Sensitivity and stability analysis for groundwater numerical modeling: a field study of finite element application in the arid region

• Autorzy: Jafarzadeh Ahmad , Pourreza-Bilondi Mohsen , Akbarpour Abolfazl , Khashei-Siuki Abbas , Azizi Mohsen

Identyfikatory

DOI

10.1007/s11600-022-00949-7

• Języki publikacji: EN

Abstrakty

EN

This study intends to investigate the impacts of scheme type, time step, and error threshold on the stability of numerical simulation in the groundwater modeling. Hence, a two-dimensional finite element (FE) was implemented to simulate groundwater flow in a synthetic test case and a real-world study (Birjand aquifer). To verify the proposed model in both cases, the obtained results were compared with analytical solutions and observed values. The stability of numerical results was analyzed through different schemes and time-step sizes. Besides, the effect of the error threshold was examined by considering different threshold values. The results confirmed that the FE model has a good capacity to simulate groundwater fluctuations even for the real problem with more complexities. Examination of implicit outputs indicated that groundwater simulations based on this scheme have good accuracy, stability, and proper convergence in all time intervals. However, in the explicit and Crank–Nicolson schemes the time interval should be less than or equal to 0.001 and 0.1 day, respectively. Also, results reveal that for making stability in all schemes the value of the error threshold should not be more than 0.0001 m. Moreover, it derived that the boundary conditions of the aquifer influence the stability of numerical outputs. Finally, it was comprehended that as time interval and error threshold increases, the oscillation rate propagated.

Słowa kluczowe

EN

error threshold; iterative methods; spatial correlation; stability analysis; convergence analysis; open-source MATLAB framework; oscillation ratio

PL

próg błędu; metody iteracyjne; korelacja przestrzenna; analiza stabilności; analiza zbieżności

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2023
• Tom: Vol. 71, no. 2
• Strony: 1045--1062
• Opis fizyczny: Bibliogr. 39 poz.

Twórcy

autor

Jafarzadeh Ahmad

• Department of Water Engineering, University of Birjand, Birjand, Iran

• https://orcid.org/0000-0003-4761-7940

autor

Pourreza-Bilondi Mohsen

• Department of Water Engineering, University of Birjand, Birjand, Iran
• Research Group of Drought and Climate Change, University of Birjand, Birjand, Iran

autor

Akbarpour Abolfazl

• Department of Civil Engineering, University of Birjand, Birjand, Iran

autor

Khashei-Siuki Abbas

• Department of Water Engineering, University of Birjand, Birjand, Iran
• Department of Civil Engineering, University of Torbat Heydarieh, Torbat Heydarieh, Iran

autor

Azizi Mohsen

• Department of Water Engineering, University of Birjand, Birjand, Iran

Bibliografia

• 1. Aghlmand R, Abbasi A (2019) Application of MODFLOW with boundary conditions analyses based on limited available observations: a case study of Birjand plain in. Water 11(1904):1–21
• 2. Arnold JG, Allen PM, Bernhardt G (1993) A comprehensive surface-groundwater flow model. J Hydrol 142(1–4):47–69
• 3. Balaguer A, Conde C, Del Cerro A, Lopez JA, Martinez V (1970) A finite volume characteristics method for the one-dimensional simulation of pollutant transport in groundwater. WIT Trans Ecol Environ 7:43
• 4. Bon AF, Abderamane H, Ewodo Mboudou G, Aoudou Doua S, Banakeng LA, Bontsong Boyomo SB, Wangbara Damo B (2021) Parametrization of groundwater quality of the quaternary aquifer in N’Djamena (Chad), lake Chad Basin: application of numerical and multivariate analyses. Environ Sci Pollut Res 28(10):12300–12320
• 5. Bredehoeft JD, Pinder GF (1970) Digital analysis of areal flow in multiaquifer groundwater systems: a quasi three-dimensional model. Water Resour Res 6(3):883–888
• 6. Chu WS, Strecker EW, Lettenmaier DP (1987) An evaluation of data requirements for groundwater contaminant transport modeling. Water Resour Res 23(3):408–424
• 7. Dushoff J, Plotkin JB, Levin SA, Earn DJ (2004) Dynamical resonance can account for seasonality of influenza epidemics. Proc Natl Acad Sci 101(48):16915–16916
• 8. Fahlman SE (1991) The recurrent cascade-correlation architecture. In: Advances in neural information processing systems, pp 190–196
• 9. Freeze RA, Witherspoon PA (1966) Theoretical analysis of regional groundwater flow: 1. Analytical and numerical solutions to the mathematical model. Water Resour Res 2(4):641–656
• 10. Glover RE (1974) Transient ground water hydraulics. Department of Civil Engineering College of Engineering Colorado State University, Fort Collins
• 11. Guillot V (2021) Numerical modeling of a high power triode-based self-excited oscillator: a path forward more efficient designs and a better frequency stability of low cost high power RF sources. J Microw Power Electromagn Energy 55(2):153–171
• 12. Hamraz BS, Akbarpour A, Bilondi MP, Tabas SS (2015) On the assessment of ground water parameter uncertainty over an arid aquifer. Arab J Geosci 8(12):10759–10773
• 13. Hoopes JA, Harleman DR (1967) Dispersion in radial flow from a recharge well. J Geophys Res 72(14):3595–3607
• 14. Illangasekare TH, Döll P (1989) A discrete kernel method of characteristics model of solute transport in water table aquifers. Water Resour Res 25(5):857–867
• 15. Jafarzadeh A, Pourreza-Bilondi M, Aghakhani Afshar A, Khashei-Siuki A, Yaghoobzadeh M (2019) Estimating the reliability of a rainwater catchment system using the output data of general circulation models for the future period (case study: Birjand City, Iran). Theor Appl Climatol 137(3):1975–1986
• 16. Jafarzadeh A, Khashei-Siuki A, Pourreza-Bilondi M (2021a) Performance assessment of model averaging techniques to reduce structural uncertainty of groundwater modeling. Water Resour Manage 36:353–377
• 17. Jafarzadeh A, Pourreza-Bilondi M, Akbarpour A, Khashei-Siuki A, Samadi S (2021b) Application of multi-model ensemble averaging techniques for groundwater simulation: synthetic and real-world case studies. J Hydroinform 23(6):1271–1289
• 18. Javandel I, Witherspoon PA (1968) Application of the finite element method to transient flow in porous media. Soc Petrol Eng J 8(03):241–252
• 19. Kaliakin VN (2018) Introduction to approximate solution techniques, numerical modeling, and finite element methods. CRC Press, Boca Raton
• 20. Knox JB, Rawson DE, Korver JA (1965) Analysis of a groundwater anomaly created by an underground nuclear explosion. J Geophys Res 70(4):823–835
• 21. Larkin BK (1964) Some stable explicit difference approximations to the diffusion equation. Math Comput 18(86):196–202
• 22. Liu GR, Gu YT (2005) An introduction to meshfree methods and their programming. Springer, Berlin
• 23. Mohtashami A, Akbarpour A, Mollazadeh M (2017) Development of two-dimensional groundwater flow simulation model using meshless method based on MLS approximation function in unconfined aquifer in transient state. J Hydroinform 19(5):640–652
• 24. Moridis GJ, Anantraksakul N, Blasingame TA (2020) TDM-based semi-analytical solutions of the 3D problem of oil production from shale reservoirs. In: SPE Latin American and Caribbean petroleum engineering conference. OnePetro
• 25. Owais S, Atal S, Sreedevi PD (2008) Governing equations of groundwater flow and aquifer modelling using finite difference method. In: Groundwater Dynamics in Hard Rock Aquifers. Springer, Dordrecht, pp. 201–218
• 26. Patankar SV (1980) Numerical fluid flow and heat transfer. Hemisphere, New York
• 27. Pathak AP (1982) Z-oscillations in channeling stopping power. Nucl Instrum Methods Phys Res 194(1–3):31–34
• 28. Pinder GF, Cooper HH Jr (1970) A numerical technique for calculating the transient position of the saltwater front. Water Resour Res 6(3):875–882
• 29. Qin H (2021) Numerical groundwater modeling and scenario analysis of Beijing plain: implications for sustainable groundwater management in a region with intense groundwater depletion. Environ Earth Sci 80(15):1–14
• 30. Quon D, Dranchuk PM, Allada SR, Leung PK (1965) A stable, explicit, computationally efficient method for solving two-dimensional mathematical models of petroleum reservoirs. J Can Pet Technol 4(02):53–58
• 31. Regazzoni F, Quarteroni A (2021) An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics. Comput Methods Appl Mech Eng 373:113506. https://doi.org/10.1016/j.cma.2020.113506
• 32. Remson I, Hornberger GM, Molz FJ (1971) Numerical methods in subsurface hydrology. Wiley, New York
• 33. Rushton KR, Redshaw SC (1979) Seepage and groundwater flow: numerical analysis by analog and digital methods. Wiley, Hoboken
• 34. Sadeghi-Tabas S, Samadi SZ, Akbarpour A, Pourreza-Bilondi M (2017) Sustainable groundwater modeling using single-and multi-objective optimization algorithms. J Hydroinform 19(1):97–114
• 35. Sadr A, Kaliakin VN, Hataf N, Manahiloh KN (2022) Numerical study of soilbag columns and comparison to encased soil columns in loose sand. Comput Geotech 142:104588
• 36. Van Dam JC, Feddes RA (2000) Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation. J Hydrol 233(1–4):72–85
• 37. Wang HF, Anderson MP (1995) Introduction to groundwater modeling: finite difference and finite element methods. Academic Press, Cambridge
• 38. Witherspoon PA, Mueller TD, Donovan RW (1962) Evaluation of underground gas-storage conditions in aquifers through investigations of groundwater hydrology. J Petrol Technol 14(05):555–561
• 39. Zienkiewichz OC, Mayer P, Cheung YK (1966) Solution of anisotropic seepage problem by finite elements. Proc ASCE 92:111–120

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).