[Nek5000-users] Accuracy & errors

[nek5000-users at lists.mcs.anl.gov]

Typically you will see spatial convergence down to a point where temporal errors dominate, then things will level off.


See for example Fig. 4 in


www.mcs.anl.gov/~fischer/users.pdf<http://www.mcs.anl.gov/~fischer/users.pdf>


for Figs. 4 and 5 in "Recent Developments in Spectral Element Simulations of Moving Domain Problems", Fischer, Schmitt, Tomboulides.


The benefits of high order in space, despite relatively low order in time, derive from the fact that the costs are multiplicative (number of spatial dofs X number of timesteps),  and from the fact that spatial errors typically dominate most high Reynolds number flow problems because of numerical dispersion and dissipation.   Having a high-order method allows you to realize minimal numerical dispersion at a relatively low number of points per wavelength.


Paul


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From: Nek5000-users <nek5000-users-bounces at lists.mcs.anl.gov> on behalf of nek5000-users--- via Nek5000-users <nek5000-users at lists.mcs.anl.gov>
Sent: Wednesday, November 14, 2018 8:13:06 PM
To: NEK5000
Subject: [Nek5000-users] Accuracy & errors


Dear Nek users,



I would like to do a quick test to see the difference in accuracy using two different P-orders, i.e. N = 7, and N = 11. The question I have is about the role of time integration errors.  If the code uses  2nd or 3rd order of integration in time. That means that at some point the time-integration error will be larger than the spatial error.  I wonder what are conditions under which it happens?  Because once you are in that regime you will not see any difference between the various methods.



Thanks for the help.


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