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There are many situations where groundwater flow has high flow rates, causing large seepage forces. Examples are flows around highly conductive fractures and tunnels. We present a new analytic element for a tunnel in an elastic medium. We combined the analytic element method for groundwater flow with that for linear elasticity, and include the seepage force as a body force in the linearly elastic model. We represent tunnels and fractures as analytic elements. The solution for the case considered is limited to steady state flow and fluid-to-solid coupling. We present examples of the computed seepage forces around a tunnel and a fracture as well as a comparison with another numerical model. [ABSTRACT FROM AUTHOR]

The aim of our work is to study two-dimensional fractured flow simulations for groundwater by using non-identical aperture of fractures via Analytic Element Method, and make a comparison between processing time of both techniques i.e. iterative and matrix method. Numerical solutions for the considered problems are totally based on series expansions, whereas the effects of every fracture are expressed as a series which obey Laplace's equation. In all examined cases, it is evident that the iterative method is not able to converge, while by introducing the matrix method, the expected results are obtained with minimum computational cost (processing time).

We consider unconfined flow in aquifers with a small sloping base, a magnitude of no more than a few percent at maximum and aim the analysis to large-scale regional modeling using analytic elements. We write the equations for the vertically integrated discharge, and find that the resulting two-dimensional discharge vector is rotational, as opposed to the specific discharge vector. We propose an approximate model for describing three-dimensional flow in an aquifer with a sloping base, and apply the approach to cases of flow between two parallel rivers and flow with a well in an aquifer bounded by a long river. We apply Wirtinger calculus and are able to estimate the error due to the approximation. [ABSTRACT FROM AUTHOR]

The aim of our work is to study two-dimensional fractured flow simulations for groundwater by using non-identical aperture of fractures via Analytic Element Method, and make a comparison between processing time of both techniques i.e. iterative and matrix method. Numerical solutions for the considered problems are totally based on series expansions, whereas the effects of every fracture are expressed as a series which obey Laplace's equation. In all examined cases, it is evident that the iterative method is not able to converge, while by introducing the matrix method, the expected results are obtained with minimum computational cost (processing time). [ABSTRACT FROM AUTHOR]

The stream network is a major feature of a landscape, conveying water, sediment, and solute from hillslopes to the ocean. Noticeably, from a large-scale point of view, the elevation of the talwegs of perennial streams is an important head boundary condition for both surface and groundwater flow originating from hillslopes. Assuming a wireframe (1D) representation of talweg lines, the problem of interpolating elevation between talwegs has received attention for applications such as flood mapping using Height Above Nearest Drainage (HAND, [Nobre et al., 2011]), or groundwater level interpolation in low-conductivity aquifer systems. In this study we propose an alternate definition of this large-scale base level concept introduced by [Wyns et al., 2004], namely the Basal Envelope Surface of Talwegs (BEST) and the associated Height Above the Basal Envelope Surface of Talwegs (HABEST), along with a procedure to compute it using the Analytic Element Method (AEM). It can be defined as the head distribution satisfying Laplace equation (Darcy flow with vanishing divergence), with stream segments set as Dirichlet boundary conditions. The BEST is thus the real part of a complex analytic (holomorphic) function which can be modeled using analytic slit elements, with very low computational requirements and without the need for kriging, as it is often seen in the literature. This analytic model is extended to the case of a non-zero, uniform divergence flow (head distribution satisfying a Poisson equation) which can be useful to analyse groundwater levels at catchment scale.

The stream network is a major feature of a landscape, conveying water, sediment, and solute from hillslopes to the ocean. Noticeably, from a large-scale point of view, the elevation of the talwegs of perennial streams is an important head boundary condition for both surface and groundwater flow originating from hillslopes. Assuming a wireframe (1D) representation of talweg lines, the problem of interpolating elevation between talwegs has received attention for applications such as flood mapping using Height Above Nearest Drainage (HAND, Nobre et al. [2011]), or groundwater level interpolation in low-conductivity aquifer systems. In this study we propose an alternate definition of this largescale base level concept introduced by Wyns et al. [2004], namely the Basal Envelope Surface of Talwegs (BEST) and the associated Height Above the Basal Envelope Surface of Talwegs (HABEST), along with a procedure to compute it using the Analytic Element Method (AEM). It can be defined as the head distribution satisfying Laplace equation (Darcy flow with vanishing divergence), with stream segments set as Dirichlet boundary conditions. The BEST is thus the real part of a complex analytic (holomorphic) function which can be modeled using analytic slit elements, with very low computational requirements and without the need for kriging, as it is often seen in the literature. This analytic model is extended to the case of a non-zero, uniform divergence flow (head distribution satisfying a Poisson equation) which can be useful to analyse groundwater levels at catchment scale. [ABSTRACT FROM AUTHOR]

The work presented in this article is composed of 2-dimensional groundwater flow simulations for fractured porous media with different aperture of fractures by using the Analytic Element Method. In order to investigate the flow behavior and its effect on fractures, we considered different systems of fractures with varying apertures, hydraulic conductivities and orientations in the presence of uniform flow field and a well. We also introduced the matrix method to solve the problems for which the unknown coefficients are obtained from the discharge potential of all the elements present in the systems. The numerical solution of the prescribed problem is based on a series expansion, while the influence of each fracture is expressed in a series that satisfy Laplace's equation. [ABSTRACT FROM AUTHOR]

This study attempts to integrate a Surface Water (SW) model Soil and Water Assessment Tool (SWAT) with an existing steady-state, single layer, unconfined heterogeneous aquifer Analytic Element Method (AEM) based Ground Water (GW) model, named Bluebird AEM engine, for a comprehensive assessment of SW and GW resources and its management. The main reason for integrating SWAT with the GW model is that the SWAT model does not simulate the distribution and dynamics of GW levels and recharge rates. To overcome this issue, often the SWAT model is coupled with the numerical GW model (either using MODFLOW or FEFLOW), wherein the spatial and temporal patterns of the interactions are better captured and assessed. However, the major drawback in integrating the two models (SWAT with—MODFLOW/FEM) is its conversion from Hydrological Response Unit's (HRU)/sub-basins to grid/elements. To couple them, a spatial translation system is necessary to move the inputs and outputs back and forth between the two models due to the difference in discretization. Hence, for effective coupling of SW and GW models, it may be desirable to have both models with a similar spatial discretization and reduce the need for rigorous numerical techniques for solving the PDEs. The objective of this paper is to test the proof of concept of integrating a distributed hydrologic model with an AEM model at the same spatial units, primarily focused on surface water and groundwater interaction with a shallow unconfined aquifer. Analytic Element Method (AEM) based GW models seem to be ideal for coupling with SWAT due to their innate character to consider the HRU, sub-basin, River, and lake boundaries as individual analytic elements directly without the need for any further discretization or modeling units. This study explores the spatio-temporal patterns of groundwater (GW) discharge rates to a river system in a moist-sub humid region with SWAT-AEM applied to the San Jacinto River basin (SJRB) in Texas. The SW-GW interactions are explored throughout the watershed from 2000–2017 using the integrated SWAT-AEM model, which is tested against stream flow and GW levels. The integrated SWAT-AEM model results show good improvement in predicting the stream flow (R2 = 0.65–0.80) and GW levels as compared to the standalone SWAT model. Further, the integrated model predicted the low flows better compared to the standalone SWAT model, thus accounting for the SW-GW interactions. Almost 80% of the stream network experiences an increase in groundwater discharge rate between 2000 and 2017 with an annual average GW discharge rate of 1853 Mm3/year. The result from the study seems promising for potential applications of SWAT-AEM coupling in regions with considerable SW-GW interactions. [ABSTRACT FROM AUTHOR]

Intersecting fractures often dominate the rock though which groundwater flows and they represent a crucial feature in groundwater models. In this paper, limitless analytic elements were used to model intersecting and heterogeneous fractures with either high or low transmissivity relative to that of the surrounding medium. To handle the singular behavior at the intersections, fractures were modeled as multiple elements, the tips of which meet at the point of intersection. The same approach was used to model heterogeneous fractures where the transmissivity is discontinuous along a fracture. Representing the fractures analytically in the continuum allows for an exact representation of the groundwater exchange between the fractures and the continuum. Thereby producing an accurate model of flow through a network of fractures in a continuum. This solution is capable of accurately computing the groundwater flow for both a network of fractures with a high transmissivity and an assembly of heterogeneous fractures near a tunnel. Key Points: The limitless analytic elements were applied to a continuum that contains a network of intersecting fracturesThe effects of low‐ and high‐transmissivity fractures were estimated and the accuracy of the model was evaluatedThe effects of heterogeneous fracture flow on the pressure distribution around a tunnel through fractured medium were analyzed [ABSTRACT FROM AUTHOR]

We present an analytic formulation for an elastic medium under uniform stress and in plane strain, with a very large number of cracks that are allowed to intersect. The singularities at the tips of the cracks are represented exactly; the solution is written in terms of series expansions of negative powers of a complex variable defined outside the unit circle in a complex reference plane. We modeled an assembly of 10,000 cracks and show stress trajectories both for the whole model and for individual cracks, chosen at random from the assembly. [ABSTRACT FROM AUTHOR]

Abstract The prediction of contaminant transport in porous media is an important problem in order to prevent the pollution propagation in groundwater. The present model is developed by coupling two mesh-free approaches in order to overcome the restrictions of mesh-dependent methods. In this model, the ground water flow model is developed by analytic-element method and the contaminant transport model is developed by point collocation method in an unconfined aquifer. The model was developed and implemented by Python object-oriented programming language. A particle swarm optimization algorithm has been also utilized to calibrate the model. The model was applied for contamination transport in Astaneh-Kuchesfahan groundwater in north of Iran. Comparison of the model results with the observed data represents a reasonable agreement and capability of the present model in contaminant transport modeling. Moreover, the calculated value for coefficient of determination (R 2 = 0.89) indicates that the calibrated parameters are acceptable.

The work presented in this article is composed of 2-dimensional groundwater flow simulations for fractured porous media with different aperture of fractures by using the Analytic Element Method. In order to investigate the flow behavior and its effect on fractures, we considered different systems of fractures with varying apertures, hydraulic conductivities and orientations in the presence of uniform flow field and a well. We also introduced the matrix method to solve the problems for which the unknown coefficients are obtained from the discharge potential of all the elements present in the systems. The numerical solution of the prescribed problem is based on a series expansion, while the influence of each fracture is expressed in a series that satisfy Laplace’s equation.

This study attempts to integrate a Surface Water (SW) model Soil and Water Assessment Tool (SWAT) with an existing steady-state, single layer, unconfined heterogeneous aquifer Analytic Element Method (AEM) based Ground Water (GW) model, named Bluebird AEM engine, for a comprehensive assessment of SW and GW resources and its management. The main reason for integrating SWAT with the GW model is that the SWAT model does not simulate the distribution and dynamics of GW levels and recharge rates. To overcome this issue, often the SWAT model is coupled with the numerical GW model (either using MODFLOW or FEFLOW), wherein the spatial and temporal patterns of the interactions are better captured and assessed. However, the major drawback in integrating the two models (SWAT with—MODFLOW/FEM) is its conversion from Hydrological Response Unit’s (HRU)/sub-basins to grid/elements. To couple them, a spatial translation system is necessary to move the inputs and outputs back and forth between the two models due to the difference in discretization. Hence, for effective coupling of SW and GW models, it may be desirable to have both models with a similar spatial discretization and reduce the need for rigorous numerical techniques for solving the PDEs. The objective of this paper is to test the proof of concept of integrating a distributed hydrologic model with an AEM model at the same spatial units, primarily focused on surface water and groundwater interaction with a shallow unconfined aquifer. Analytic Element Method (AEM) based GW models seem to be ideal for coupling with SWAT due to their innate character to consider the HRU, sub-basin, River, and lake boundaries as individual analytic elements directly without the need for any further discretization or modeling units. This study explores the spatio-temporal patterns of groundwater (GW) discharge rates to a river system in a moist-sub humid region with SWAT-AEM applied to the San Jacinto River basin (SJRB) in Texas. The SW-GW interactions are explored throughout the watershed from 2000–2017 using the integrated SWAT-AEM model, which is tested against stream flow and GW levels. The integrated SWAT-AEM model results show good improvement in predicting the stream flow (R2 = 0.65–0.80) and GW levels as compared to the standalone SWAT model. Further, the integrated model predicted the low flows better compared to the standalone SWAT model, thus accounting for the SW-GW interactions. Almost 80% of the stream network experiences an increase in groundwater discharge rate between 2000 and 2017 with an annual average GW discharge rate of 1853 Mm3/year. The result from the study seems promising for potential applications of SWAT-AEM coupling in regions with considerable SW-GW interactions.

The prediction of contaminant transport in porous media is an important problem in order to prevent the pollution propagation in groundwater. The present model is developed by coupling two mesh-free approaches in order to overcome the restrictions of mesh-dependent methods. In this model, the ground water flow model is developed by analytic-element method and the contaminant transport model is developed by point collocation method in an unconfined aquifer. The model was developed and implemented by Python object-oriented programming language. A particle swarm optimization algorithm has been also utilized to calibrate the model. The model was applied for contamination transport in Astaneh-Kuchesfahan groundwater in north of Iran. Comparison of the model results with the observed data represents a reasonable agreement and capability of the present model in contaminant transport modeling. Moreover, the calculated value for coefficient of determination (R2 = 0.89) indicates that the calibrated parameters are acceptable. [ABSTRACT FROM AUTHOR]

We present an approach for solving problems of saltwater intrusion in aquifers with an hydraulic conductivity that varies in the vertical direction. The approach is based on the concept of a comprehensive potential, whose gradient exactly represents the vertically integrated discharge, which is, by definition, a two‐dimensional vector. We apply the approach to an island in Sweden and use it to estimate maximum allowable pumping rates of wells that recover part of the infiltration on the island. Key Points: We present a discharge potential for interface flow in crystalline rock with exponentially varying hydraulic conductivityWe examined the effect of exponentially varying hydraulic conductivity on the interface between fresh and salt groundwater at restWe applied the approach to an island in Sweden in the Baltic Sea [ABSTRACT FROM AUTHOR]

ABSTRACT The recent drought events and the population growth in São Paulo State (Brazil) have caused many municipalities to increase the groundwater exploitation of the Guarani Aquifer System (GAS) for the public water supply. In Bauru City/SP, the extraction of water from this Aquifer is expected to increase from 3699 m3/h (2014) to 4465 m3/h (2034). However, its long-term overexploitation may compromise the amount of available groundwater. The Analytic Element Method was used for groundwater flow modeling at steady-state, which includes the regional flow, the water withdrawal from wells and the main local geological conditions. The hydraulic gradient 0.82 m/km was estimated in the GAS in Bauru City. The potentiometric drawdown in the GAS in Bauru was estimated as 50 m since the beginning of the groundwater exploitation. The drawdown for the groundwater pumping scenario in 2014 is higher than 15 m in Piratininga and Agudos and lower than 10 m in further cities. The expected drawdown for the scenario of 2034 can reach 15 m in comparison with the scenario of 2014, in the North of Bauru City, where the future wells will be located.

Abstract: We present equations for new limitless analytic line elements. These elements possess a virtually unlimited number of degrees of freedom. We apply these new limitless analytic elements to head‐specified boundaries and to problems with inhomogeneities in hydraulic conductivity. Applications of these new analytic elements to practical problems involving head‐specified boundaries require the solution of a very large number of equations. To make the new elements useful in practice, an efficient iterative scheme is required. We present an improved version of the scheme presented by Bandilla et al. (2007), based on the application of Cauchy integrals. The limitless analytic elements are useful when modeling strings of elements, rivers for example, where local conditions are difficult to model, e.g., when a well is close to a river. The solution of such problems is facilitated by increasing the order of the elements to obtain a good solution. This makes it unnecessary to resort to dividing the element in question into many smaller elements to obtain a satisfactory solution. [ABSTRACT FROM AUTHOR]