A comparative study on using metaheuristic algorithms for simultaneously estimating parameters of space fractional advection-dispersion equation

2021 ◽  
pp. 126757
Author(s):  
Halimeh Maroufi ◽  
Behrouz Mehdinejadiani
Keyword(s):  
Comparative Study ◽  
Dispersion Equation ◽  
Metaheuristic Algorithms ◽  
Advection Dispersion

A Comparative Study of Finite Element and Finite Difference Methods for Two-Dimensional Space-Fractional Advection-Dispersion Equation

2015 ◽  
Vol 8 (1) ◽  
pp. 166-186 ◽  
Author(s):  
Guofei Pang ◽  
Wen Chen ◽  
Kam Yim Sze
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Comparative Study ◽  
Dispersion Equation ◽  
Dimensional Space ◽  
Finite Difference Methods ◽  
Rectangular Domain ◽  
Two Dimensional ◽  
Element Analysis ◽  
Advection Dispersion

AbstractThe paper makes a comparative study of the finite element method (FEM) and the finite difference method (FDM) for two-dimensional fractional advection-dispersion equation (FADE) which has recently been considered a promising tool in modeling non-Fickian solute transport in groundwater. Due to the non-local property of integro-differential operator of the space-fractional derivative, numerical solution of FADE is very challenging and little has been reported in literature, especially for high-dimensional case. In order to effectively apply the FEM and the FDM to the FADE on a rectangular domain, a backward-distance algorithm is presented to extend the triangular elements to generic polygon elements in the finite element analysis, and a variable-step vector Grünwald formula is proposed to improve the solution accuracy of the conventional finite difference scheme. Numerical investigation shows that the FEM compares favorably with the FDM in terms of accuracy and convergence rate whereas the latter enjoys less computational effort.

scholarly journals Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

2021 ◽  
Author(s):  
Thomas TJOCK-MBAGA ◽  
Patrice Ele Abiama ◽  
Jean Marie Ema'a Ema'a ◽  
Germain Hubert Ben-Bolie
Keyword(s):  
Analytical Solution ◽  
Linear Function ◽  
Dispersion Equation ◽  
Source Term ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Liouville Problem ◽  
Finite Domain ◽  
Advection Dispersion ◽  
Sink Term

Abstract This study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport with two contaminant sources that takes into account the source term. For a heterogeneous medium, groundwater velocity is considered as a linear function while the dispersion as a nth-power of linear function of space and analytical solutions are obtained for and . The solution in a heterogeneous finite domain with unsteady coefficients is obtained using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). The solutions are validated with the numerical solutions obtained using MATLAB pedpe solver and the existing solution from the proposed solutions. We exanimated the influence of the source term, the heterogeneity parameters and the unsteady coefficient on the solute concentration distribution. The results show that the source term produces a solute build-up while the heterogeneity level decreases the concentration level in the medium. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public.

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