A non‐standard finite difference method for space fractional advection–diffusion equation

2020 ◽  
Author(s):  
Ziting Liu ◽  
Qi Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Anup Singh ◽  
S. Das ◽  
S. H. Ong ◽  
H. Jafari
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Conservative System ◽  
Computational Time ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nonlinear Reaction ◽  
Sink Term

In the present article, the advection–diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method.

scholarly journals FINITE DIFFERENCE SOLUTION OF TWO-DIMENSIONAL SOLUTE TRANSPORT WITH PERIODIC FLOW IN HOMOGENOUS POROUS MEDIA

2017 ◽  
Vol 8 (2) ◽  
Author(s):  
Alexandar Djordjevich ◽  
Svetislav Savović ◽  
Aco Janićijević
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Variable Coefficients ◽  
Two Dimensional ◽  
Seepage Velocity ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

Two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finite-difference method for the transport of solutes through a homogeneous, finite, porous, two-dimensional, domain. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity). Included are the first-order decay and zero-order production parameters proportional to the seepage velocity, periodic boundary conditions at the origin and the end of the domain. Results are compared to analytical solutions reported in the literature for special cases and a good agreement was found. The solute concentration profile is greatly influenced by the periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in a finite media, which is especially important when arbitrary initial and boundary conditions are required.

scholarly journals Explicit finite difference solution for contaminant transport problems with constant and oscillating boundary conditions

2020 ◽  
Vol 24 (3 Part B) ◽  
pp. 2225-2231
Author(s):  
Svetislav Savovic ◽  
Alexandar Djordjevich
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Oscillating Boundary ◽  
Constant Coefficients ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

For constant and oscillating boundary conditions, the 1-D advection-diffusion equation with constant coefficients, which describes a contaminant flow, is solved by the explicit finite difference method in a semi-infinite medium. It is shown how far the periodicity of the oscillating boundary carries on until diminishing to below appreciable levels a specified distance away, which depends on the oscillation characteristics of the source. Results are tested against an analytical solution reported for a special case. The explicit finite difference method is shown to be effective for solving the advection-diffusion equation with constant coefficients in semi-infinite media with constant and oscillating boundary conditions.

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