Hi

To do direct numerical simulation of isotropic turbulence, I think I have to run a code for 3D N-S equations.

I have written the 3D NS code. I am wondering about the initial condition and boundary condition.

Many papers say that i must setup a random field as initial condition.

Can someone explain me mathematically how to setup a random field as an initial condition for this simulation? Do i have to use random number generator? I am not sure whether DNS needs random number generator. I see the fluctuating component of velocity in several books wavering from negative to positive values and repeating its trend. Do i have to give this condition as my input with psuedo random number generator. If so, then what function should i use to obtain this fluctating velocity trend?

Please help me

thanks

You could use periodic boundary conditions everywhere.

If the Reynolds number is large enough I would guess that any initial conditions with enough "randomness" would lead to turbulence. If you put too much "randomness" then your numerical scheme might not be able to resolve it. I mean you have to be carefull that the randomness is smoothed out a little so that you don't have all kind of discontinuities in your velocities, pressure, density, as some codes do not handle that very well. For example the code can suddenly give infinity and awfull oscillations. You will need artificial viscosity adequate for the problem, where it helps get rid of the high frequency oscillations (in the k-space; that means the oscillations occuring on 2-3-4.. points).

You have to progress slowly, one does not write a code overnight, it is a whole project and you need to do a lot of reading before you write a code, to make sure you write the correct code. And you need to do a lot of testing of your code by first solving very simple problems for which you do have a known analytical simple solution, then you can pass to something more complex.

good luck.

Thanks for the message. Can you please let me know how should I put the randomness?

As of now, I have my plan to do pretty low reynolds number cases. This is what has been suggested by many people for DNS exercise due to limitations of computer.

Why do you want to simulate isotropic turbulence? So many people have already done that. Are you really adding something new?

What kind of simulations are you going to carry out? With forcing or just decaying turbulence?

For isotropic turbulence the best method is to create the initial field in spectral space. Then it is rather easy to prescribe the spectrum and to make sure that the divergence of the velocity field is zero.

sir

This is my starting step in the research. I learnt that reactive flow with turbulence and shock has not been done in detail.

Of course, I knew so many people have done this simulation of isotropic turbulence already quite long back.

In my simulation, I need this step as my initial condition and then I can take up other things that I am planning to add at a later stage.

My plan is to simulate isotropic turbulence and will let it decay after some time(decaying turbulence.)

Can you explain how to create the initial field in spectral space?