What velocity value to use for time step size?

violethill · February 7, 2018, 15:08

Hi CFD earthlings,

I understand that when calculating the time step size, you take into account the delta x( of the smallest mesh cell) and the velocity. But what velocity value do I use? The maximum velocity? Free stream velocity?

My geometry resembles a cylinder with pipes. However, the inlet surface area is much bigger than the area in the small pipes. Which maximum velocity do I take into account? The one at the inlet surface or once the velocity has been developed in the narrower pipes? Thank you.

LuckyTran · February 7, 2018, 16:43

You take the velocity of the same cell, the "smallest mesh cell" one. Use your best judgment to guess what that velocity will be. Note that it doesn't have to be the smallest mesh cell, but guessing from the global maximum velocity and global minimum cell size are both good places to start.

praveen · February 7, 2018, 21:59

You compute time step for each cell using the velocity in that cell and size of that cell. This is usually called the local time step. Then take the minimum of all the cell time steps and use that as your global time step. For example in 1-D this would look like
$\Delta t = CFL \cdot \min_i \Delta t_i, \qquad \Delta t_i = \frac{\Delta x_i}{|v_i|}$

FMDenaro · February 8, 2018, 03:35

The correct stability analysis considers the most critical value of the ratio between the grid size and the velocity. OF course for homogeneous grid size one considers only the most critical velocity.
Be careful that in multidimensional case the constraint of the CFL extends to the sum of each term

February 7, 2018, 15:08	What velocity value to use for time step size?	#1
violethill New Member Violet Join Date: Jun 2016 Posts: 8 Rep Power: 9	Hi CFD earthlings, I understand that when calculating the time step size, you take into account the delta x( of the smallest mesh cell) and the velocity. But what velocity value do I use? The maximum velocity? Free stream velocity? My geometry resembles a cylinder with pipes. However, the inlet surface area is much bigger than the area in the small pipes. Which maximum velocity do I take into account? The one at the inlet surface or once the velocity has been developed in the narrower pipes? Thank you.

February 7, 2018, 16:43		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,668 Rep Power: 65	You take the velocity of the same cell, the "smallest mesh cell" one. Use your best judgment to guess what that velocity will be. Note that it doesn't have to be the smallest mesh cell, but guessing from the global maximum velocity and global minimum cell size are both good places to start. lcarasik likes this.

February 7, 2018, 21:59		#3
praveen Super Moderator Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 342 Blog Entries: 6 Rep Power: 18	You compute time step for each cell using the velocity in that cell and size of that cell. This is usually called the local time step. Then take the minimum of all the cell time steps and use that as your global time step. For example in 1-D this would look like $\Delta t = CFL \cdot \min_i \Delta t_i, \qquad \Delta t_i = \frac{\Delta x_i}{\|v_i\|}$ lcarasik likes this. __________________ http://cpraveen.github.io http://twitter.com/cfdlab http://github.com/cpraveen

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February 8, 2018, 03:35		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	The correct stability analysis considers the most critical value of the ratio between the grid size and the velocity. OF course for homogeneous grid size one considers only the most critical velocity. Be careful that in multidimensional case the constraint of the CFL extends to the sum of each term