A semi-Lagrangian Crank-Nicolson algorithm for the numerical solution of advection-diffusion problems

2006 ◽  
Vol 7 (4) ◽  
pp. n/a-n/a ◽  
Author(s):  
Marc Spiegelman ◽  
Richard F. Katz
Keyword(s):  
Numerical Solution ◽  
Advection Diffusion ◽  
Diffusion Problems ◽  
Crank Nicolson

scholarly journals Numerical solution of advection-diffusion equation using finite difference schemes

2020 ◽  
Vol 55 (1) ◽  
pp. 15-22
Author(s):  
LS Andallah ◽  
MR Khatun
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Numerical Scheme ◽  
Finite Difference Schemes ◽  
Qualitative Behavior ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nicolson Scheme ◽  
And Diffusion ◽  
Crank Nicolson

This paper presents numerical simulation of one-dimensional advection-diffusion equation. We study the analytical solution of advection diffusion equation as an initial value problem in infinite space and realize the qualitative behavior of the solution in terms of advection and diffusion co-efficient. We obtain the numerical solution of this equation by using explicit centered difference scheme and Crank-Nicolson scheme for prescribed initial and boundary data. We implement the numerical scheme by developing a computer programming code and present the stability analysis of Crank-Nicolson scheme for ADE. For the validity test, we perform error estimation of the numerical scheme and presented the numerical features of rate of convergence graphically. The qualitative behavior of the ADE for different choice of the advection and diffusion co-efficient is verified. Finally, we estimate the pollutant in a river at different times and different points by using these numerical scheme. Bangladesh J. Sci. Ind. Res.55(1), 15-22, 2020

scholarly journals The numerical solution of advection–diffusion problems using new cubic trigonometric B-splines approach

2016 ◽  
Vol 40 (7-8) ◽  
pp. 4586-4611 ◽  
Author(s):  
Tahir Nazir ◽  
Muhammad Abbas ◽  
Ahmad Izani Md. Ismail ◽  
Ahmad Abd. Majid ◽  
Abdur Rashid
Keyword(s):  
Numerical Solution ◽  
B Splines ◽  
Advection Diffusion ◽  
Diffusion Problems
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