Probabilistic simulation of advection-reaction-dispersion equation using random lattice Boltzmann method

Hekmatzadeh, Ali Akbar; Al-Gheethi, Adel; Zarei, Farshad; Haghighi, Ali Torabi

doi:10.1016/j.ijheatmasstransfer.2019.118647

Cited by 6 publications

(3 citation statements)

References 46 publications

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“…Moreover, the LB methods benefit from fast computational ability and admirable stability, especially in time-dependent problems. This method shows superior capability to meet with parallel programming techniques utilizing graphics processing unit (GPU) [2,3]. This method has various applications in the simulation of different physical phenomena such as solitary wave [4], convection-diffusion equations [5], shallow water [6], heat conduction [7], and kinetic equations [8].…”

Section: Introductionmentioning

confidence: 99%

“…In the last decade, this method has been employed to simulate mass transfer problems as with groundwater flow equation as well as solute transport equation. The diffusion equation governs groundwater flow, while advection-diffusion equation describes the solute transport [2,9,10]. It is worth noting that various lattice configurations have been developed for LBM to solve mass transfer equations, containing D1Q2 and D1Q3 for one dimensional problems, D2Q4, D2D5, and D2Q9 for two dimensional problems, in addition to, D3Q15 and D3Q19 for the three dimensions [3,[11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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“…Therefore, many researchers are more prefer to the numerical method to solve. Special for the advectiondispersion model, some numerical methods were developed such as random lattice Boltzmann method [10], Haar wavelets coupled with finite differences [11], unified transform/Fokas method [12], a numerical method based on Legendre scaling functions [13] and many more. Each of these methods had some superiority and weakness.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation on Two-Dimensional Advection-Dispersion Model of Biological Oxygen Demand in Facultative Waste Water Stabilization Pond: Case Study at Sewon Wastewater Treatment Facility

Sunarsih¹,

Sasongko²,

Sutrisno³

2020

Adv. sci. technol. eng. syst. j.

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To build a precise mathematical model describing a natural phenomenon, parameter estimation is needed to achieve the best parameter value. In this paper, we have calculated the best parameter value for a two-dimensional advection-dispersion differential equation of the biological oxygen demand degradation process in a facultative wastewater stabilization pond. This research was conducted with case study data collected from Sewon, Bantul facultative wastewater treatment facility located in Yogyakarta, Indonesia. The method employed in this research is based on the least square value by minimizing the difference between the observed data and the simulated data via quadratic programming using the interior point algorithm. This method gave the best value for the parameters observed in the model i.e. dispersion constant and the flow rate velocity. From the results, we have achieved that the best value for dispersion constant is 0.25, the velocity of the flow rate in the x-direction is 0.1, and the velocity of the flow rate in the y-direction is 0.15 whereas the relative error of this parameter estimation was 11.5% that is acceptable.

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Probabilistic simulation of hydraulic jump in a riverbed in presence and absence of stilling basin

Hajizadehmishi,

Amiri,

Hekmatzadeh

et al. 2024

Stoch Environ Res Risk Assess

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Probabilistic simulation of advection-reaction-dispersion equation using random lattice Boltzmann method

Cited by 6 publications

References 46 publications

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

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

Parameter Estimation on Two-Dimensional Advection-Dispersion Model of Biological Oxygen Demand in Facultative Waste Water Stabilization Pond: Case Study at Sewon Wastewater Treatment Facility

Probabilistic simulation of hydraulic jump in a riverbed in presence and absence of stilling basin

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