Locally conservative groundwater flow in the continuous <scp>G</scp>alerkin method using 3‐<scp>D</scp> prismatic patches

Wu, Qiang; Zhao, Yingwang; Lin, Yu Feng; Xu, Hua

doi:10.1002/2016wr018967

Cited by 6 publications

(13 citation statements)

References 30 publications

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“…The need to calculate the internal flux often arises when detailed inflow/outflow components are to be examined at the subdomain level during the calibration and verification phase of modeling studies. On the other hand, an alternative postprocessing method that calculates the internal flux was developed by assuming that the flow field is irrotational [17][18][19][20]. The alternative postprocessing method subdivides elements into patches and individual fluxes for each patch are computed to calculate flow rates through each of the element faces such that flow through the boundary of any subdomain can be calculated by summing the flow rates at those faces that define the boundary.…”

Section: Introductionmentioning

confidence: 99%

Practical Application of the Galerkin Finite Element Method with a Mass Conservation Scheme under Dirichlet Boundary Conditions to Solve Groundwater Problems

et al. 2020

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The Galerkin finite element method (FEM) has long been used to solve groundwater flow equations and compute the mass balance in a region. In this study, we proposed a simple, new computational FEM procedure for global mass balance computations that can simultaneously obtain boundary fluxes at Dirichlet boundary nodes and finite element hydraulic heads at all nodes in only one step, whereas previous approaches usually require two steps. In previous approaches, the first step obtains the Galerkin finite element hydraulic heads at all nodes, and then, the boundary fluxes are calculated using the obtained Galerkin finite element hydraulic heads in a second step. Comparisons between the new approach proposed in this study and previous approaches, such as Yeh’s approach and a conventional differential approach, were performed using two practical groundwater problems to illustrate the improved accuracy and efficiency of the new approach when computing the global mass balance or boundary fluxes. From the results of the numerical experiments, it can be concluded that the new approach provides a more efficient mass balance computation scheme and a much more accurate mass balance computation compared to previous approaches that have been widely used in commercial and public groundwater software.

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Section: Introductionmentioning

confidence: 99%

Practical Application of the Galerkin Finite Element Method with a Mass Conservation Scheme under Dirichlet Boundary Conditions to Solve Groundwater Problems

et al. 2020

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“…The relationship between the pressure gradient and the velocity of the groundwater inrush in granular rock mass does not generally satisfy the Darcy equation, but a distinct nonlinear correlation [15,18], that is, non-Darcy flow Forchheimer equation [19]. It is of great theoretical and practical significance to establish a nonlinear flow model for the identification of seepage mechanisms and the reasonable prediction of groundwater inrush [20]. A nonlinear dynamic model of variable mass system for non-Darcy flow in granular rocks was established based on the mechanical plug in porous media [6].…”

Section: Introductionmentioning

confidence: 99%

Experimental Investigation on Hydraulic Properties of Granular Sandstone and Mudstone Mixtures

Cai

Zhou

et al. 2018

Geofluids

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The caved zone during longwall mining has high permeability, resulting in a mass of groundwater storage which causes a threat of groundwater inrush hazard to the safe mining. To investigate the hazard mechanism of granular sandstone and mudstone mixture (SMM) in caved zone, this paper presents an experimental study on the effect of sandstone particle (SP) and mudstone particle (MP) weight ratio on the non-Darcy hydraulic properties evolution. A self-designed granular rock seepage experimental equipment has been applied to conduct the experiments. The variation of particle size distribution was induced by loading and water seepage during the test, which indicated that the particle crushing and erosion properties of mudstone were higher than those of sandstone. Porosity evolution of SMM was strongly influenced by loading (sample height) and SP/MP weight ratio. The sample with higher sample height and higher weight ratio of SP achieved higher porosity value. In particular, a non-Darcy equation, for hydraulic properties (permeability and non-Darcy coefficient ) calculation, was sufficient to fit the relation between the hydraulic gradient and seepage velocity. The test results indicated that, due to the absence and narrowing of fracture and void during loading, the permeability decreases and the non-Darcy coefficient increases. The variation of the hydraulic properties of the sample within the same particle size and SP/MP weight ratio indicated that groundwater inrush hazard showed a higher probability of occurrence in sandstone strata and crushed zone (e.g., faults). Moreover, isolated fractures and voids were able to achieve the changeover from self-extension to interconnection at the last loading stage, which caused the fluctuation tendency of and . Fluctuation ability in mudstone was higher than that in sandstone. The performance of an empirical model was also investigated for the non-Darcy hydraulic properties evolution prediction of crushing and seepage processes. The predictive results indicated that particle crushing and water erosion caused the increase of hydraulic properties, being the main reason that the experimental values are typically higher than those obtained from the predictive model. The empirical model has a high degree of predictive accuracy; however, has a higher predictive accuracy than . Furthermore, the predictive accuracy of increases and decreases with increasing weight ratio of SP.

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“…Wu et al () enhanced the CK method (referred to hereafter as the ECK method) in a two‐dimensional (2‐D) domain by transforming the advection flux depending on various flux types, such as vertical infiltration, storage change, and wells. They also extended their ECK method to 3‐D models, which they termed the 3‐D prismatic patches (3DPP) method.…”

Section: Introductionmentioning

confidence: 99%

“…However, the CK method does not work on vertical infiltration, storage change, or threedimensional (3-D) elements, and the theory of Berger and Howington (2002) is limited to one dimension. Wu et al (2016) enhanced the CK method (referred to hereafter as the ECK method) in a two-dimensional (2-D) domain by transforming the advection flux depending on various flux types, such as vertical infiltration, storage change, and wells. They also extended their ECK method to 3-D models, which they termed the 3-D prismatic patches (3DPP) method.…”

Section: Introductionmentioning

confidence: 99%

“…Violating local conservation could cause spurious sources and sinks in flow and mass transport simulations, which might lead to substantial numerical inaccuracy in transport solutions. The refraction of streamlines across a material interface could be depicted incorrectly because of locally nonconservative velocity fields (Wu et al ). Zhang et al () stated that this property is critical for two‐phase flow simulations, in which a lack of local conservation can cause errors in saturation, pressure, and velocity.…”

Section: Introductionmentioning

confidence: 99%

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Direct Conservative Domain in the Continuous Galerkin Method for Groundwater Models

Zhao

Lin

et al. 2017

Groundwater

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The continuous Galerkin finite element method is commonly considered locally nonconservative because a single element with fluxes computed directly from its potential distribution is unable to conserve its mass and fluxes across edges that are discontinuous. Some literature sources have demonstrated that the continuous Galerkin method can be locally conservative with postprocessed fluxes. This paper proposes the concept of a direct conservative domain (DCD), which could conserve mass when fluxes are computed directly from the potential distribution. Also presented here is a method for modifying the advection fluxes to obtain different conservative domains from the DCDs. Furthermore, DCDs are used to analyze the local conservation of several postprocessing algorithms, for which DCDs provide the theoretical basis. The local conservation of DCDs and the proposed method are illustrated and verified by using a hypothetical 2-D model.

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Locally conservative groundwater flow in the continuous Galerkin method using 3‐D prismatic patches

Cited by 6 publications

References 30 publications

Practical Application of the Galerkin Finite Element Method with a Mass Conservation Scheme under Dirichlet Boundary Conditions to Solve Groundwater Problems

Practical Application of the Galerkin Finite Element Method with a Mass Conservation Scheme under Dirichlet Boundary Conditions to Solve Groundwater Problems

Experimental Investigation on Hydraulic Properties of Granular Sandstone and Mudstone Mixtures

Direct Conservative Domain in the Continuous Galerkin Method for Groundwater Models

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