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January 24, 2014, 23:25 |
Spatial accuracy vs. Temporal accuracy
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#1 |
Member
yehanyu
Join Date: Mar 2012
Location: Beijing, China
Posts: 48
Rep Power: 14 |
In many CFD codes, spatial discretization scheme is often less accurate than temporal discretization scheme. For example, one might adopt a second-order spatial scheme and use the fourth-order Runge-Kutta method to perform temporal integration. I just don’t understand the reason behind this scenario. Since the spatial scheme is second-order accurate, it seems that a fourth-order accurate temporal scheme doesn’t help to improve the overall accuracy of the solution. Is my point of view correct? Thank you very much.
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January 25, 2014, 05:35 |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73 |
Quote:
In principle, you are correct. However, high order time integration is expecially suited for simulation of turbulence, with LES/DNS. This is due to the fact that one wants to exclude effects of filtering/truncation errors over the temporal scales and focus only on spatial scale. Furthermore, it is quite obvious that for stability reason O(dt) = (1/U) O(h) |
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February 20, 2014, 04:42 |
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#3 |
Member
yehanyu
Join Date: Mar 2012
Location: Beijing, China
Posts: 48
Rep Power: 14 |
Thank you very much.
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February 20, 2014, 07:06 |
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#4 | |
Senior Member
duri
Join Date: May 2010
Posts: 245
Rep Power: 17 |
Quote:
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February 20, 2014, 08:42 |
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#5 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,897
Rep Power: 73 |
Quote:
well, I am not sure what you want to say with "The purpose of RK is to damp high frequency errors" ... When the dt is fixed, you implicitly cut-off all the frequencies over pi/dt. The frequencies below have to be resolved at best without damping... |
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Tags |
accuracy, spatial, temporal |
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