非饱和土壤中溶质运移对流占优问题的通量校正运移解法

描述非饱和土壤中溶质运移的对流弥散方程可分成两部分，对流部分用通量校正运移（FCT）算法求解；弥散部分用常规的隐式差分方法求解，FCT算法包括两个阶段，一个是低阶运移阶段，这一阶段的解，可能会引进过量的数值弥散，另一个是高阶通量校正阶段，通过对反扩散通量进行校正（限定），可有效地消除数值弥散和数值振荡，而水体积分数用FUCG方法求得，能保持质量守恒，通过数值例子验证了FCT算法的有效性。     

饱和水流溶质运移问题数值解法综述

本文总结了饱和水流中溶质运移方程求解的各种数值方法，分析各种方法的本质特征以及各自的优缺点，并指出了求解对流—弥散方程的各种数值方法的研究进展和值得重视的问题。研究结果表明，自适应欧拉—拉格朗日法(EM)是溶质运移问题中，求解对流—弥散方程是比较有发展潜力的方法之一。以MMOC法为基础在陡峰值高价插值和其它区域低价插值相结合的ELM法，将是未来发展的趋势。而寻求非规则网格上高精度的空间单元插值模式，已开始成为求解对流问题数值方法研究的重点和关键问题。     

利用算子分裂迎风均衡格式解对流为主溶质运移问题

水污染模拟问题是水流问题与溶质运移问题的耦合问题.各种常见的数值解法在以对流为主溶质运移问题的求解中都会遇到困难,如用有限单元法或有限差分法时,会产生数值弥散与过量这两类误差.引入算子分裂迎风均衡格式法求解对流为主的水污染模拟问题,较好地克服了数值弥散和数值解出现振荡问题,该格式具有良好的稳定性、单调性及守恒性特点.     

求解对流占优地下水水质模型的有限元高精度广义迎风单元均衡格式及应用

根据水质模型的具体特点，对不同的方程采用不同方法，水流问题用有限元法；对流弥散方程先用算子分裂的方法分解为两个方程，即对流方程和弥散方程，前者用高精度广义迎风格式求解，对弥散方程则采用多单元均衡格式法求解，最后合成为高精度广义迎风均衡格式求出溶质浓度。通过对数值实验例子的计算和实验溶质迁移的模拟，可以看出在求解对流弥散定解问题时，广义迎风均衡格式克服了有限元数值波动和浓度出现负值的问题，与有限元相比有较大改进。     

三维溶质运移问题的分步广义迎风解法

对对流占优的三维溶质运移问题提出了分步广义迎风解法，首先利用Ｎ．Ｎ．Ｙａ－ｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节点速度这一步，节省运算步骤，对井点的浓度变化给出了更合适的求解方法。     

三维溶质运移问题的分步广义迎风解法

对对流占优的三维溶质运移问题提出了分步广义的迎风解法，首先利用Ｎ，Ｎ，Ｙａｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节眯速度     

地下水溶质运移数值模拟中减少误差的新方法

地下水中污染物运移的数值模拟方法一直是学界的研究热点问题.而如何减少与消除对流-弥散方程数值解中浓度陡锋面附近的数值振荡与数值弥散,更是研究的前沿与难点.提出了一种地下水溶质运移数值模拟中减少数值弥散的新方法.该方法的核心思想是在水动力弥散系数上加上一个数值弥散估算值,得到一个修正弥散系数,用其替代方程中有明确物理意义的水动力弥散系数进行计算.并提出了一个参数——数值弥散因子(μ_NDF),可以根据研究需要进行参数分区并适当调节该因子的大小,从而达到控制数值振荡,减小数值弥散的目的.从一维到二维的多个数值算例的模拟计算结果表明,该方法能在消除数值振荡的基础上,较好地减少数值弥散,达到满意的精度.     

山东淄博市大武水源地裂隙岩溶水中污染物运移的数值研究

在分析研究淄博市大武水源地裂隙岩溶含水层的水力性质和污染物运移特征的基础上 ,对裂隙岩溶水的水头和污染物运移进行数值研究。目前国内外对裂隙岩溶水进行数值计算时 ,通常用等价多孔介质模型 ,但裂隙岩溶介质和多孔介质有很大不同。裂隙岩溶介质的储水和导水空间为裂隙网络 ,导水系数大 ,地下水的实际平均流速比孔隙水大得多 ,但给水度和贮水系数小。当用等价多孔介质模型进行模拟时应考虑这些特点。对于污染物运移的模拟 ,要同时求解水头方程和对流弥散方程 ,可采用MODFLOW和MT3D软件进行模拟。研究区裂隙岩溶水水头的数值计算表明 ,等效多孔介质模型水头的拟合误差能满足国标GB/T144 97- 93的要求。各时段地下水水量均衡计算的精度也满足要求。对流弥散方程的数值计算 ,由于Peclet数高达 95 .6 7,对流占绝对优势 ,可能存在数值弥散和数值振荡 ,因而采用多种方法进行了比较。对于同一问题 ,同时采用上游有限差分法 (UFDM) ,混合的欧拉拉格朗日方法 (特征线法MOC、改进特征线法MMOC和混合特征线法HMOC) ,总变异消减法(TVD)进行计算 ,并比较其结果。结果表明 ,混合特征线法 (HMOC)和总变异消减法 (TVD)比较适合于对流占优势的运移问题计算。由于渗透系数K和有效孔隙度θ对溶质运移结果的影响很大 ,?     

改进时间分数阶模型模拟非Fick溶质运移

通过将经典时间分数阶对流-弥散方程的等待时间分布函数的尾部修改为指数型,推导出了改进时间分数阶对流-弥散方程,并提出有效的时空算子分裂数值求解方法。对两个理想算例和一个实际算例进行计算,结果表明,改进的时间分数阶对流-弥散方程继承了时间分数阶对流-弥散方程能模拟穿透曲线幂率型拖尾分布的优点,还可模拟穿透曲线尾部由幂率型转换到指数型的过程;特征时间λ、分数阶指数γ和两相容量比例系数β共同决定了运移行为。改进的新模型可以区分非均质介质中流动相和非流动相中的溶质浓度, 更细微地模拟非Fick溶质运移行为。     

LNAPL在二维含水介质中运移规律的研究

为研究LNAPL(轻质非水相液体)污染物在均匀含水介质中的运移规律,本文建立微元模型推导出LNAPL在均匀含水介质中的对流--弥散方程。针对不同的介质模型,对二维对流--弥散方程运用差分法进行数值模拟,求其数值解。分析LNAPL污染物的运移特征,得出在均匀介质和非均匀层状介质中运移规律:LNAPL污染物在含水介质中的运移规律遵循对流--弥散方程,介质的弥散系数是影响LNAPL污染物运移的主要因素。     

隐伏活断层地震勘探正演模拟方法

浅层高分辨率地震勘探是城市活断层探测手段中最有效、最可靠的方法之一,但是由于隐伏活断层勘探时存在着勘探深度浅、地层的属性差异小以及环境噪声大等因素,导致地震勘探数据信噪比低、反射信号弱等问题,严重影响地震数据的采集、处理和解释。采用一阶应力-速度方程的高阶交错网格有限差分方法, 结合完全匹配层(PML)的边界处理方法和通量校正(FCT)法消除频散的技术手段,对活断层模型地震勘探进行正演模拟,清晰直观地表现了断层处的细微差别,有助于地震勘探中对信号的分析与理解。结果表明,这些处理手段结合波动方程有限差分算法,能够有效实现薄层、弱反射的隐伏活断层模型的波场正演模拟,可有效识别隐伏活断层的断层倾角、断距、规模、跨越范围、断层深度以及断裂带影响范围,为分析这些参数对地震记录的影响提供有力帮助,同时结合实测地震数据的处理、解释,为防灾减灾提供具体有力的判据。     

一维不恒定明流计算的三种高性能差分格式

本文首先讨论了从物理上对差分格式提出的四项要求,即守恒性、逆风性,正性(或保持单调性)和对间断的高分辨率.最近十多年来,在空气动力学领域中已提出许多满足这些要求的高性能格式.本文将其中广泛应用的三类格式,即通量向量分裂格式、通量差分裂格式及通量校正输运格式,移用到一维不恒定明流计算中.结合圣维南方程组的具体形式,并考虑天然河道的几何不规则性,导出了有关公式.最后通过一个溃坝算例对各种方法进行了验证,其结果十分接近,说明这些方法具有广阔的应用前景.     

Contaminant transport with non‐equilibrium processes in unsaturated soils and implicit characteristic Galerkin scheme

A non‐equilibrium sorption—advection—diffusion model to simulate miscible pollutant transport in saturated–unsaturated soils is presented. The governing phenomena modelled in the present simulation are: convection, molecular diffusion, mechanical dispersion, sorption, immobile water effect and degradation, including both physical and chemical non‐equilibrium processes. A finite element procedure, based on the characteristic Galerkin method with an implicit algorithm is developed to numerically solve the model equations. The implicit algorithm is formulated by means of a combination of both the precise and the traditional numerical integration procedures. The stability analysis of the algorithm shows that the unconditional stability of the present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results illustrate good performance of the present algorithm in stability and accuracy, and in simulating the effects of all the mentioned phenomena governing the contaminant transport and the concentration distribution. Copyright © 2000 John Wiley & Sons, Ltd.     

二维输运方程高精度数值模拟

采用剖开算子法,把二维输运问题剖分为两个子初值问题(对流分步、扩散分步)。在任意三角形网格中,分别对不同性质的算子采用各自适合的算法,即采用特征线法求解对流分步,采用半隐式有限元法求解扩散分步。重点探讨了对流插值问题,给出了一种完全对称三次插值模式,有效地减少了数值阻尼。为了克服高阶插值数值震荡问题,计算中保证了函数及其一阶偏导数连续。算例表明,数值方法模拟结果与精确解吻合较好。该算法在求解输运方程(包括纯对流输运方程)时,既能有效减少数值阻尼,也能保证计算中不出现数值震荡。     

Three-Dimensional Modeling of Mass Transfer in Porous Media Using the Mixed Hybrid Finite Elements and the Random-Walk Methods

A three-dimensional (3D) mass transport numerical model is presented. The code is based on a particle tracking technique: the random-walk method, which is based on the analogy between the advection–dispersion equation and the Fokker–Planck equation. The velocity field is calculated by the mixed hybrid finite element formulation of the flow equation. A new efficient method is developed to handle the dissimilarity between Fokker–Planck equation and advection–dispersion equation to avoid accumulation of particles in low dispersive regions. A comparison made on a layered aquifer example between this method and other algorithms commonly used, shows the efficiency of the new method. The code is validated by a simulation of a 3D tracer transport experiment performed on a laboratory model. It represents a heterogeneous aquifer of about 6-m length, 1-m width, and 1-m depth. The porous medium is made of three different sorts of sand. Sodium chloride is used as a tracer. Comparisons between simulated and measured values, with and without the presented method, also proves the accuracy of the new algorithm.     

Transport in a 2-D saturated porous medium: A new method for particle tracking

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.     

饱和多孔介质中水力-力学-传质耦合过程的混合有限元法

对饱和多孔介质提出了一个含溶混污染物输运（传质）过程的混合元方法,其中污染物输运过程数学模型包含了对流、机械逸散、分子弥散和吸附等机制。固相位移、应变和有效应力,孔隙水压力、压力空间梯度和Darcy速度,污染物浓度、浓度空间梯度和浓度流量在单元内均为独立变量分别插值。基于胡海昌-Washizu三变量广义变分原理,结合可以滤掉虚假振荡的特征线方法,推导出饱和土中水力-力学-传质耦合问题控制方程的单元弱形式,并导出了混合元计算公式。数值模拟证明了所提出的方法可以提供与传统4点积分方案同样精度,同时能够提高计算效率。     

Application of a solute transport model under variable velocity conditions in a conduit flow aquifer: Olalde karst system, Basque Country, Spain

A model based on numerical solutions, which allows for solving the dispersion equation under variable recharge and velocity conditions, is developed to simulate solute transport in conduit flow aquifers during flow recession periods. As an example, the evolution of a tracer in the little known karst conduit that links the sinking stream of Oma valley to the Olalde spring is investigated in the karstic region of Santa Eufemia-Ereñozar (Basque Country, Spain). The model, with different hypothetical structures, allows for obtaining series of tracer breakthrough curves, which are fitted to experimental data using an optimization algorithm. These results, although they can be used to simulate the tracer evolution between the two points considered, do not allow for determining the internal structure and spatial disposition of contributions in the aquifer.     

Comparison of Mineral Weathering and Biomass Macronutrient Uptake in Two Small Forested Watersheds Underlain by Quartzite Bedrock,Catoctin Mountain,Maryland, USA

To quantify chemical weathering and biological uptake, mass-balance calculations were performed on two small forested watersheds located in the Blue Ridge Physiographic Province in north-central Maryland, USA. Both watersheds, Bear Branch (BB) and Fishing Creek Tributary (FCT), are underlain by relatively unreactive quartzite bedrock. Such unreactive bedrock and associated low chemical-weathering rates offer the opportunity to quantify biological processes operating within the watershed. Hydrologic and stream-water chemistry data were collected from the two watersheds for the 9-year period from June 1, 1990 to May 31, 1999. Of the two watersheds, FCT exhibited both higher chemical-weathering rates and biomass nutrient uptake rates, suggesting that forest biomass aggradation was limited by the rate of chemical weathering of the bedrock. Although the chemical-weathering rate in the FCT watershed was low relative to the global average, it masked the influence of biomass base-cation uptake on stream-water chemistry. Any differences in bedrock mineralogy between the two watersheds did not exert a significant influence on the overall weathering stoichiometry. The difference in chemical-weathering rates between the two watersheds is best explained by a larger proportion of reactive phyllitic layers within the bedrock of the FCT watershed. Although the stream gradient of BB is about two-times greater than that of FCT, its influence on chemical weathering appears to be negligible. The findings of this study support the biomass nutrient uptake stoichiometry of K_1.0Mg_1.1Ca_0.97 previously determined for the study site. Investigations of the chemical weathering of relatively unreactive quartzite bedrock may provide insight into critical zone processes.