Lattice Boltzmann method for groundwater flow in non-orthogonal structured lattices

Budinski, Ljubomir; Fabian, Julius; Stipić, Matija

doi:10.1016/j.camwa.2015.09.027

Cited by 14 publications

(8 citation statements)

References 29 publications

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“…So far, several papers have discussed the groundwater model and obtained approximate solutions for this model. Liu et al [23] solved prevention of groundwater contamination model with modified upwind finite volume (MUFV) and two-grid modified upwind finite volume element (TG-MUFV) methods, Wang et al [40] studied estimating evapotranspiration from groundwater, Zhang et al [43] studied heat transfer of pile foundation ground heat exchanger with three-dimensional groundwater seepage, Ilati and Dehghan [15] solved remediation of contaminated groundwater model by meshless local weak forms such as meshless local Petrov-Galerkin (MLPG), direct meshless local Petrov-Galerkin (DMLPG), local weak moving kriging (LWMK) and local weak radial point interpolation (LWRPIM) methods, Budinski et al [4] studied groundwater flow in non-orthogonal structured lattices model with lattice Boltzmann method, Tambue [36] studied groundwater model using an exponential integrator for finite volume discretization. A numerical model for 2D free boundary analysis of groundwater in slopes stabilized by drain trenches has been developed in [8].…”

Section: A Brief Review On Proper Orthogonal Decomposition Techniquementioning

confidence: 99%

Numerical simulation based on a combination of finite-element method and proper orthogonal decomposition to prevent the groundwater contamination

Dehghan

Hooshyarfarzin

Abbaszadeh

2021

Engineering with Computers

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In this paper, the coupled advection-dominated diffusion-reaction equations which arise in the prevention of groundwater contamination problem are approximated by usual finite element method (FEM). It is clear that by increasing the number of elements to improve computational accuracy, we have to incur a lot of costs. The main presented idea is to reduce the used CPU time for employing the finite-element method by combining that with a technique which reduces the dimension of the problem. To this end, we apply the proper orthogonal decomposition (POD) technique to the usual FEM for the prevention of groundwater contamination problem to reduce CPU time with acceptable accuracy. Numerical examples are provided to illustrate efficiency and validity of the proposed method.

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Section: A Brief Review On Proper Orthogonal Decomposition Techniquementioning

confidence: 99%

Numerical simulation based on a combination of finite-element method and proper orthogonal decomposition to prevent the groundwater contamination

Dehghan

Hooshyarfarzin

Abbaszadeh

2021

Engineering with Computers

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“…The lattice Boltzmann method (LBM) as an innovative numerical method in hydraulic problems (Ru et al 2021), is one approach in this regard. The LBM is identified with its comfort of performance, parallel processing ability, and easy handling of boundary conditions which make it an appropriate method to simulate the complicated flows with complex boundaries (Budinski et al 2015). The first application of the LBM was implemented by Gladrow (Gladrow 1994) who proposed Lattice Boltzmann equation (LBE) models for diffusion instead of lattice gas automata due to its greater flexibility and freedom.…”

Section: Introductionmentioning

confidence: 99%

“…The first application of the LBM was implemented by Gladrow (Gladrow 1994) who proposed Lattice Boltzmann equation (LBE) models for diffusion instead of lattice gas automata due to its greater flexibility and freedom. The LBM has been successful performance in fluid flow modelling such as Navier-Stokes (Ansumali et al 2007), shallow water [Liu et al 2013, Peng et al 2011, Zhou 2004, groundwater (Zhou 2007a;Zhou 2011;Budinski et al 2015;Arsyad et al 2017;Hekmatzadeh et al 2018;, and especially multiphase flow in porous media [Anwar and Sukop 2008;Fattahi et al 2016;Gharibi and Ashrafizaadeh 2020). LBM has been widely applied to explore heat and mass transfer problems such as pollutant transport (Lei et al 2013), thermal response (Gao et al 2021), saltwater intrusion (Servan-Camas and T.-C. Tsai 2009) and reaction diffusion (Lin et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Understanding the effects of subsidence on unconfined aquifer parameters by integration of Lattice Boltzmann Method (LBM) and Genetic Algorithm (GA)

Yousefi

Talebbeydokhti²,

Afzali³

et al. 2022

Nat Hazards

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Excessive exploitation of groundwater has led to a significant subsidence in Darab plain, located in Fars province, Iran. The compaction of aquifer layers especially in fine-grain sediments leads to changes in aquifer parameters including hydraulic conductivity, specific yield, and compressibility which consequently changes the permeability and storage of the aquifer. Accordingly, a precise estimation of aquifer parameters are essential for both future water resources planning and management. The main objective of this paper is to determine the most optimum values of aquifer parameters based on the groundwater information and subsidence measurements spanning from 2010 to 2016. The proposed approach for inverse solution of groundwater flow is based on Lattice Boltzmann Method (LBM) integrated with Genetic Algorithm for optimization (GA). Subsidence measurements made by previous studies as well as the initial values of unknown parameters obtained from piezometric information are incorporated into the inverse modeling. The whole process of inverse modeling is repeated from 2010 to 2016 which leads to annually estimation of the aquifer parameters. Due to the compaction occurring in the aquifer system, a decreasing temporal trend is observed in the aquifer parameters in most parts of the plain. By fitting a function to time-dependent aquifer parameters, their corresponding values and consequently the amount of subsidence in 2017 are predicted. The small average relative error (~3.5%) between the predicted land subsidence and the measurements demonstrates the high performance of the proposed inverse modeling approach.

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“…In so doing, they employed the altered-velocity model in the simulations with the latter method. Moreover, the lattice Boltzmann solution for groundwater flow in non-orthogonal structured lattices was developed by Budinski et al [32].…”

Section: Introductionmentioning

confidence: 99%

The solution of unconfined groundwater flow with an innovative lattice Boltzmann method

et al. 2021

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Lattice Boltzmann method (LBM) has emerged as a fast, precise, and efficient numerical solution to solve differential equations. There seems to be a dearth of research regarding the solution for groundwater flow in unconfined aquifer using LBM. Accordingly, in this study, an innovative numerical solution based on LBM was introduced to solve groundwater flow in unconfined aquifers, taking into account D2Q9 scheme. The solutions obtained from the proposed LBM were compared to results stemmed from three different unconfined groundwater problems with known solutions.Both steady and transient conditions for groundwater flow were considered in simulations. It was deduced that the proposed LBM could simulate the unconfined groundwater flow satisfactorily.

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Lattice Boltzmann method for groundwater flow in non-orthogonal structured lattices

Cited by 14 publications

References 29 publications

Numerical simulation based on a combination of finite-element method and proper orthogonal decomposition to prevent the groundwater contamination

Numerical simulation based on a combination of finite-element method and proper orthogonal decomposition to prevent the groundwater contamination

Understanding the effects of subsidence on unconfined aquifer parameters by integration of Lattice Boltzmann Method (LBM) and Genetic Algorithm (GA)

The solution of unconfined groundwater flow with an innovative lattice Boltzmann method

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