scholarly journals The Numerical Solution of the One-Dimensional Advection–Diffusion Equation in Layered Coordinates

2000 ◽  
Vol 128 (7) ◽  
pp. 2575-2587 ◽  
Author(s):  
William K. Dewar ◽  
Trevor J. McDougall
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The One

scholarly journals Time-Splitting Procedures for the Numerical Solution of the 2D Advection-Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
A. R. Appadu ◽  
H. H. Gidey
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Optimization Technique ◽  
Step Size ◽  
One Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Optimal Value ◽  
Time Splitting ◽  
Dispersion And Dissipation Errors

We perform a spectral analysis of the dispersive and dissipative properties of two time-splitting procedures, namely, locally one-dimensional (LOD) Lax-Wendroff and LOD (1, 5) [9] for the numerical solution of the 2D advection-diffusion equation. We solve a 2D numerical experiment described by an advection-diffusion partial differential equation with specified initial and boundary conditions for which the exact solution is known. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion and dissipation errors. Lastly, an optimization technique is implemented to find the optimal value of temporal step size that minimizes the dispersion error for both schemes when the spatial step is chosen as 0.025, and this is validated by numerical experiments.

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.

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