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Numerical diffusion/dispersion/dissipation

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Old   February 28, 2005, 05:41
Default Numerical diffusion/dispersion/dissipation
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Hadian
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Hi I want to know more about the concept of Numerical diffusion, dissipation and dispersion. can you introduce any reference or link for this. i would like to know about the effect of them in a CFD code individually. Thanks in advance. Hadian
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Old   March 29, 2005, 17:33
Default Re: Numerical diffusion/dispersion/dissipation
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debs
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The numerical dissipation dispersion and diffusion arise depending on the kind of truncation you use . Let us consider an example of a finite difference sequence. When you trauncate the terms greater than dx^2 you have second order accuracy and u have higher order terms like dx^3,dx^4,dx^5.. the odd powered terms givs rise to dispersion of your numerical solution and the even powered terms give rise to dissipation of your numerical solution. When dissipation and dispersion are combined together you get diffusion.

eg. say exact solution is y=a sin(t)

dissipation results in

y=0.8a sin(t)

dispersion results in

y= asin(t+ - q)

diffusion

y= 0.8 a sin(t + - q)

Have a look at any numerical methods book for partial differential equations.
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