利用方面和意见词之间的依赖指示信息进行更准确的抽取,以端到端的方式处理AFOE任务。相比基线模型,对于方面意见对抽取任务,改进的模型在中英文数据集上的F1值提高了0.89%~4.11%,对于三元组抽取任务提高了1.36%~3.11%,实验结果表明,改进的模型能有效地对中英文评论的意见元素进行抽取,性能显著优于基线模型。

体育馆大跨钢网架分步外扩顶升施工方法

针对乌鲁木齐市某体育馆大跨度屋盖钢网架安装工程,开展了不同施工方案的比选,确定了顶升与外扩交替进行的分步外扩顶升法施工方案。通过数值模拟讨论了顶升点布置位置,对比四种不同的顶升点布置方案,综合内力和变形等因素选取了较为合理的布置方案,同时对整个分步外扩顶升法施工过程与控制要点进行了讨论。顶升点与曲面网架结构两对边固定铰支座连线的杆件容易出现较大应力,在施工过程中先后围绕顶升点及结构受力较大、传力直接的部位布置了101个振弦应变计,通过应力监测来监测结构的应力大小,以校核施工方案的合理性。本文明确了体育馆大跨钢网架采用分步外扩顶升施工方法的工艺特点,为大跨度网格结构安装施工方法的选取提供借鉴。

兼顾短路与断线故障识别的柔性直流电网行波保护方案

目前大多数柔性直流电网行波保护在配置时仅考虑短路故障,当发生断线故障时,保护动作的正确性尚不明确。对此,首先分析了断线故障下传统行波保护的动作特性,得出了传统行波保护无法正确识别短路与断线故障的结论。在此基础上,探索了断线与短路故障下线路受端的第二个电流波头特征和线路电压特征,研究了两种故障下线路送端的电流首行波特征以及两端电压与电流变化量乘积的特征,提出了一种兼顾短路与断线故障识别的行波保护方案。基于PSCAD/EMTDC仿真平台对所提保护方案进行了性能验证。结果表明,该保护方案能准确识别并应对各种条件的故障,且具有较高的速动性和抗噪声干扰能力。

联网型中原农宅综合能源系统鲁棒优化调度

设计农村住宅综合能源系统与电网互动的优化调度方案是提高农宅节能效果及经济性的关键。针对综合能源系统规划中光伏出力及用能负荷等不确定性因素,建立了完善的电-冷-热综合能源系统模型框架,提出考虑需求响应的两阶段鲁棒优化方法。同时,考虑需求侧调控对能源优化调度的作用,根据实时电价以及相关激励措施,灵活调整用电需求,以达到优化与大电网购售电互动的目的。通过算例分析,分别得到日前、日内的具体调度方案。结果表明:优化调度后的农宅节能效果和成本节约均有显著提升。优化方案能够充分利用光伏发电,合理安排电力、冷热负荷,并根据实时电价进行灵活调整,实现农宅与电网的有效互动。

HLLCE格式构造及其在气动热计算中应用

飞行器表面热环境是临近空间高超声速飞行器研究中的一个重点问题,它对飞行器的气动、热环境和安全性有重要影响。受试验手段的限制,风洞试验无法准确模拟真实飞行条件,数值计算是研究气动加热问题的重要手段。格式的耗散性、网格尺度是影响气动热模拟的两个重要因素。气动热计算要求格式耗散越小越好,但低耗散性会引起激波不稳定现象。构造了兼具HLLE格式稳定性和HLLC格式低耗散性的HLLCE格式,该格式在较低马赫数下表现出HLLC的性质,是一种低耗散性格式,在高马赫数下则具有HLLE格式的性质,能够克服激波不稳定现象。针对气动热计算中最小网格尺度的选取,提出以边界层线性底层厚度为参考尺度,以特征长度计算的边界层线性底层厚度的1/10作为热环境计算的壁面最小网格尺度参考值。基于这一尺度确定了高超声速球头算例气动力热计算网格,计算结果验证了低耗散格式在临近空间高超声速气动力热计算中的良好性能。

Axisymmetric alternating direction explicit scheme for efficient coupled simulation of hydro-mechanical interaction in geotechnical engineering-Application to circular footing and deep tunnel in saturated ground

Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.