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Total variation diminishing scheme for advection or advection dispersion equation 

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July 21, 2012, 14:34 
Total variation diminishing scheme for advection or advection dispersion equation

#1 
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Jdbaba
Join Date: Jul 2012
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HI I want to write a total variation diminishing code for the simple advection equation and advection diffusion transport equation. I am using excel VBA to write a code. I have use bacward difference in time and central difference implicit scheme for space. The scheme is showing a lot of oscillation so I want to use the total variation diminishing scheme. Does anyone have a sample code with discretization which I can look at and start developing code ? Thank you so much.


July 21, 2012, 15:15 

#2  
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cfdnewbie
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Quote:
Dont use a central scheme for your advection, use upwind, and your oscillations will go away! 

July 22, 2012, 14:46 

#3 
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Jdbaba
Join Date: Jul 2012
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Thank you for your reply.
I think the implicit scheme is stable but I want to know how to implement the TVD scheme for diffusion advection equation. I knew some theory about the TVD scheme but I am having difficulty on how to start the scheme. Can anyone suggest me any sources or provide sample code to start with ? I am working on this code as a part of my research and one paper has stated that using TVD scheme gives better result. So, I want to see how does the result vary when we use TVD scheme. Thanks. 

July 22, 2012, 15:27 

#4  
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check this book: http://www.amazon.com/IntroductionC.../dp/0131274988 You will learn everything you have ever wanted to know about TVD implementation. very usefull wand clear. 

July 22, 2012, 15:41 

#5 
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Jdbaba
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Hi Leflix,
Thank you for your reply. As the name of the book suggests, it will talk more about the finite volume method. I am implementing finite difference method and I am completely new to finite volume method. Do you still suggest to go and read that book or is there any specific book for the implementation of TVD scheme in Finite difference method ? Thanks a lot. 

July 23, 2012, 05:25 

#6  
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The main task is to understand how upwindbiased TVD schemes are implemented regardless the type of discretization method. I guess there exist some books about TVD schemes using finite difference method. But if I could give you an advise, if you are not specifically interested in highorder schemes I would advise you to switch from finite difference to finite volume for CFD problems. 

July 25, 2012, 03:34 

#7  
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Ren/Xingyue
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Location: Nagoya , Japan
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Quote:
Last edited by hilllike; July 25, 2012 at 03:49. 

July 27, 2012, 08:32 

#8  
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duri
Join Date: May 2010
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Quote:
The following books have some direct formulation of finite difference methods. Computational Fluid Mechanics and Heat Transfer By John C. Tannehill, Dale Arden Anderson, Richard H. Pletcher Computational Fluid Dynamics By T. J. Chung 

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