Series solutions for saturated–unsaturated flow in multi-layer unconfined aquifers

Ameli, Ali; Craig, James R.; Wong, Susanna

doi:10.1016/j.advwatres.2013.07.004

Cited by 24 publications

(24 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many of these works build on decades of research with integrated flow and transport models that have helped reveal the linkages between watershed-scale processes and regional and local scale groundwater systems (as outlined in M. P. Anderson et al, 2015). Since the early benchmark works of Toth (1963) and Freeze and Witherspoon (1967), useful simulations of steady state local and regional groundwater flow and transport have been conducted using analytical and numerical modeling approaches (Ameli et al, 2013;Cardenas & Jiang, 2010;Fiori & Russo, 2008;Janković et al, 2003;Marklund & Wörman, 2011).…”

Section: Introductionmentioning

confidence: 99%

Groundwater Subsidy From Headwaters to Their Parent Water Watershed: A Combined Field‐Modeling Approach

Ameli

Gabrielli

Morgenstern

et al. 2018

Water Resources Research

View full text Add to dashboard Cite

Headwater groundwater subsidy, defined here as out‐of‐catchment groundwater flow contribution from a headwater catchment to its larger parent watershed (i.e., higher‐order stream), can influence the water quality and quantity of regional water resources. But the integrated flow and transport modeling approaches currently being implemented to quantify this subsidy are limited by an absence of critical field observations, such as water table dynamics and groundwater age that are required to test such models. Here we couple tracer (and hydrometric) observations from the well‐studied 4.5‐ha M8 headwater catchment in the Maimai experimental watershed with a new semianalytical free‐surface integrated flow and transport model. Our main research goals are to quantify the magnitude, age, and flow paths of the headwaters groundwater subsidies at the Maimai experimental watershed. Additionally, we explore through virtual experiments the effects of watershed slope, watershed active thickness, and recharge rate on the age, flow path, and magnitude of out‐of‐catchment headwater groundwater subsidies versus within‐catchment (or local) groundwater flow contributions. Our results show that more than 50% of groundwater recharged in the Maimai headwaters subsidizes their parent watershed. The relative proportion of headwaters groundwater subsidies is inversely proportional to recharge rate and/or directly proportional to slope angle. Our results also show that the age of the headwater groundwater subsidies is more than 500 years, almost 9 times older than the age of within‐catchment groundwater flow contributions. These findings highlight the need to consider headwaters groundwater subsidies in groundwater management area considerations.

show abstract

Section: Introductionmentioning

confidence: 99%

Groundwater Subsidy From Headwaters to Their Parent Water Watershed: A Combined Field‐Modeling Approach

Ameli

Gabrielli

Morgenstern

et al. 2018

Water Resources Research

View full text Add to dashboard Cite

show abstract

“…Semianalytical solutions are often obtained in 2‐D problems using the FG method (Peyret, ). Ameli et al () used the Fourier series method to solve saturated‐unsaturated flow equations in multilayer unconfined aquifers. Fahs et al () developed a new implementation of the FG method and suggested a new 2‐D benchmark for DDF.…”

Section: Solution Methodsologymentioning

confidence: 99%

A 3‐D Semianalytical Solution for Density‐Driven Flow in Porous Media

Shao

Fahs

Hoteit

et al. 2018

Water Resources Research

View full text Add to dashboard Cite

Existing analytical and semianalytical solutions for density-driven flow (DDF) in porous media are limited to 2-D domains. In this work, we develop a semianalytical solution using the Fourier Galerkin method to describe DDF induced by salinity gradients in a 3-D porous enclosure. The solution is constructed by deriving the vector potential form of the governing equations and changing variables to obtain periodic boundary conditions. Solving the 3-D spectral system of equations can be computationally challenging. To alleviate computations, we develop an efficient approach, based on reducing the number of primary unknowns and simplifying the nonlinear terms, which allows us to simplify and solve the problem using only salt concentration as primary unknown. Test cases dealing with different Rayleigh numbers are solved to analyze the solution and gain physical insight into 3-D DDF processes. In fact, the solution displays a 3-D convective cell (actually a vortex) that resembles the quarter of a torus, which would not be possible in 2-D. Results also show that 3-D effects become more important at high Rayleigh number. We compare the semianalytical solution to research (Transport of RadioACtive Elements in Subsurface) and industrial (COMSOL Multiphysics®) codes. We show cases (high Raleigh number) where the numerical solution suffers from numerical artifacts, which highlight the worthiness of our semianalytical solution for code verification and benchmarking. In this context, we propose quantitative indicators based on several metrics characterizing the fluid flow and mass transfer processes and we provide open access to the source code of the semianalytical solution and to the corresponding numerical models. SHAO ET AL.10,094

show abstract

“…The FG method can give high accuracy solutions with relatively few Fourier modes as it converges exponentially to the exact solution. However, in the case of sharp solutions, the number of Fourier modes should be considerably increased in order to prevent the occurrence of nonphysical oscillations related to the Gibbs phenomenon (Ameli et al, 2013). For the surface contamination scenario, there is a discontinuity in the boundary condition as the source of contamination is imposed at a given interval of the top surface.…”

Section: Adaptation Of the Fg Methodsmentioning

confidence: 99%

“…As mention previously, the Fourier series solution may suffer from unphysical oscillations when the solution is relatively sharp. These oscillations are related to the Gibbs phenomenon (Durran, 1999;Ameli et al, 2013;Fahs et al, 2014). In such a case, a large number of Fourier modes should be used to obtain stable concentration contours.…”

Section: Stability Of the Semi-analytical Solution And Effect Of Thementioning

confidence: 99%

Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

Koohbor

Fahs

Ataie-Ashtiani

et al. 2018

Journal of Hydrology

View full text Add to dashboard Cite

Existing closed-form solutions of contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. These solutions cannot be used to investigate contaminant transport in coastal aquifers where seawater intrusion induces a variable velocity field. An adaptation of the Fourier-Galerkin method is introduced to obtain semianalytical solutions for contaminant transport in a confined coastal aquifer in which the saltwater wedge is in equilibrium with a freshwater discharge flow. Two scenarios dealing with contaminant leakage from the aquifer top surface and contaminant migration from a source at the landward boundary are considered. Robust implementation of the Fourier-Galerkin method is developed to efficiently solve the coupled flow, salt and contaminant transport equations. Various illustrative examples are generated and the semi-analytical solutions are compared against an in-house numerical code. The Fourier series are used to evaluate relevant metrics characterizing contaminant transport such as the discharge flux to the sea, amount of contaminant persisting in the groundwater and solute flux from the source. These metrics represent quantitative data for numerical code validation and are relevant to understand the effect of seawater intrusion on contaminant transport. It is observed that, for the surface contamination scenario, seawater intrusion limits the spread of the contaminant but intensifies the contaminant discharge to the sea. For the landward contamination scenario, moderate seawater intrusion affects only the spatial distribution of the contaminant plume while extreme seawater intrusion can increase the contaminant discharge to the sea. The developed semi-analytical solution presents an efficient tool for the verification of numerical models. It provides a clear interpretation of the contaminant transport processes in coastal aquifers subject to seawater 3 intrusion. For practical usage in further studies, the full open source semi-analytical codes are made available at the website https://lhyges.unistra.fr/FAHS-Marwan.

show abstract

Series solutions for saturated–unsaturated flow in multi-layer unconfined aquifers

Cited by 24 publications

References 30 publications

Groundwater Subsidy From Headwaters to Their Parent Water Watershed: A Combined Field‐Modeling Approach

Groundwater Subsidy From Headwaters to Their Parent Water Watershed: A Combined Field‐Modeling Approach

A 3‐D Semianalytical Solution for Density‐Driven Flow in Porous Media

Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

Contact Info

Product

Resources

About