Numerical simulation of an unsaturated flow equation

A numerical model for an unsaturated flow problem by using the finite element method is established in order to simulate liquid moisture flow In an unsaturated zone with homogeneous soil and deep subsurface water, and with different initial and boundary conditions. For infiltration or evaporation problems, a traditional method usually yields oscillatory non-physics profiles. However, nonoscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method. Moreover, the kind of boundary condition is handled very well. Project supported by the National Key Project of Fundamental Research ”Climate Dynamics and Climate Prediction Theory“ and China Postdoctoral Science Foundation.     

The transition of flow patterns through critical stagnation points in two-dimensional groundwater flow

A flow pattern is characterized by aquifer features and the number, type, and distribution of stagnation points (locations where the discharge is zero). This article identifies a condition for transition of flow patterns in two-dimensional groundwater flow obeying Darcy’s law by examining changes in stagnation points, using the Taylor series expansion of the discharge vector. It is found that the three standard types of stagnation points (minimums, maximums, and saddle points) are completely characterized by the first-order term containing the discharge gradient tensor. However, when the determinant of the tensor becomes zero, stagnation points of other types characterized by higher-order terms come into existence. In this article, we call these zero-determinant stagnation points as critical stagnation points; they may emerge suddenly, split to a set of new stagnation points, or disappear from the flow, resulting in transitions of flow patterns. Examples of both transient and steady flows are used to illustrate the usefulness and significance of critical stagnation points.     

Estimating groundwater discharge to surface waters using heat as a tracer in low flux environments: the role of thermal conductivity

Analytical modelling of heat transport was used to address effects of uncertainty in thermal conductivity on groundwater–surface water exchange. In situ thermal conductivities and temperature profiles were measured in a coastal lagoon bed where groundwater is known to discharge. The field site could be divided into three sediment zones where significant spatial changes in thermal conductivity on metre to centimetre scale show that spatial variability connected to the sediment properties must be considered. The application of a literature‐based bulk thermal conductivity of 1.84 Wm^?1 °C^?1, instead of field data that ranged from 0.62 to 2.19 W m^?1 °C^?1, produced a mean overestimation of 2.33 cm d^?1 that, considering the low fluxes of the study area, represents an 89% increase and up to a factor of 3 in the most extreme cases. Incorporating the uncertainty due to sediment heterogeneities leads to an irregular trend of the flux distribution from the shore towards the lagoon. The natural variability of the thermal conductivity associated with changes in the sediment composition resulted in a mean variation of ±0.66 cm d^?1 in fluxes corresponding to a change of ±25.4%. The presence of organic matter in the sediments, a common situation in the near‐shore areas of surface water bodies, is responsible for the decrease of thermal conductivity. The results show that the natural variability of sediment thermal conductivity is a parameter to be considered for low flux environments, and it contributes to a better understanding of groundwater–surface water interactions in natural environments. Copyright © 2015 John Wiley & Sons, Ltd.     

于桥水库风季流场的计算与分析

本文依据水流运动的基本理论,并考虑风对水体的剪切作用,应用改进的移步ADI法,建立了风作用下流场的数值模似系统,其结果与连续四年的实测资料验证相吻合。计算预报了于桥水库三个典型水文年定常风不同风速、风向的流场,并由计算机绘制出彩色流场图。文中还针对计算应用成果进行了分析。     

Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.     

Effect of variable‐density groundwater flow on nitrate flux to coastal waters

A two‐dimensional variable‐density groundwater flow and transport model was developed to provide a conceptual understanding of past and future conditions of nitrate (NO₃) transport and estimate groundwater nitrate flux to the Gulf of Mexico. Simulation results show that contaminant discharge to the coast decreases as the extent of saltwater intrusion increases. Other natural and/or artificial surface waters such as navigation channels may serve as major sinks for contaminant loading and act to alter expected transport pathways discharging contaminants to other areas. Concentrations of NO₃ in the saturated zone were estimated to range between 30 and 160 mg?L^?1 as NO₃. Relatively high hydraulic vertical gradients and mixing likely play a significant role in the transport processes, enhancing dilution and contaminant migration to depth. Residence times of NO₃ in the deeper aquifers vary from 100 (locally) to about 300 years through the investigated aquifer system. NO₃ mass fluxes from the shallow aquifers (0 to 5.7 × 10⁴ mg?m^?2?day^?1) were primarily directed towards the navigation channel, which intersects and captures a portion of the shallow groundwater flow/discharge. Direct NO₃ discharge to the sea (i.e. Gulf of Mexico) from the shallow aquifer was very low (0 to 9.0 × 10¹ mg · m^?2?day^?1) compared with discharge from the deeper aquifer system (0 to 8.2 × 10³ mg?m^?2?day^?1). Both model‐calibrated and radiocarbon tracer‐determined contaminant flux estimates reveal similar discharge trends, validating the use of the model for density‐dependent flow conditions. The modelling approach shows promise to evaluate contaminant and nutrient loading for similar coastal regions worldwide. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical simulation of the influence of lower-crustal flow on the deformation of the Sichuan-Yunnan Region

On the basis of distribution of active fault and regional rheological structure, a three-dimensional finite element model of Sichuan-Yunnan region, China, is constructed to simulate contemporary crustal motion and stress distri- bution and discuss the dynamic mechanism of crustal motion and deformation in the Sichuan-Yunnan region. Lin- ear Maxwell visco-elastic model is applied, which includes the active fault zones, the elastic upper crust and vis- cous lower crust and upper mantle. Four different models with different boundary conditions and deep structure are calculated. Some conclusions are drawn through comparison. Firstly, the crustal rotation about the eastern syntaxis of the Himalaya in the Sicuan-Yunnan region may be controlled by the special dynamic boundary condition. The drag force of the lower-crust on the upper crust is not negligible. At the same time, the main active fault zones play an important role in the contemporary crustal motion and deformation in Sichuan-Yunnan region.     

Simulation of groundwater flow in a crystalline rock aquifer system in Southern Ghana – An evaluation of the effects of increased groundwater abstraction on the aquifers using a transient groundwater flow model

Monitored groundwater level data, well logs, and aquifer data as well as the relevant surface hydrological data were used to conceptualise the hydrogeological system of the Densu Basin in Southern Ghana. The objective was to numerically derive the hydraulic conductivity field for better characterization of the aquifer system and for simulating the effects of increasing groundwater abstraction on the aquifer system in the basin. The hydraulic conductivity field has been generated in this study through model calibration. This study finds that hydraulic conductivity ranges between a low of 2 m/d in the middle sections of the basin and about 40 m/d in the south. Clear differences in the underlying geology have been indicated in the distribution of aquifer hydraulic conductivities. This is in consonance with the general assertion that the hydrogeological properties of the aquifers in the crystalline basement terrains are controlled by the degree of fracturing and/or weathering of the country rock. The transient model suggest aquifer specific storage values to range between 6.0 × 10^?5 m^?1 and 2.1 × 10^?4 m^?1 which are within acceptable range of values normally quoted for similar lithologies in the literature. There is an apparent subtle decrease in groundwater recharge from about 13% of the annual precipitation in 2005 to about 10.3% of the precipitation in 2008. The transient model was used to simulate responses of the system to annual increment of groundwater abstraction by 20% at the 2008 recharge rates for the period 2009 – 2024. The results suggest that the system will not be able to sustain this level of abstraction as it would lead to a basin wide drawdown in the hydraulic head by 4 m by the end of the prediction period. It further suggests a safe annual increment in groundwater abstraction by 5% under business as usual recharge conditions. Identification and protection of groundwater recharge areas in the basin are recommended in order to safeguard the integrity of the resource under the scenario of increased abstraction for commercial activities in the basin. Copyright © 2012 John Wiley & Sons, Ltd.     

Simultaneous identification of parameter,initial condition,and boundary condition in groundwater modelling

In this paper, we perform an inverse method to simultaneously estimate aquifer parameters, initial condition, and boundary conditions in groundwater modelling. The parameter estimation is extended to a complete inverse problem that makes the calibrated groundwater flow model more realistic. The adjoint state method, the gradient search method, and the least square error algorithm are combined to build the optimization procedure. Horizontal two‐dimensional groundwater flow in a confined aquifer is exemplified to demonstrate the correlation between unknowns, the contribution of observation, as well as the suitability of applying the inverse method. The correlation analysis shows the connection between storage coefficient and initial condition. Besides, transmissivity and boundary conditions are also highly correlated. More observations at different location and time are necessary to provide sufficient information. A time series of unsteady head is requested for estimation of storage coefficient and initial condition. Observation near boundary is very effective for boundary condition estimation. The observation at pumping well mostly contributes to the estimation of transmissivity. According to all observations, it is possible to identify parameters, initial condition, and boundary condition simultaneously. Furthermore, the results not only illustrate the traditional assumption of known boundary condition but also initial condition, which may cause an incorrect estimation. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of multilayered groundwater mounds on water dynamics beneath a recharge basin: Numerical simulation and assessment of surface injection

Interactions between groundwater mounds caused by a geologic layer contrast affect the efficiency of managed aquifer recharge in arid areas. However, research has rarely examined the roles of groundwater mounding size variations on soil water dynamics in a stratified vadose zone in response to a sustained infiltration source. Numerical experiments were conducted on a two-dimensional vertical-section domain using HYDRUS software to simulate the behaviours of two adjacent (upper and lower) groundwater mounds underlying an infiltration basin subjected to clay loam and sandy alternately-layered soil profiles. The model successfully predicted the volume and extent of perched water and approximated vertical travel times during events generating downward fluxes from the surface injection. The response time of the mounding width (lateral extension) to the surface injection was delayed as compared to that of the mounding height (vertical extension), especially for the lower water mound. The mounding heights and widths show a strongly positive correlation with the infiltration rates of both high- and low-permeability layers where the injected water mounded, while the water storage amounts in the high- and low-permeability layers were governed by the mounding height and width, respectively. Exploratory simulations were then employed to assess the dependence of groundwater mounding behaviours and recharge performances on surface injection strategies. Results suggest that, by reducing injection rate or shortening injection duration, the near-term fraction of the surface injection converted to deep recharge is likely to be increased due to the narrowed groundwater mounding size, which would be limited by the water-retarding effect of layer contrasts. This study has important implications for predicting and understanding multilayered groundwater mounding behaviours and associated water mass balance under the geologic stratification, and is expected to aid in optimizing the infiltration basin operation for aquifer recharge.     

三层地铁车站振动台试验的数值模拟

进行了三层地铁车站大型振动台试验,获得了可靠的试验数据。通过室内实验获取了模型材料和土体材料的力学参数。基于ABAQUS有限元计算平台,建立了振动台试验的二维有限元模型,处理了混凝土本构模型及其参数的选取、土体本构模型及其参数的选取、阻尼设置、边界条件设置等问题。对多种工况下的试验结果和模拟结果进行了对比分析。结果表明,按照本文建议的建模方法,可以很好地重现振动台试验,数值模拟结果无论在趋势上还是数值上都和试验结果符合得很好。     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

Direct observation of complex Tóthian groundwater flow systems in the laboratory

Based on the theory of gravity‐driven groundwater flow systems, we have developed a complex Flow System Sand‐Box Model (FSM). It enables the visual observations of the development and characteristics and temporal evolution of complex Tóthian flow systems in the laboratory. The configuration of the regional, intermediate and local flow systems can be controlled and observed; hydraulic head, flow direction and travel time can be measured; and the scale and shape of the sub‐flow systems as well as the path lines and flow lines can be observed directly. The experiments demonstrate the Tóthian flow systems in a small basin with multiple sources and sinks. Greater local topographic (water table) undulation will lead to larger local flow systems. Greater regional and less local topographic undulation will enhance the development of intermediate and regional flow systems. In homogeneous media, increasing fluid‐potential differences between source and sink increase the spatial scale of the generated flow systems. The FSM is a useful teaching aid and experimental device to study and develop an intuitive insight into gravity‐driven groundwater flow systems. It helps to visualize and understand the hydraulic properties and controlling factors of Tóthian flow systems and may be used to study problems related to the chemical and temperature characteristics of the flow systems as well. Copyright © 2010 John Wiley & Sons, Ltd.     

Temporal sampling and role of flux measurements for subsurface heterogeneous characterization in groundwater basins using hydraulic tomography

Accurate characterization of heterogeneity in groundwater basins is crucial to the sustainable management of groundwater resources. This study explores the temporal sampling issues and the role of flux measurements in the characterization of heterogeneity in groundwater basins using numerical experiments. The experiments involve a digital basin imitating the groundwater basin of the North China Plain (NCP), where the groundwater exploitation reduction program is ongoing. Using the experiments, we champion that the reduction program could collect groundwater level information induced by operational variations of existing pumping wells at different locations in the basin. Such a dataset could serve as a basin-scale hydraulic tomography (HT) to characterize the basin-scale heterogeneity cost-effectively. Both steady-state and transient-state inversion experiments demonstrate the advantage of HT surveys in characterizing basin-scale heterogeneity over conventional pumping tests at fixed well locations. Additionally, head data at the early, intermediate, and late time from well hydrographs should be selected for the HT analysis to maximize HT's power and save computational costs. When accurate geological zones are incorporated in prior information, flux measurements significantly improve parameter estimates based on conventional pumping tests. However, their effects are less noticeable for long-term HT surveys in such basin-scale aquifers without fissures or fractures. This basin-scale tomographic survey example serves a guide for field data collection and optimization of the analysis of future basin-scale HT.     

A simulation of large‐scale groundwater flow and travel time in a fractured rock environment for waste disposal purposes

Two‐dimensional regional groundwater flow was simulated based on a conceptual model of low‐permeability crystalline rocks of the Whiteshell Research Area (WRA) in south‐eastern Manitoba. The conceptual model consists of fracture zones that strike in different directions and dip at various angles in the background rock mass. The thickness and hydraulic properties of the fracture zones in the conceptual model were varied as were the fluid properties and the boundary conditions of the groundwater flow system. The effects of these variations on the groundwater flow pattern and on the convective travel time along pathways from a hypothetical disposal vault at 500 m depth to discharge locations at the ground surface were evaluated. The vault was located in the regional discharge area of the groundwater system. A homogeneous conceptual model of the WRA, having only freshwater flow, formed a groundwater flow pattern with a regional flow system. Local flow systems developed increasingly with the introduction of fracture zones 20 m and 3 m thick, and depth‐dependent fluid density. This indicates a reduction in groundwater residence time by fracture zones and fluid density. Flow pathways were analysed using both a stream‐function and a particle‐tracking technique. The pathways and their lengths from the location of the vault to the surface varied spatially according to the flow patterns. The minimum travel time along these pathways was less than 150 000 and greater than 4 000 000 years in models with and without fracture zones, respectively, indicating that the presence of fracture zones was the major controlling factor. A precise knowledge and refinement of conceptual model parameters is necessary during site selection for waste disposal purposes. Copyright © 2004 John Wiley & Sons, Ltd.     

淄博市王旺庄水源地地下水开采预测的数值模拟

王旺庄水源地是淄博市晴纶工程的后备水源地,设计供水能力20000m^2／d。利用Ritz有限元数值分析方法。结合单纯性线性规划,在完成了对山东省淄博市临淄区王旺庄一朱台地段的淄博市腈纶工程水源地的水文地质模型建造的基础上,成功地对水源地进行地下水开采模拟,同时对该水源地的未来10年开采作了两种大气降水条件下的地下水动态预测。为腈纶工程水源地地下水开采提供了充分的设计依据。     

木星磁尾重联产生的磁通量管向内运动的数值模拟

本文通过利用包含离心力的自洽、轴对称稳态木星磁层模型,以及等离子体细丝运动理论对磁尾重联产生的磁通量管向内输运进行研究.基于细丝运动理论模型,通过MHD数值模拟我们可以得到磁通量管随时间变化的许多特性.模拟结果表明,重联产生的磁通量管向内运动可到达10R_J以内,磁通量管赤道部分的速度可以达到350 km·s^-1左右,表现出很强的向行星方向的流动.初始磁通量管中的等离子体密度和压强均小于周围介质,随着它迅速向木星方向运动,它的等离子体密度由于体积压缩逐渐上升,等离子体压强则逐渐上升到与周围介质相当.磁通量管在电离层上足点向赤道方向的运动滞后于它在赤道面上向行星方向的运动.

     

Numerical groundwater modelling as an effective tool for management of water resources in arid areas

Abstract

Groundwater, possibly of fossil origin, is used for water supply in some arid regions where the replenishment of groundwater by precipitation is low. Numerical modelling is a helpful tool in the assessment of groundwater resources and analysis of future exploitation scenarios. To quantify the groundwater resources of the East Owienat area in the southwest of the Western Desert, Egypt, the present study assesses the groundwater resources management of the Nubian aquifer. Groundwater withdrawals have increased in this area, resulting in a disturbance of the aquifer’s natural equilibrium, and the large-scale and ongoing depletion of this critical water reserve. Negative impacts, such as a decline in water levels and increase in salinity, have been experienced. The methodology includes application of numerical groundwater modelling in steady and transient states under different measured and abstraction scenarios. The numerical simulation model developed was applied to assess the responses of the Nubian aquifer water level under different pumping scenarios during the next 30 years. Groundwater management scenarios are evaluated to find an optimal management solution to satisfy future needs. Based on analysis of three different development schemes that were formulated to predict the future response of the aquifer under long-term water stress, a gradual increase in groundwater pumping to 150% of present levels should be adopted for protection and better management of the aquifer. Similar techniques could be used to improve groundwater management in other parts of the country, as well as other similar arid regions.

Editor D. Koutsoyiannis; Associate editor X. Chen     

Do not only connect: a model of infiltration‐excess overland flow based on simulation

The paper focusses on connectivity in the context of infiltration‐excess overland flow and its integrated response as slope‐base overland flow hydrographs. Overland flow is simulated on a sloping surface with some minor topographic expression and spatially differing infiltration rates. In each cell of a 128 × 128 grid, water from upslope is combined with incident rainfall to generate local overland flow, which is stochastically routed downslope, partitioning the flow between downslope neighbours. Simulations show the evolution of connectivity during simple storms. As a first approximation, total storm runoff is similar everywhere, discharge increasing proportionally with drainage area. Moderate differences in plan topography appear to have only a second‐order impact on hydrograph form and runoff amount. Total storm response is expressed as total runoff, runoff coefficient or total volume infiltrated; each plotted against total storm rainfall, and allowing variations in average gradient, overland flow roughness, infiltration rate and storm duration. A one‐parameter algebraic expression is proposed that fits simulation results for total runoff, has appropriate asymptotic behaviour and responds rationally to the variables tested. Slope length is seen to influence connectivity, expressed as a scale distance that increases with storm magnitude and can be explicitly incorporated into the expression to indicate runoff response to simple events as a function of storm size, storm duration, slope length and gradient. The model has also been applied to a 10‐year rainfall record, using both hourly and daily time steps, and the implications explored for coarser scale models. Initial trails incorporating erosion continuously update topography and suggest that successive storms produce an initial increase in erosion as rilling develops, while runoff totals are only slightly modified. Other factors not yet considered include the dynamics of soil crusting and vegetation growth. Copyright © 2014 John Wiley & Sons, Ltd.     

Similarity solutions to the second boundary value problem of unsaturated flow through porous media

Similarity solutions to the second boundary value problem of unsaturated flow are studied in one-dimensional, semi-infinite porous media with the soil-water diffusivity proportional to some power of the water content. The existence and uniqueness of two types of similarity solutions to the problem are investigated and the properties of these solutions are presented. It is shown that these two types of similarity solutions exist and that they may not be unique for every parameter range studied. The use of the similarity solutions is discussed for the experimental determination of soil-water diffusivity.