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Normalization or non-dimensionalization. Why?

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Old   October 17, 2007, 09:23
Default Normalization or non-dimensionalization. Why?
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jinwon park
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Could I ask you about the term, 'normalization or non-dimensionalization' in solving compressible flow? I am currently solving compressible two-dimensional flow based on Euler equations. I am understanding how to normalize density and pressure but I don't know how to do time and length. Could you let me know how to normalize the time and length in Euler computations.

For example, density in left=1630kg/m^3 <--> density in right=1000kg/m^3. when normalizing 1.63 and 1.0

Pressure in left=1e9Pa <--> Pressure in right=1e5Pa When normalizing 1.0 and 0.0001

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Old   October 17, 2007, 12:04
Default Re: Normalization or non-dimensionalization. Why?
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ag
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One standard method of nondimensionalization for the compressible Euler/NS equations is to define a reference density rho_ref, reference velocity, typically taken as the speed of sound at some reference temperature T_ref and reference density rho_ref, and a reference length L_ref which can be the grid dimension or it could be related to some physical dimension of the problem. Then pressure is non-dimensionalized as p_non = p/(rho_ref*a_ref**2), density is non-dimensionalized as rho_non = rho/rho_ref, time is non-dimensionalized as t_non = t*a_ref/L_ref, etc.
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Old   October 17, 2007, 12:06
Default Re: Normalization or non-dimensionalization. Why?
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jinwon park
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Can I ask you a reference on this?
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Old   October 17, 2007, 13:29
Default Re: Normalization or non-dimensionalization. Why?
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ag
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Just about any basic textbook that deals with density-based schemes will have this. See Hoffman & Chiang, "Computational Fluid Dynamics for Engineers", for one.
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Old   October 17, 2007, 13:31
Default Re: Normalization or non-dimensionalization. Why?
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jinwon park
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I really appreciate your kind help. Thanks.
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Old   October 18, 2007, 23:40
Default Re: Normalization or non-dimensionalization. Why?
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billpeace
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Can i find the code for book "Computational Fluid Dynamics for Engineers" free?

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