Stability Analysis of Finite Difference Schemes for the Advection-Diffusion Equation

1984 ◽  
Vol 21 (2) ◽  
pp. 272-284 ◽  
Author(s):  
Tony F. Chan
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

scholarly journals Stability analysis of finite difference schemes for an advection diffusion equation

2017 ◽  
Vol 29 (2) ◽  
pp. 143-151 ◽  
Author(s):  
TMAK Azad ◽  
LS Andallah
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Time Step ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
The Stability ◽  
Stability Results

The paper studies stability analysis for two standard finite difference schemes FTBSCS (forward time backward space and centered space) and FTCS (forward time and centered space). One-dimensional advection diffusion equation is solved by using the schemes with appropriate initial and boundary conditions. Numerical experiments are performed to verify the stability results obtained in this study. It is found that FTCS scheme gives better point-wise solutions than FTBSCS in terms of time step selection.Bangladesh J. Sci. Res. 29(2): 143-151, December-2016

scholarly journals Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
A. R. Appadu
Keyword(s):  
Finite Difference ◽  
Diffusion Equation ◽  
Finite Difference Schemes ◽  
Time Step ◽  
Partial Differential ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Dispersion And Dissipation Errors ◽  
Nicolson Scheme ◽  
Nonstandard Finite Difference

Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit, and a nonstandard finite difference scheme (Mickens 1991). We solve a 1D numerical experiment with specified initial and boundary conditions, for which the exact solution is known using all these three schemes using some different values for the space and time step sizes denoted byhandk, respectively, for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values ofkandh. Two optimisation techniques are then implemented to find the optimal values ofkwhenh=0.02for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.

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