Browsing by Author "Mehdinejadiani, B."

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Citation - WoS: 35
Citation - Scopus: 40
Derivation of a fractional Boussinesq equation for modelling unconfined groundwater
(Springer Heidelberg, 2013) Mehdinejadiani, B.; Baleanu, Dumitru; Jafari, H.; Baleanu, D.; 56389; Matematik
In this manuscript, a fractional Boussinesq equation is obtained by assuming power-law changes of flux in a control volume and using a fractional Taylor series. Furthermore, it was assumed that the average thickness of the watery layer of an aquifer is constant, and the linear fractional Boussinesq equation was derived. Unlike classical Boussinesq equation, due to the non-locality property of fractional derivatives, the parameters of the fractional Boussinesq equation are constant and scale-invariant. In addition, the fractional Boussinesq equation has two various fractional orders of differentiation with respect to x and y that indicate the degree of heterogeneity in the x and y directions, respectively.
Citation - Scopus: 10
Fractional calculus for modeling unconfined groundwater
(De Gruyter, 2019) Jafari, H.; Baleanu, Dumitru; Mehdinejadiani, B.; Baleanu, D.; 56389; Matematik
The porous medium which groundwater flows in is heterogeneous at all scales. This complicates the simulation of groundwater flow. Fractional derivatives, because of their non-locality property, can reduce the scale effects on the parameters and, consequently, better simulate the hydrogeological processes. In this chapter a fractional governing partial differential equation on unconfined groundwater (fractional Boussinesq equation [FBE]) is derived using the fractional mass conservation law. The FBE is a generalization of the Boussinesq equation (BE) that can be used in both homogeneous and heterogeneous unconfined aquifers. Compared to the BE, the FBE includes an additional parameter which represents the heterogeneity degree of the porous medium. This parameter changes within the range of 0 to 1 in the non-linear form of the FBE. The smaller the value of the heterogeneity degree, the more heterogeneous the aquifer is, and vice versa. To investigate the applicability of the FBE to real problems in groundwater flow, a fractional Glover-Dumm equation (FGDE) was obtained using an analytical solution of the linear form of the FBE for onedimensional unsteady flow towards parallel subsurface drains. The FGDE was fitted to water table profiles observed at laboratory and field scales, and its performance was compared to that of the Glover-Dumm equation (GDE). The parameters of the FGDE and the GDE were estimated using the inverse problem method. The results indicate that one can recognize the heterogeneity degree of porous media examined according to the obtained values for the indicator of the heterogeneity degree. The FGDE and the GDE showed similar performances in homogeneous soil, while the performance of the FGDE was significantly better than that of the GDE in heterogeneous soil. In summary, the FBE can be used as a highly general differential equation governing groundwater flow in unconfined aquifers. © 2019 Walter de Gruyter GmbH, Berlin/Boston.