Hi all,

I'm simulating an unsteady problem by using Upwind scheme. Could anybody please suggest me, how to know the suitable time step value (delta t) that made the program give the accurate result. For the value I'm using now is normally generate an overflow in every running time. Jackie

Hi

Try and make sure the time step is much less than the period of the unsteady problem. Try and make a guess at the period of the unsteadiness from experimental data if you have it to hand i.e. Strouhal number.

The more time steps you can have within the period the more accurate the approximation of the CFD solution. If the time step is greater than the natural period of the unsteady problem, you will fail to model the unsteadiness correctly.

James

Thank you for your kind answer James. But i have more questions.

Do the time step selection have to relate to size of grid? I'm now using upwind scheme and in order to get the stable result. We have to fine the stability criterion (CFL value). For example in 1D simulation upwind mehod with c=u*delta(X)/delta(t), in this case c should less than or equal 1. However this case is for 1D struture grid that delta(X) must be unity.

My problem is the mesh generating in domain is 3D unstructure grid. Delta X, Y and Z are not equal. So, how to calculate delta t (time step) for my problem is my question. Do you have any idea or sugesstion please.

Sincerely,

Jackie

Jackie,

You should calculate a local CFL number at any cell based on the cells dimensions and velocity.

For steady problems, you can advance the solution using local time steps. However, as your problem is time-dependent, you should use a single (global) time step to maintain your solution time-accurate. To guarantee stability, you should ensure that this global time step does not violate the CFL stability condition in ANY cell.

IMHO time step selection has little in common with your spatial differencing scheme - it depends upon temporal differencing scheme. For example, you can use implicit temporal differencing which doesn't become unstable with CFL>1.0

Yep, the CFL < 1.0 must be satisfied at all locations in the fluid domain. Thus the global time step must equal to that needed for the smallest cell. You can make a quick guess of the time step using the v (fluid velocity) and d (smallest cell size) to give t. s/v=t then make it an order smaller to be on the safe side, you can always make it bigger later on.

A book that explains this simply is:

Using Computational Fluid Dynmaics, An introductory CFD book by C. T. Shaw. Available in full text directly online.

http://www.eng.warwick.ac.uk/staff/cts/cfdbook/

Hope this helps.

James