Unconditional stable explicit finite difference technique for the advection–diffusion equation using spreadsheets

2007 ◽  
Vol 38 (2) ◽  
pp. 80-86 ◽  
Author(s):  
Halil Karahan
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Finite Difference Technique ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Explicit Finite Difference

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.

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

2017 ◽  
Vol 65 (4) ◽  
pp. 426-432 ◽  
Author(s):  
Alexandar Djordjevich ◽  
Svetislav Savović ◽  
Aco Janićijević
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Variable Coefficients ◽  
Two Dimensional ◽  
Seepage Velocity ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Special Cases ◽  
Explicit Finite Difference

AbstractThe two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. 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 firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by 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 finite media, which is especially important when arbitrary initial and boundary conditions are required.

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