Third‐ and fifth‐order finite volume schemes for advection–diffusion equation with variable coefficients in semi‐infinite domain

Abstract

In the present paper, a novel numerical model based on the finite volume method is established to predict a time‐dependent, one‐dimensional, advection‐diffusion equation with variable coefficients in a semi‐infinite domain. The third‐and fifth‐order schemes are employed to solve the above‐mentioned equation. Totally, two dispersion problems are used to simulate various conditions as follows: (i) solute dispersion along steady flow through inhomogeneous domain and (ii) solute dispersion along temporally dependent unsteady flow through inhomogeneous domain. The inhomogeneity of the domain is provided by spatially dependent flow. The uniform node distribution is considered to divide the problem domain into a collection of smaller parts. Analytical solutions proposed in the literature are employed to demonstrate the accuracy and reliability of the suggested model. Meanwhile, the results of the aforementioned approaches are compared with the performance of the quadratic upstream interpolation for convective kinetics scheme. Lastly, the accuracy of the implemented schemes in developed model are discussed and evaluated.

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

“…Finally, the EFDM used in this work for solving ADE, besides it is the simplest among other FDMs (Dehghan, 2004), FEMs (Huang et al, (2008)) and FVMs (Gharehbaghi, (2017)), it is effective and accurate for solving time-dependent ADEs in twodimensional space. Stability of the explicit finite difference scheme proposed in this work and high accuracy of the obtained numerical results have easily been achieved by using a sufficiently small discrete time step length of Δt = 0.0005 days.…”

Fully Implicit Form of Differential Quadrature Method for Multi-Species Solute Transport in Porous Media

“…Due to the impact of this issue in human life, numerous experimental studies carried out in this field, and various numerical and analytical models have been developed by researchers. Nevertheless, the overwhelming majority of the analytical and numerical models developed only for describing singlemember transport of various contaminants (Kumar et al, 2010; Savovic and Djordjevich 2012; Singh et al, 2012;Gharehbaghi 2016Gharehbaghi & 2017Ciftci, 2017;Das et al, 2018; among many). But, the transport processes of some dangerous contaminants, e.g., pesticides and their degradation products, generally include a more complicated series of first-order or pseudo-first-order decay.…”

Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters

“…The author stated that numerical predictions of the implicit form gave better results than the explicit one. Gharehbaghi [41] used the third-and fifth-order finite volume schemes [42] to solve a time-dependent, onedimensional ADE with variable parameters in a semi-infinite domain. Numerical solutions were obtained using the first-order explicit time integration approach.…”