Dear Cheng, Many thanks for confirming this and good to know it is running correctly (up to the time step error). Cheers, Spencer. On 18 Sep 2018, at 19:15, Xiao, Chengnian <CHX33@pitt.edu<mailto:CHX33@pitt.edu>> wrote: Dear all, Many thanks for your helpful responses. I have followed your recommendations and reduced the time step, and the L_2 error has indeed been reduced by a factor of around the square of the time step ratio, indicative of a second order temporal scheme. There appears to be no error with the analytic solution formula. Best regards, Cheng ________________________________ From: Cassinelli, Andrea <andrea.cassinelli15@imperial.ac.uk<mailto:andrea.cassinelli15@imperial.ac.uk>> Sent: Tuesday, September 18, 2018 9:51:37 AM To: Sherwin, Spencer J; Shervin Sammak Cc: nektar-users; Xiao, Chengnian Subject: Re: [Nektar-users] TGV- L2 norm analysis Hi Shervin, Spencer, I have actually not looked into the TGV problem to date. However, I agree with Spencer as to me it would look like there might be a discrepancy with the exact solution, especially if at P higher than 6 no further change is observed. Cheers, Andrea From: "Sherwin, Spencer J" <s.sherwin@imperial.ac.uk<mailto:s.sherwin@imperial.ac.uk>> Date: Tuesday, 18 September 2018 at 11:50 To: Shervin Sammak <shervin.sammak@gmail.com<mailto:shervin.sammak@gmail.com>> Cc: nektar-users <nektar-users@imperial.ac.uk<mailto:nektar-users@imperial.ac.uk>>, "Xiao, Chengnian" <chx33@pitt.edu<mailto:chx33@pitt.edu>>, "Cassinelli, Andrea" <andrea.cassinelli15@imperial.ac.uk<mailto:andrea.cassinelli15@imperial.ac.uk>> Subject: Re: [Nektar-users] TGV- L2 norm analysis HI Shervin, I do not recall if this has been explored previously. I am guessing it is saturating due to an formulation issue possibly as you suggest to do with the exact solution. However is this saturation also related to the time discretisation error or are you hitting that error boundary? Have you tried reducing the time step. @Andrea: you were looking at this recently, have you seen this issue before? Cheers, Spencer On 17 Sep 2018, at 19:52, Shervin Sammak <shervin.sammak@gmail.com<mailto:shervin.sammak@gmail.com>> wrote: Dear all, Here at Pitt, we are trying to solve the 2D Taylor Green Vortex solution from the tutorial and study the effect of resolution on L2 norm. As it is shown in the attached file, it appears that there is no difference at all between p=5 and p=6. It also looks like that the L2-error cannot be reduced below approx. 7e-6. I assume that the L2 norm provided at the end of simulation output is the comparison to the exact solution of the TGV. Are we missing something? Regards, Shervin -- ----------------------------------------------------------- Shervin Sammak Research Assistant Professor Center for Research Computing University of Pittsburgh 4420 Bayard St Pittsburgh, PA 15213 E-mail: shervin.sammak@pitt.edu<mailto:shervin.sammak@pitt.edu> Website: www.crc.pitt.edu<http://www.crc.pitt.edu/> ~ You chase quality and quantity will chase you. <l2-u.jpeg>_______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users Spencer Sherwin FREng, FRAeS Head, Aerodynamics, Director of Research Computing Service, Professor of Computational Fluid Mechanics, Department of Aeronautics, s.sherwin@imperial.ac.uk<mailto:s.sherwin@imperial.ac.uk> South Kensington Campus, Phone: +44 (0)20 7594 5052 Imperial College London, Fax: +44 (0)20 7594 1974 London, SW7 2AZ, UK http://www.imperial.ac.uk/people/s.sherwin/<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imperial.ac.uk%2Fpeople%2Fs.sherwin%2F&data=02%7C01%7Cchx33%40pitt.edu%7C72fa569a40b941f3619308d61d7ea087%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1%7C0%7C636728827063228122&sdata=o8Lf6Y4OIxuzUrq8JqcVeRHr2DjzSAoFw8iMPcwuyVE%3D&reserved=0> Spencer Sherwin FREng, FRAeS Head, Aerodynamics, Director of Research Computing Service, Professor of Computational Fluid Mechanics, Department of Aeronautics, s.sherwin@imperial.ac.uk<mailto:s.sherwin@imperial.ac.uk> South Kensington Campus, Phone: +44 (0)20 7594 5052 Imperial College London, Fax: +44 (0)20 7594 1974 London, SW7 2AZ, UK http://www.imperial.ac.uk/people/s.sherwin/