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Malan, Reshma, ‎Desai, ‎Narendrasinh. (1402). Contaminant transportation modeling with time dependent dispersion. سامانه مدیریت نشریات علمی, 11(3), 605-614. doi: 10.22034/cmde.2023.51014.2125
Reshma Rajesh Malan; ‎Narendrasinh B. ‎Desai. "Contaminant transportation modeling with time dependent dispersion". سامانه مدیریت نشریات علمی, 11, 3, 1402, 605-614. doi: 10.22034/cmde.2023.51014.2125
Malan, Reshma, ‎Desai, ‎Narendrasinh. (1402). 'Contaminant transportation modeling with time dependent dispersion', سامانه مدیریت نشریات علمی, 11(3), pp. 605-614. doi: 10.22034/cmde.2023.51014.2125
Malan, Reshma, ‎Desai, ‎Narendrasinh. Contaminant transportation modeling with time dependent dispersion. سامانه مدیریت نشریات علمی, 1402; 11(3): 605-614. doi: 10.22034/cmde.2023.51014.2125

Contaminant transportation modeling with time dependent dispersion

Computational Methods for Differential Equations
مقاله 12، دوره 11، شماره 3، شهریور 2023، صفحه 605-614    اصل مقاله (381.8 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.51014.2125
نویسندگان
Reshma Rajesh Malan* 1؛ ‎Narendrasinh B. ‎Desai2
1Department of Mathematics, Government Engineering College, Valsad-Gujarat, India.
2Department of Mathematics‎, ‎A‎. ‎D‎. ‎Patel Institute of Technology‎, ‎Anand-388121‎, ‎India.
چکیده
A mathematical modeling of contaminate transportation has been presented in the current paper. The time-dependent dispersion has been considered in the transportation of contaminant in a  nite homogeneous porous medium. The study of contaminants concentration has been presented for the uniform unsteady flow of ground-water. Instead of a constant dispersion, in order to consider the effect of groundwater velocity on contaminant transportation, dispersion has been considered as a groundwater velocity-dependent quantity. As found in the many practical aspects, a linear increase in concentration at a source point with time has been assumed for the present modeling. The spread of the initial contaminant concentration has been considered linearly decreasing along the direction of one-dimensional  flow. The contaminant transport equation for the above-mentioned conditions and environment has been solved. The Laplace transform variation iteration method (LVIM) has been adopted to obtain a solution. Spatial and temporal variations of concentration for a developed model have been presented graphically by varying dispersion. The LVIM has been found suitable for the present study of contaminant transport modeling. The MATHEMATICA package has been used for the present study.
کلیدواژه‌ها
Contaminant transport؛ Correlation function؛ Laplace transform variational iteration method
مراجع
  • [1] J. Bear and A. H. D. Cheng, Modeling groundwater flow and contaminant transport, Springer, 23, 2010.
  • [2] N. B. Desai, The study of problems arises in single phase and multi phase flow through porous media, Thesis (Ph.D.), South Gujarat University, Surat-India.
  • [3] R. A. Freeze and J. A. Cherry, Groundwater, Printice Hall, 1979.
  • [4] J. J. Fried, Groundwater pollution, Elsevier, 1975.
  • [5] Ji. H. He, A new approach to non-linear partial differential equations, Communications in Non-linear Science and Numerical Simulation, 2 (1997), 230–235.
  • [6] Ji. H. He, Variational iteration method–a kind of non-linear analytical technique: some examples, International journal of non-linear mechanics, 34 (1999), 699–708.
  • [7] Ji. H. He, Variational iteration methodsome recent results and new interpretations, Journal of computational and applied mathematics, 207 (2007), 3–17.
  • [8] Ji. H. He, Variational principles for some non-linear partial differential equations with variable coefficients, Chaos, Solitons & Fractals, 19 (2004), 847–851.
  • [9] Ji. H. He, Variational theory for linear magneto-electro-elasticity,  International Journal of Non-linear Sciences  and Numerical Simulation, 2 (2001), 309–316.
  • [10] Ji. H. He and H. Latifizadeh, A general numerical algorithm for non-linear differential equations by the variational iteration method, International Journal of Numerical Methods for Heat & Fluid Flow, 30 (2020), 4797-4810.
  • [11] Ji. H. He and Xu. H. Wu, Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons & Fractals, 29 (2006), 108–113.
  • [12] D. K. Jaiswal, A. Kumar, N. Kumar, and R. R. Yadav, Analytical solutions for temporally and spatially dependent solute dispersion of pulse type  input concentration in one-dimensional semi-infinite media, International Journal    of Pure and Applied Mathematics, 2 (2009), 254–263.
  • [13] M. S. Joshi, N. B. Desai, and M. N. Mehta, Solution of the burgers equation for longitudinal dispersion phenomena occurring in miscible phase flow through porous media, ITB Journal of Engineering Sciences, 44 (2012), 61–76.
  • [14] S. A. Khuri and A. Sayfy, A Laplace variational iteration strategy for the solution of differential equations, Applied Mathematics Letters, 25 (2012), 2298–2305.
  • [15] S. A. Khuri and A. Sayfy, Generalizing the variational iteration method for BVPs: proper setting of the correction functional, Applied Mathematics Letters, 68 (2017), 68–75.
  • [16] C. J. Leo and J. R. Booker, A boundary element method for analysis of contaminant transport in porous mediaII: non-homogeneous porous media, International journal for numerical and analytical methods in geomechanics, 23 (1999), 1701–1715.
  • [17] C. J. Leo and J. R. Booker, A boundary element method for analysis of contaminant transport in fractured and non-fractured porous media, Computers and Geotechnics, 23 (1998), 165–181.
  • [18] M. Matinfar, M. Saeidy, and M. Ghasemi, The combined Laplace-variational iteration method for partial differ- ential equations, International Journal of Non-linear Sciences and Numerical Simulation, 14 (2013), 93–101.
  • [19] A. J. Mohamad-Jawad, M. D. Petkovi, and A. Biswas, Applications of Hes principles to partial differential equations, International Journal of Pure and Applied Mathematics, 217 (2011), 7039–7047.
  • [20] M. M. Nezhad, A. A. Javadi, A. Al-Tabbaa, and F. Abbasi, Numerical study of soil heterogeneity effects on contaminant transport in unsaturated soil model development and validation, International Journal for Numerical and Analytical Methods in Geomechanics, 37 (2013), 278–298.
  • [21] Z. M. Odibat, A study on the convergence of variational iteration method, Mathematical and Computer Modeling, 51 (2010), 1181–1192.
  • [22] Y. Patel and J. M. Dhodiya, Application of differential transform method to solve linear, non-linear reaction convection diffusion and convection diffusion problem, International Journal of Pure and Applied Mathematics, 109 (2016), 529–538.
  • [23] A. E. Scheidegger, General theory of dispersion in porous media, Journal of Geophysical Research, 66 (1961), 327332785.
  • [24] A. E. Scheidegger, The physics of flow through porous media, University of Toronto press, 3, 1974.
  • [25] K. Shah, H. Naz, M. Sarwar, and T. Abdeljawad, On spectral numerical method for variable-order partial differ- ential equations, AIMS Mathematics, 7 (2020), 10422–10438.
  • [26] K. Shah, H. Naz, M. Sarwar, and T. Abdeljawad, On computational analysis of highly nonlinear model addressing real world applications, Results in Physics, 36 (2022), 105431.
  • [27] K. Shah, M. Arfan, A. Ullah, Q. Al-Mdallal, and K. J. Ansari, Computational study on the dynamics of fractional order differential equations with applications, Chaos, Solitons & Fractals, 157 (2020), 111955.
  • [28] D. C-F. Shih, G. F. Lin, and I. S. Wang, Contaminant transport in fractured media: analytical solution and sensitivity study considering pulse, Dirac delta and sinusoid input sources, Hydrological processes, 16 (2002), 3265–3278.
  • [29] G. Singh and I. Singh, New Laplace variational iterative method for solving  3D Schr¨odinger equations, J. Math. Comput. Sci., 10 (2020), 2015–2024.
  • [30] M. Uddin and I. U. Din, A numerical method for solving variable-order solute transport models, Computational and Applied Mathematics, 39 (2020), 1–10.
  • [31] M. Uddin, K. Kamran, M. Usman, and A. Ali, On the Laplace-transformed-based local meshless method for fractional-order diffusion equation, International Journal for Computational Methods in Engineering Science and Mechanics, 39 (2020), 221–225.
  • [26] M. Uddin and M. Uddin, On the numerical approximation of Volterra integro-differential equation using Laplace transform, Computational Methods for Differential Equations, 8 (2020), 305–313.
  • [33] C. S. Yim and M. F. N. Mohsen, Simulation of tidal effects on contaminant transport in porous media, Ground- water, 30 (1992), 78–86.
  • [34] Y. Zang and J. Pang, Laplace-based variational iteration method for non-linear oscillators in micro electro me- chanical system, Mathematical Methods in the Applied Sciences, (2020), 1-7.
  • [35] X. W. Zhou and L. Yao, The variational iteration method for Cauchy problems, International Journal of Pure and Applied Mathematics, 60 (2010), 756–760.
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