Non dimensional code
 

Hello everybody.

I am writting a code for the solution of the Euler equations. Does anybody know how can I non-dimensionalise the Euler equations? (or a book describing the method)

I think there are two ways. The first is to non-domensionalise the equations and the other is to non-dimensionalise the initial conditions.

Thanks for the help

Re: Non dimensional code
 

Hello Giorgos,

you have to non-dimesionalize both, the Euler equations as well as the initial conditions. In the simplest case, you need a reference length, a reference velocity and a reference density.

Regards, Markus

Re: Non dimensional code
 

Markus, thanks for the reply.

Do you have in mind any paper or book that explains the methodology. It is very important for me to understand in details the whole proccess

Re: Non dimensional code
 

Computational Fluid mechanics and heat transfer - Anderson et. al

Re: Non dimensional code
 

Hi,

The Euler code can be used as such in a non dimensionalization form. You can see many reference solutions with u=1, Rho = 1, P=1 etc. The key factor would be the ratio of specific heat.

The key factor, as mentioned by one member, is the boundary condition. See to that you adhere to the non-dimensionalized BCs and the reference scales. The rest will fall in place.

For example, ambient pressure can be 1, inlet velocity 1 etc.

Example: Reference solutions for forward facing step at Mach 3.

Regards, Shyam

Re: Non dimensional code
 

Bird, Stewart, Lightfoot - "Transport Phenomena". towards the end of each section (Momentum/Energy/Mass Transfer), there is a kind of chapter on 'dimensional analysis of the equation of change'.