Free Surface Flow in a Microfluidic Corner and in an Unconfined Aquifer with Accretion: The Signorini and Saint-Venant Analytical Techniques Revisited

Kacimov, A. R.; Maklakov, D. V.; Kayumov, I. R.; Al-Futaisi, Ahmed

doi:10.1007/s11242-016-0767-y

Cited by 10 publications

(41 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, an analytical solution is proposed in this study to evaluate the spatiotemporal distribution of the drawdown at any location in the L-shaped aquifer. This paper develops a 2-D mathematical model for describing the groundwater flow in an approximately L-shaped fluvial aquifer which is very close to the case of numerical simulations reported in Kihm et al (2007). The aquifer is divided into two rectangular subregions.…”

Section: Introductionmentioning

confidence: 85%

“…The aquifer type and shape are important factors influencing the groundwater flow. Many studies have been devoted to the development of analytical models for describing flow in finite aquifers with a rectangular boundary (e.g., Chan et al, 1976Chan et al, , 1977Daly and Morel-Seytoux, 1981;Latinopoulos, 1982Latinopoulos, , 1984Latinopoulos, , 1985Corapcioglu et al, 1983;Lu et al, 2015), a wedge-shaped boundary (Chan et al, 1978;Falade, 1982;Holzbecher, 2005;Yeh et al, 2008;Chen et al, 2009;Samani and Zarei-Doudeji, 2012;Samani and Sedghi, 2015;Kacimov et al, 2016), a triangle boundary (Asadi-Aghbolaghi et al, 2010), a trapezoidal-shaped boundary (Mahdavi and Seyyedian, 2014), or a meniscus-shaped domain (Kacimov et al, 2017). So far, the case of re-entrant angle (L-shaped) boundaries has been treated analytically in different fields such as torsion of elastic bars (Kantorovich and Krylov, 1958), head fluctuation problems for tidal aquifers (Sun, 1997;Li and Jiao, 2002), and heat conduction in plates (Mackowski, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…For the application of FEMs, Taigbenu (2003) solved the transient flow problems based on the Green element method for multi-aquifer systems with arbitrary geometries. Kihm et al (2007) used a general multidimensional hydrogeomechanical Galerkin FEM to analyze three-dimensional (3-D) problems of saturated-unsaturated flow and land displacement induced by pumping in a fluvial aquifer in the Yongpoong 2 Agriculture District, Gyeonggi-do, Korea. The domain of the aquifer is L-shaped and bounded by streams and impermeable bedrock.…”

Section: Introductionmentioning

confidence: 99%

“…The impacts of groundwater extraction by wells should therefore be thoroughly investigated before pumping. Theoretically, numerical methods, such as FEM are good tools to simulate groundwater flow in irregularly shaped aquifer such as the approximately L-shaped aquifer in Kihm et al (2007). However, they are generally time consuming and computationally demanding (Younger, 2007), and it is necessary to regenerate the mesh of problem domain for different sizes of L-shaped aquifers.…”

Section: Introductionmentioning

confidence: 99%

“…The SDR solution is also derived based on the head solution and Darcy's law and then used to evaluate the contribution of filtration water from each of two streams toward the pumping well. Figure 1 shows a fluvial plain located in the Yongpoong 2 Agriculture District, Gyeonggi-do, Korea whose characteristics are reported in Kihm et al (2007). The west side of the plain is a mountainous area, where impermeable bedrock outcrops, and the Poonggye stream flows along the east side from the southwest corner toward the northeast corner.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers

Lin¹,

Chang²,

Yeh³

2018

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. Understanding the head distribution in aquifers is crucial for the evaluation of groundwater resources. This article develops a model for describing flow induced by pumping in an L-shaped fluvial aquifer bounded by impermeable bedrocks and two nearly fully penetrating streams. A similar scenario for numerical studies was reported in Kihm et al. (2007). The water level of the streams is assumed to be linearly varying with distance. The aquifer is divided into two subregions and the continuity conditions of the hydraulic head and flux are imposed at the interface of the subregions. The steady-state solution describing the head distribution for the model without pumping is first developed by the method of separation of variables. The transient solution for the head distribution induced by pumping is then derived based on the steady-state solution as initial condition and the methods of finite Fourier transform and Laplace transform. Moreover, the solution for stream depletion rate (SDR) from each of the two streams is also developed based on the head solution and Darcy's law. Both head and SDR solutions in the real time domain are obtained by a numerical inversion scheme called the Stehfest algorithm. The software MODFLOW is chosen to compare with the proposed head solution for the L-shaped aquifer. The steady-state and transient head distributions within the L-shaped aquifer predicted by the present solution are compared with the numerical simulations and measurement data presented in Kihm et al. (2007).

show abstract

Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers

Lin¹,

Chang²,

Yeh³

2018

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

show abstract

The Saint‐Venant type isoperimetric inequalities for assessing saturated water storage in lacunary shallow perched aquifers

Avkhadiev

Kacimov

2022

Z Angew Math Mech

View full text Add to dashboard Cite

The Dupuit-Forchheimer (DF) approximation for unconfined groundwater flows is reduced to 2D Poisson's equation (PE), the right hand side of which involves an intensive evapotranspiration (ET) rate. A shallow water table dips inward from a constant piezometric head boundary (closed curve) such that a "dry gap," demarcated by another closed curve (unknown front), may emerge. Apriori estimates of the volume of the saturated zone and of the "dry gap" area are important for water resources management in drylands. We use the results from the theory of linear elasticity, torsion of elastic bars, for which PE is solved for the Prandtl function. Using the Poincaré metrics with the Gaussian constant curvature 𝑐 = −4, isoperimetric inequalities are obtained for steady-state DF flows. Conformal moments and confromal radii of the domains and 2-D Hardy's type inequalities in domains, modeling the Saint Venant bar torsion problem, are involved in the obtained estimates. The studied boundary value problems (BVPs) are nonlinear for ET rates depending on the depth of the water table.In the DF model, the vadose zone (VZ) is considered as a "distributed sink" (similar to a standard "distributed source," which models recharge to the water table in humid climates). The analytical VZ is collated with one obtained from a numerical solution to BVP for Richards' equation in a 3-D saturated-unsaturated flow. BVPs for Richards' equation in cylindrical domains, solved by HYDRUS software, give the pressure head, moisture content, Darcian velocity fields, and streamlines.

show abstract

Is the Thermal Diffusivity of Unsaturated Soils a Mono-Maximum Function of their Moisture Content?

Kacimov,

Obnosov

2023

J Eng Phys Thermophy

View full text Add to dashboard Cite

Free Surface Flow in a Microfluidic Corner and in an Unconfined Aquifer with Accretion: The Signorini and Saint-Venant Analytical Techniques Revisited

Cited by 10 publications

References 57 publications

Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers

Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers

The Saint‐Venant type isoperimetric inequalities for assessing saturated water storage in lacunary shallow perched aquifers

Is the Thermal Diffusivity of Unsaturated Soils a Mono-Maximum Function of their Moisture Content?

Contact Info

Product

Resources

About