Normalization or non-dimensionalization. Why?
 

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

Re: Normalization or non-dimensionalization. Why?
 

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.

Re: Normalization or non-dimensionalization. Why?
 

Can I ask you a reference on this?

Re: Normalization or non-dimensionalization. Why?
 

Just about any basic textbook that deals with density-based schemes will have this. See Hoffman & Chiang, "Computational Fluid Dynamics for Engineers", for one.

Re: Normalization or non-dimensionalization. Why?
 

I really appreciate your kind help. Thanks.

Re: Normalization or non-dimensionalization. Why?
 

Can i find the code for book "Computational Fluid Dynamics for Engineers" free?