[MITgcm-support] MITgcm-support Digest, Vol 216, Issue 4 [Conservation of total energy for Internal Wave Simulation (Adham El Zaher)]

Wed Jun 16 04:06:30 EDT 2021

Hi,

I didn’t quite understand your diagnostic, but in a numerical model with a time stepping scheme, there is always either numerical dissipation, dispersion or both. In any problem, I would not expect that the total energy is conserved, but that it slowly dissipates. When you write “no dissipation or diffusivity”, I assume that you mean you set all viscosity and diffusivity coefficients =0. In this case, the advection scheme may still add some dissipation, and all “stable” schemes, like 3, 33, 7 do so at a different level, and the semi-implicit time stepping (free surface/pressure solver) also adds some damping. Advection scheme 2, and 4 add dispersion that will lead to noise in the solution, if there’s no addition damping of some sort.
As far as I know, we have a Lax-Wendroff scheme implemented for the free surface (see the internal_wave example and the documentation), and some tracer advection schemes are better than others (see GAD.h for all available schemes), I would probably try 20, because it’s also a Lax-Wendroff scheme.
You can also try to turn off advection altogether (momAdvection=.FALSE., tempAdvection =.FALSE., etc.) to see if you get a constant energy level without advection, before turning them back on.

Martin

> On 16. Jun 2021, at 06:46, Adham El Zaher <adham_zaher at live.com> wrote:
> 
> Hi Pengyang,
> 
> Thank you for your answer !
> 
> I have tried using linear advection schemes but unfortunately this didn't help. When using these schemes, the oscillations remain, and the total energy starts decreasing slowly with time.
> 
> Best regards,
> Zaher
> From: MITgcm-support <mitgcm-support-bounces at mitgcm.org> on behalf of SONG Pengyang <peterspy at outlook.com>
> Sent: Monday, June 14, 2021 8:05 PM
> To: mitgcm-support at mitgcm.org <mitgcm-support at mitgcm.org>
> Subject: Re: [MITgcm-support] MITgcm-support Digest, Vol 216, Issue 4 [Conservation of total energy for Internal Wave Simulation (Adham El Zaher)]
>  
> Hi Zaher,
> I guess this is caused by the nonlinear advection.
> Have you tried other advection schemes? For example, advection code equals to 2 or 4, which is linear for both \tau and \vec{v}.
> See table 2.2 of 2.17.1. Linear advection schemes ― MITgcm checkpoint67y-20-gb7589390f documentation
> Kind regards,
> Pengyang
>  
> ----------------------------------------------------------------
> SONG Pengyang（宋朋洋）
> PhD candidate in Paleoclimate Dynamics
> Department of Climate Sciences
> Alfred Wegener Institute,
> Helmholtz Centre for Polar and Marine Research
> Address: Bussestr. 24, 27570 Bremerhaven, Germany
> Tel: (+49) 471 4831 1811
> Mobile: (+49) 17667211481 (DE)
>              (+86) 15762264643 (CN)
>  
> 发件人: mitgcm-support-request at mitgcm.org
> 发送时间: 2021年6月14日 18:00
> 收件人: mitgcm-support at mitgcm.org
> 主题: MITgcm-support Digest, Vol 216, Issue 4
>  
> Send MITgcm-support mailing list submissions to
>         mitgcm-support at mitgcm.org
> 
> To subscribe or unsubscribe via the World Wide Web, visit
>         http://mailman.mitgcm.org/mailman/listinfo/mitgcm-support
> or, via email, send a message with subject or body 'help' to
>         mitgcm-support-request at mitgcm.org
> 
> You can reach the person managing the list at
>         mitgcm-support-owner at mitgcm.org
> 
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of MITgcm-support digest..."
> 
> 
> Today's Topics:
> 
>    1. Conservation of total energy for Internal Wave    Simulation
>       (Adham El Zaher)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Sun, 13 Jun 2021 23:11:29 +0000
> From: Adham El Zaher <adham_zaher at live.com>
> To: "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
> Subject: [MITgcm-support] Conservation of total energy for Internal
>         Wave    Simulation
> Message-ID:
>         <DB6PR10MB1733AE5A54A62E117D695643F9329 at DB6PR10MB1733.EURPRD10.PROD.OUTLOOK.COM>
>         
> Content-Type: text/plain; charset="iso-8859-1"
> 
> Hi everyone!
> 
> I am working on an internal wave simulation in a rectangular domain with no dissipation or diffusivity and with a periodic boundary condition on both ends in the x-direction, a free-slip wall at the bottom.
> 
> Theoretically, the total energy of the system is conserved and does not change with the time, but instead of that, numerically, I always get undamped oscillations (at the same frequency as this of the single wave specified in the gendata file), so there is time dependency in the numerical simulations.
> 
> I have tried several time-stepping (implicit time-stepping scheme, Crank-Nicolson scheme) and advection schemes ( 3rd order upwind scheme, 7th order one-step method) to get rid of these oscillations but unfortunately none of them worked.
> 
>  Does anyone have any idea on how to solve this problem or the reason of the presence of these oscillations, please?
> 
> Thanks in advance for all your help.
> 
> Best regards,
> Zaher
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL: <http://mailman.mitgcm.org/pipermail/mitgcm-support/attachments/20210613/f6639077/attachment-0001.html>
> 
> ------------------------------
> 
> Subject: Digest Footer
> 
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mailman.mitgcm.org/mailman/listinfo/mitgcm-support
> 
> 
> ------------------------------
> 
> End of MITgcm-support Digest, Vol 216, Issue 4
> **********************************************
>  
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mailman.mitgcm.org/mailman/listinfo/mitgcm-support

-------------- next part --------------
A non-text attachment was scrubbed...
Name: smime.p7s
Type: application/pkcs7-signature
Size: 1665 bytes
Desc: not available
URL: <http://mailman.mitgcm.org/pipermail/mitgcm-support/attachments/20210616/92a5c604/attachment.p7s>