scholarly journals Explicit Numerical Solution of High - Dimensional Advection - Diffusion

2013 ◽  
Vol 2 (3) ◽  
pp. 17-22
Author(s):  
Elham Bayatmanesh
Keyword(s):  
High Dimensional ◽  
Numerical Techniques ◽  
Science And Engineering ◽  
Numerical Examples ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Constant Coefficients ◽  
The Subject ◽  
The One

The Several numerical techniques have been developed and compared for solving the one-dimensional and three-dimentional advection-diffusion equation with constant coefficients. the subject has played very important roles to fluid dynamics as well as many other field of science and engineering. In this article, we will be presenting the of n-dimentional and we neglect the numerical examples.

A COMPARISON OF SPLINES INTERPOLATIONS WITH STANDARD FINITE DIFFERENCE METHODS FOR ONE-DIMENSIONAL ADVECTION-DIFFUSION EQUATION

2008 ◽  
Vol 19 (08) ◽  
pp. 1291-1304 ◽  
Author(s):  
MONTRI THONGMOON ◽  
SUWON TANGMANEE ◽  
ROBERT MCKIBBIN
Keyword(s):  
Finite Difference Methods ◽  
Cubic Spline ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Constant Coefficients ◽  
Difference Methods ◽  
The One ◽  
Natural Cubic Spline ◽  
And Diffusion

Four types of numerical methods namely: Natural Cubic Spline, Special A-D Cubic Spline, FTCS and Crank–Nicolson are applied to both advection and diffusion terms of the one-dimensional advection-diffusion equations with constant coefficients. The numerical results from two examples are tested with the known analytical solution. The errors are compared when using different Peclet numbers.

scholarly journals ANALYTICAL SOLUTION OF A NON - HOMOGENEOUS ONE - DIMENSIONAL ADVECTION DIFFUSION EQUATION WITH TEMPORALLY VARYING COEFFICIENTS .

2020 ◽  
Vol 9 (12) ◽  
pp. 49-58
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Transform Method ◽  
One Dimensional ◽  
Varying Coefficients ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Advection Term ◽  
Constant Coefficients ◽  
Instantaneous Point

Advection Diffusion Equation is a partial differential equation that describes the transport of pollutants in rivers. Its coefficients (dispersion and velocity) can be constant, dependent on space or time or both space and time. This study presents an analytical solution of a one dimensional non - homogeneous advection diffusion equation with temporally dependent coefficients, describing one dimensional pollutant transport in a section of a river. Temporal dependence is accounted for by considering a temporally dependent dispersion coefficient along an unsteady flow assuming that dispersion is proportional to the velocity. Transformations are used to convert the time dependent coefficients to constant coefficients and to eliminate the advection term. Analytical solution is obtained using Fourier transform method considering an instantaneous point source. Numerical results are presented. The findings show that concentration monotonically decreases with increasing distance and increasing time.

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