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Hi Martin,</div>
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<span style="caret-color:rgb(0, 0, 0);background-color:rgb(255, 255, 255);display:inline !important">Thank you for your clarification!</span><br>
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Yes, exactly that's what I meant when I wrote no dissipation or diffusivity.</div>
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I have found a solution that stabilizes the total energy which is to stop the simulation at a time which is equal to an integer times the period of the initial wave implemented. However, I have found the process a bit weird as I am unable to fully explain it
in physics or numerical terms.</div>
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Any help would be appreciated.</div>
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Best regards,</div>
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Zaher</div>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> MITgcm-support <mitgcm-support-bounces@mitgcm.org> on behalf of Martin Losch <Martin.Losch@awi.de><br>
<b>Sent:</b> Wednesday, June 16, 2021 11:06 AM<br>
<b>To:</b> MITgcm Support <mitgcm-support@mitgcm.org><br>
<b>Subject:</b> Re: [MITgcm-support] MITgcm-support Digest, Vol 216, Issue 4 [Conservation of total energy for Internal Wave Simulation (Adham El Zaher)]</font>
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<div class="PlainText">Hi,<br>
<br>
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.<br>
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.<br>
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.<br>
<br>
Martin<br>
<br>
> On 16. Jun 2021, at 06:46, Adham El Zaher <adham_zaher@live.com> wrote:<br>
> <br>
> Hi Pengyang,<br>
> <br>
> Thank you for your answer !<br>
> <br>
> 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.<br>
> <br>
> Best regards,<br>
> Zaher<br>
> From: MITgcm-support <mitgcm-support-bounces@mitgcm.org> on behalf of SONG Pengyang <peterspy@outlook.com><br>
> Sent: Monday, June 14, 2021 8:05 PM<br>
> To: mitgcm-support@mitgcm.org <mitgcm-support@mitgcm.org><br>
> Subject: Re: [MITgcm-support] MITgcm-support Digest, Vol 216, Issue 4 [Conservation of total energy for Internal Wave Simulation (Adham El Zaher)]<br>
> <br>
> Hi Zaher,<br>
> I guess this is caused by the nonlinear advection.<br>
> Have you tried other advection schemes? For example, advection code equals to 2 or 4, which is linear for both \tau and \vec{v}.<br>
> See table 2.2 of 2.17.1. Linear advection schemes ― MITgcm checkpoint67y-20-gb7589390f documentation<br>
> Kind regards,<br>
> Pengyang<br>
> <br>
> ----------------------------------------------------------------<br>
> SONG Pengyang（宋朋洋）<br>
> PhD candidate in Paleoclimate Dynamics<br>
> Department of Climate Sciences<br>
> Alfred Wegener Institute,<br>
> Helmholtz Centre for Polar and Marine Research<br>
> Address: Bussestr. 24, 27570 Bremerhaven, Germany<br>
> Tel: (+49) 471 4831 1811<br>
> Mobile: (+49) 17667211481 (DE)<br>
> (+86) 15762264643 (CN)<br>
> <br>
> 发件人: mitgcm-support-request@mitgcm.org<br>
> 发送时间: 2021年6月14日 18:00<br>
> 收件人: mitgcm-support@mitgcm.org<br>
> 主题: MITgcm-support Digest, Vol 216, Issue 4<br>
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> 1. Conservation of total energy for Internal Wave Simulation<br>
> (Adham El Zaher)<br>
> <br>
> <br>
> ----------------------------------------------------------------------<br>
> <br>
> Message: 1<br>
> Date: Sun, 13 Jun 2021 23:11:29 +0000<br>
> From: Adham El Zaher <adham_zaher@live.com><br>
> To: "mitgcm-support@mitgcm.org" <mitgcm-support@mitgcm.org><br>
> Subject: [MITgcm-support] Conservation of total energy for Internal<br>
> Wave Simulation<br>
> Message-ID:<br>
> <DB6PR10MB1733AE5A54A62E117D695643F9329@DB6PR10MB1733.EURPRD10.PROD.OUTLOOK.COM><br>
> <br>
> Content-Type: text/plain; charset="iso-8859-1"<br>
> <br>
> Hi everyone!<br>
> <br>
> 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.<br>
> <br>
> 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.<br>
> <br>
> 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.<br>
> <br>
> Does anyone have any idea on how to solve this problem or the reason of the presence of these oscillations, please?<br>
> <br>
> Thanks in advance for all your help.<br>
> <br>
> Best regards,<br>
> Zaher<br>
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