无结构网格上二维浅水流动的数值模拟

提出在无结构网格上建立有限体积高性能格式族的统一框架,通过引入跨单元界面法向数值通量的逆风分解,将一维Osher、TVD两种通量分裂格式自然地推广至二维浅水方程组。给出了各种情况下浅水方程组有限体积法边界处理的计算公式。最后,利用该格式对穹包溢流、陆地动边界和河口潮流三个问题进行计算。结果表明,这类守恒格式具有高精度、无振荡性以及处理复杂流态过渡、自动捕俘间断和模拟陆地动边界的功能。     

通量差分裂格式的二维水流水质计算的适用性分析

将通量差分裂(FDS)格式应用于二维水流水质数值模拟中.应用若干理想条件下的简化模型对格式的计算精度进行分析,结果表明:FDS格式不仅能高精度地模拟浓度梯度较缓的污染物稳定排放情况,且其二阶格式能高分辨率捕俘水质间断,与理论值吻合很好,说明FDS二阶格式能高精度地计算污染物间断排放引起的大浓度梯度或水质突跃情况.该格式在长江南通江段水环境数值模拟中的应用验证了它的实际应用能力.     

通量差分裂方法在一维河网模型中的应用

以通量差分裂格式离散非守恒型圣维南方程组,为保证河网整体离散形式的一致性,采用特征线方法离散边界节点,并引入限制器和熵修正使离散模型具有TVD（Total Variation Diminishing）特性,在线性隐式化的基础上最终构建基于隐式TVD类方法的一维河网水流模型。通过实例验证,表明提出的方法能处理跨临界流变化,而且在实际复杂河网中对水位及主、支河道分流比都能较好地模拟,具有一定实用性。     

裂隙岩石介质中核素迁移的模型及其算子分裂、迎风、均衡格式

建立了放射性核素在裂隙岩石介质中迁移的双重介质模型,对模型的求解提出了一种新的数值方法—Galerkin有限元法与算子分裂、迎风、均衡格式相结合的新方法,给出了水质模型算子分裂、迎风、均衡格式的稳定性条件,且所得到的计算格式是非负的。最后通过对核素90Sr 100年、99Tc 1000年的预测计算,验证了本文所提方法的有效性和稳定性,并得出了一些有重要意义的结论。     

间断水波在梯级水库中的传播

基于矢通量分裂得到了一维浅水方程组的隐式守恒有限差分格式,并对有底坡、有摩阻的梯级水库同时溃坝和相继溃坝的溃坝波传播进行了数值模拟。对数值结果作了分析。结果合理,方法有效可行。     

通量向量分裂格式的二维水流-水质模拟

在有限体积法框架下应用通量向量分裂(FVS)格式进行平面二维水流 水质模拟。通过对偏微分方程进行有限体积的积分离散、利用通量的旋转不变性,把二维问题转化为一系列局部的一维问题进行求解,采用FVS格式计算各跨单元边界的水量、动量及污染物输运等通量。应用该格式计算了理想条件下的浓度输移,其结果与精确解拟合很好;模拟了长江江苏靖江段的水质及污染带,计算结果与水质监测值相当吻合,为长江江苏干流段水质评价提供了科学依据。     

二维浅水明流的一种二阶高性能算法

为了精确求解二维浅水方程组,在由任意三角形构成的无结构网格上建立了有限体积MUSCL算法,这是文献[1]中有限体积一阶Osher格式的一类二阶推广.通过采用预测校正二步时间积分和单元内引入坡度限制,该算法在时空上均可达到二阶精度.跨单元边界的法向数值通量采用通量向量分裂公式(FVS)计算.最后,通过长江口南支潮流计算和一维瞬时溃坝模型算例来说明该格式的优良性能及在浅水流动计算中的应用.     

二维浅水流动的一种普适的高性能格式——有限体积Osher格式

天然水体具有形状复杂的计算区域和水下地形。本文采用无结构的网格以适合这一情况,并能方便地根据工程应用的要求局部地和适应性地加密网格。相应地,对二维水流计算问题采用了有限体积法的数学表示。跨单元边界的法向数值通量通过用Osher格式求解黎曼问题得到。文中给出了适合于二维浅水方程组的有关单元界面和各种物理边界的法向数值通量公式。分析了这一格式所具有的优点,包括:普适性、守恒性、逆风性、单调保持性、高效性、对间断的高分辨率、边界处理和内部格式相容,以及不引入数值边界条件等。最后,通过长江口南支水流计算的实例,阐明其良好性能。     

用三角形有限体积法高密迎风格式求解地下水运移方程

本文建立了一种求解地下水中污染质运移方程的有限体积法。通过定义一种三角形控制体并求控制方程的应变量在它上面的平均值,这种格式就将有限元法处理复杂几何内蕴的灵活性和有限差法的简洁性结合起来。用高密迎风格式对平流项进行了离散。这种方法以“单调插值”原理为基础保证单调性,以保护格式的性质,它也以相邻控制体界面上局部黎曼问题的精确解为基础。这样,对所有单元peclet数都完全避免了数值振荡。在对弥散通量离散化的同时,得到了一种局部一阶。整体二阶精度的近似解与普通的迎风格式相对比,当遇到浓度尖锋时会产生少量的数值粘滞性.一些数值检验表明它与解析解很一致。本文求解了一个含有非平衡反应项的假想问题,来说明所提出的求解地下水运移方程方法的适用性。     

烃类垂向微渗漏过程的积木块模型及差分格式

这里提出以代表质量守恒的反应对流扩散方程作为主控方程的烃类垂向微渗漏方程组的差分格式,即双向一维分裂校正差分格式,并建立地层积木块模型对该格式的边界进行讨论。差分格式是预估～校正差分格式的一种改进形式,它融合了Crank-Nicolson格式、交替方向隐格式、预估～校正差分格式的特点,具有二阶差分精度,且无条件稳定。由于差分格式将每一步都归结为求解三对角线方程组,因此适合并行运算。数值实验表明,应用差分格式的数值模拟结果符合烃类垂向微渗漏过程的理论模型,可作为烃类垂向微渗漏过程分析的计算方法。     

Sequential implicit vertex approximate gradient discretization of incompressible two-phase Darcy flows with discontinuous capillary pressure

This work deals with sequential implicit schemes for incompressible and immiscible two-phase Darcy flows which are commonly used and well understood in the case of spatially homogeneous capillary pressure functions. To our knowledge, the stability of this type of splitting schemes solving sequentially a pressure equation followed by the saturation equation has not been investigated so far in the case of discontinuous capillary pressure curves at different rock type interfaces. It will be shown here to raise severe stability issues for which stabilization strategies are investigated in this work. To fix ideas, the spatial discretization is based on the Vertex Approximate Gradient (VAG) scheme accounting for unstructured polyhedral meshes combined with an Hybrid Upwinding (HU) of the transport term and an upwind positive approximation of the capillary and gravity fluxes. The sequential implicit schemes are built from the total velocity formulation of the two-phase flow model and only differ in the way the conservative VAG total velocity fluxes are approximated. The stability, accuracy and computational cost of the sequential implicit schemes studied in this work are tested on oil migration test cases in 1D, 2D and 3D basins with a large range of capillary pressure parameters for the drain and barrier rock types. It will be shown that usual splitting strategies fail to capture the right solutions for highly contrasted rock types and that it can be fixed by maintaining locally the pressure saturation coupling at different rock type interfaces in the definition of the conservative total velocity fluxes. The numerical investigation of the sequential schemes is also extended to the widely used finite volume Two-Point Flux Approximation spatial discretization.

     

声波散射数值模拟的两种新方案

声波散射的数值模拟问题一般用网格法或积分方程法解决。当模型的尺度很大时,两种方法都会遇到计算机资源不足所造成的困难。另外,在网格法中,场源的位置和场源附近的波场奇异性逼近精度都受网格点的控制,因此难以满足实际问题所提出的要求。针对这些问题,提出了两种处理声波散射问题的新方案。一种主要针对网格法,另外一种针对积分方程法。在针对网格法的方案中,通过模型分解和波场分裂,将原始的总场计算问题转化为散射场计算问题。由于背景场是由解析公式给出的,所以可以将场源放置在数值网格的任意位置,不一定非得在网格点上。基于同样的原因,场源附近的波场奇异性可以精确地算出。在针对积分方程法的方案中,通过引入拟线性近似,使得散射场的数值求解不必再借助于代数方程组,只要进行数值积分即可。所建立的数值计算方案具有普遍的适用性,其基本思想可以直接用于解决弹性波散射的数值模拟问题并用于反演密度和速度。     

Modelling in-situ upgrading of heavy oil using operator splitting method

The in-situ upgrading (ISU) of bitumen and oil shale is a very challenging process to model numerically because of the large number of components that need to be modelled using a system of equations that are both highly non-linear and strongly coupled. Operator splitting methods are one way of potentially improving computational performance. Each numerical operator in a process is modelled separately, allowing the best solution method to be used for the given numerical operator. A significant drawback to the approach is that decoupling the governing equations introduces an additional source of numerical error, known as the splitting error. The best splitting method for modelling a given process minimises the splitting error whilst improving computational performance compared to a fully implicit approach. Although operator splitting has been widely used for the modelling of reactive-transport problems, it has not yet been applied to the modelling of ISU. One reason is that it is not clear which operator splitting technique to use. Numerous such techniques are described in the literature and each leads to a different splitting error. While this error has been extensively analysed for linear operators for a wide range of methods, the results cannot be extended to general non-linear systems. It is therefore not clear which of these techniques is most appropriate for the modelling of ISU. In this paper, we investigate the application of various operator splitting techniques to the modelling of the ISU of bitumen and oil shale. The techniques were tested on a simplified model of the physical system in which a solid or heavy liquid component is decomposed by pyrolysis into lighter liquid and gas components. The operator splitting techniques examined include the sequential split operator (SSO), the Strang-Marchuk split operator (SMSO) and the iterative split operator (ISO). They were evaluated on various test cases by considering the evolution of the discretization error as a function of the time-step size compared with the results obtained from a fully implicit simulation. We observed that the error was least for a splitting scheme where the thermal conduction was performed first, followed by the chemical reaction step and finally the heat and mass convection operator (SSO-CKA). This method was then applied to a more realistic model of the ISU of bitumen with multiple components, and we were able to obtain a speed-up of between 3 and 5.     

Robust iterative schemes for non-linear poromechanics

We consider a non-linear extension of Biot’s model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. Specifically, we study the case when the volumetric stress and the fluid density are non-linear functions satisfying certain assumptions. We perform an implicit discretization in time (backward Euler) and propose two iterative schemes for solving the non-linear problems appearing within each time step: a splitting algorithm extending the undrained split and fixed stress methods to non-linear problems, and a monolithic L-scheme. The convergence of both schemes are shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results.     

On the utility of identification schemes for digital earth science data: an assessment and recommendations

In recent years, a number of data identification technologies have been developed which purport to permanently identify digital objects. In this paper, nine technologies and systems for assigning persistent identifiers are assessed for their applicability to Earth science data (ARKs, DOIs, XRIs, Handles, LSIDs, OIDs, PURLs, URIs/URNs/URLs, and UUIDs). The evaluation used four use cases that focused on the suitability of each scheme to provide Unique Identifiers for Earth science data objects, to provide Unique Locators for the objects, to serve as Citable Locators, and to uniquely identify the scientific contents of data objects if the data were reformatted. Of all the identifier schemes assessed, the one that most closely meets all of the requirements for an Unique Identifier is the UUID scheme. Any of the URL/URI/IRI-based identifier schemes assessed could be used for Unique Locators. Since there are currently no strong market leaders to help make the choice among them, the decision must be based on secondary criteria. While most publications now allow the use of URLs in citations, so that all of the URL/URI/IRI based identification schemes discussed in this paper could potentially be used as a Citable Locator, DOIs are the identification scheme currently adopted by most commercial publishers. None of the identifier schemes assessed here even minimally address identification of scientifically identical numerical data sets under reformatting.     

不同成因结构面各向异性特征及其剪切力学特性

岩体结构面具有明显的各向异性,其直接影响岩体的变形特性、力学特性与渗流特性,因此对结构面的各向异性特征开展量化分析尤为重要。针对不同成因(劈裂、剪切)结构面,利用结构面量化参数(节理粗糙度系数JRC、节理平均倾角θ、分形维数D_B)对其各向异性特征进行了分析,研究了各向异性特征对其剪切力学特性的影响。研究结果表明:(1)在劈裂断裂结构面中,平行劈裂方向的JRC与θ值普遍大于垂直方向,且随角度变化波动较小,D_B在对角线方向变化较大,其值与所取剖面线长度有关;而在剪切断裂结构面中,平行剪切方向的JRC和θ值与垂直方向无明显差别,但D_B同样在对角线方向变化较大;(2)在评价结构面各向异性时,采用θ、D_B等参数评价时,劈裂断裂结构面与剪切断裂结构面各向异性系数无明显差别,采用JRC作为评价参数时,其各向异性系数差异较大,能较好反映不同结构面之间的差异特征;(3)剪切断裂结构面的峰值剪切荷载和法向位移均高于劈裂断裂结构面,两种结构面的剪胀角达到峰值时的剪切位移相近,剪切断裂结构面的开度分布较为集中且普遍较大,劈裂断裂结构面开度分布则较为分散。     

Particle size scales and classification of sediment types based on particle size distributions: Review and recommended procedures

This paper provides a review of different particle size scales, size class terminology and particle size distribution (‘textural’) classification schemes which are widely used in sedimentology, geomorphology, soil science, aquatic ecology and civil engineering. It is concluded that a revised system of size class nomenclature, based on the Udden (1898) and Wentworth (1922) schemes, provides the most logical and consistent framework for use with sediments and a wide range of other particulate materials. A refined scheme is proposed which has five first‐order size classes (boulder, gravel, sand, silt and clay), each of which has five second‐order subdivisions with limits defined at one phi intervals. The scheme is simple and intuitively easy to understand. The paper also provides a review of previous schemes that have been proposed to describe and classify sediments on the basis of the proportions of gravel, sand and mud, or sand, silt and clay using trigons (also termed ternary diagrams). Many of these schemes do not have a logical basis and provide limited or uneven resolution. New gravel, sand and mud and sand, silt and clay classification systems are proposed that are both more logical and provide greater discriminatory power than previous schemes; they are therefore more suitable for use in environmental and forensic investigations. A new Microsoft Excel^® program, freely available to download from http://www.kpal.co.uk , allows rapid classification of sediments based on the proportions of gravel, sand and mud and sand, silt and clay proportions and graphical comparison of the data for different sample groups.     

高速公路滑坡稳定性分析及治理优化研究

在分析溪沟口滑坡工程地质概况及形成机理的基础上,采用传递系数法和有限元法对其进行了稳定性评价。结果表明,该滑坡稳定性达不到安全标准,必须进行加固治理。考虑滑坡稳定状况,采用抗滑桩结合地表排水对滑坡进行治理。在传递系数法结合有限单元法计算结果的基础上,构造出一定数量的抗滑桩加固方案,分别计算其治理后的稳定性和工程造价,以此为进化神经网络的学习样本, 建立设计参数与稳定性及加固方案造价之间的非线性映射关系,利用遗传算法在全局范围内快速搜索出最优的设计参数,选择合理的滑坡治理方案。最后利用有限元法对滑坡体治理前后的稳定状况进行分析,对所提出的优化治理方案进行稳定性验算,结果证明优化方案能够达到滑坡治理的设计要求,治理效果明显。     

青藏高寒地区沥青混合料的水稳定性与高温性能研究

青藏高寒地区年平均气温低, 温差大, 冻融循环频繁, 沥青路面性能要求不同于一般地区. 通过浸水马歇尔试验、冻融劈裂试验及车辙试验, 分析了沥青种类、级配类型、公称最大粒径类型对青藏高寒地区沥青混合料水稳定性及高温性能的影响. 结果表明:SBS110#改性沥青的混合料的残留稳定度最大, SBS70#改性沥青最小, 随着针入度等级的提高, 沥青混合料的冻融劈裂强度比减小; SBS改性沥青混合料的高温性能最好, 复合改性次之, SBR改性最差; AC-13沥青混合料级配范围中值的冻融劈裂强度比与动稳定度最大; AC-13沥青混合料的水稳定性及高温性能优于AC-20与AC-25. 在青藏高寒地区选用针入度等级不高且具有骨架密实结构的SBS改性沥青混合料或SBS/SBR复合改性沥青混合料, 将沥青混合料冻融劈裂强度比的要求提高为85%, 有利于提高沥青混合料的水稳定性和高温性能.