[MissCFD]

Hello,

I don't understand what is exactly the physical timescale in a steady flow and how it works for the Navier Stoke equations ? Is someone can explain me?

Thank you for your answer

[ghorrocks]

A short quote from the CFX theory manual "For steady state problems, the time-step behaves like an ‘acceleration parameter’, to guide the approximate solutions in a physically based manner to a steady-state solution. This reduces the number of iterations required for convergence to a steady state"

In other words, the time scale allows the user to tune how aggressively the solver marches towards convergence. If too slow the simulation will take longer than it could, if too fast the solver will diverge. It is up to the user to find a time step size which converges reasonably quickly, but remains numerically stable.

[MissCFD]

Thank you for your answer.

So, this mean that the instationnary term in Navier Stoke equation is present. But I don't see very well the difference with instationnary flow. Is that at each iteration, physical time step increases ? Or how that works exactly ?

How can I estimate this physical time step, Is it with experience ? Is it better to start with a auto timescale ?

[ghorrocks]

For steady state simulations you are not looking to get a true time accurate history of the flow, just use psuedo-time as a method to converge to the final steady solution. Because of this some of the time-accurate parts of the time step calculation are ignored as they go to zero as you head towards a converged solution. This is why it is called psuedo-time, as it is similar to real time but is simplified.

The documentation describes how to estimate the required time step. Auto-time step is also often a good starting point, but you can use "edit run in progress" to make it bigger or smaller depending on how the convergence is going.

[Bdew8556]

so does the time step just act as a relaxation factor?

[ghorrocks]

The time step is used as the method to advance the solution. Under relaxation is where you only advance a proportion of the calculated change per iteration to maintain stability. While they are both related to an accurate and stable solution, they are different things. You should read a basic textbook on CFD to have these concepts explained in more detail.

[Bdew8556]

any links you could recommend?

[Bdew8556]

Could I maybe clarify what I think is correct and where my misunderstanding comes from.
I think I was thinking that if the problem is steady state then you automatically delete/cross out the transient terms. THat could be fine if you're looking at solving it analytically but not numerically.

so taking this example:
https://en.wikipedia.org/wiki/Finite_difference_method

the time step is used even though it's a steady state problem. The relaxation is when we weight the new calculated value for the next step.

[ghorrocks]

Do not confuse the equations you are solving with the numerical method you are using to solve them.

The steady state NS equations have no transient term, obviously. This is the equation you wish to solve.

The numerical approach CFX uses to solve the steady NS equations is by using a term which is very similar tot he transient term, so the numerical solution method approaches converging to the steady state NS equation by marching through time. This is only one numerical method, there are others. But the whole idea of the iterative numerical method is that from an initially poor solution of the Steady NS equations the method gives you a new solution which is a better solution. Then you keep iterating until the solution is accurate enough. So in CFX, with the psuedo-transient approach, this iterative new solution is from an approach similar to a transient solution of the NS equations.

[Bdew8556]

Thanks Glenn,

What is the name of the method you've described there? What others are available? thats quite interesting and you've explained it well (in my opinion).

Sorry to hear about what's happening in Sydney. I'm from Australia too although I live in Florida now.

B

[ghorrocks]

Alternatives are things like SIMPLE (https://en.wikipedia.org/wiki/SIMPLE_algorithm), and all its variations like SIMPLER, SIMPLEC, PISO.

Also there are fundamentally different approaches, like streamfunctions based methods, Godunov etc.

And as a segway, do not forget that there are CFD approaches which model fluids but are not based on the Navier Stokes equations at all. Lattice Boltzmann and spherical particle hydrodynamics are examples of this.