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<p class="MsoNormal"><span lang="EN-US">Hi Zaher,</span></p>
<p class="MsoNormal"><span lang="EN-US">I guess this is caused by the nonlinear advection.</span></p>
<p class="MsoNormal"><span lang="EN-US">Have you tried other advection schemes? For example, advection code equals to 2 or 4, which is linear for both \tau and \vec{v}.</span></p>
<p class="MsoNormal"><span lang="EN-US">See table 2.2 of <a href="https://mitgcm.readthedocs.io/en/latest/algorithm/adv-schemes.html">
<span style="color:#954F72">2.17.1. Linear advection schemes — MITgcm checkpoint67y-20-gb7589390f documentation</span></a></span></p>
<p class="MsoNormal"><span lang="EN-US">Kind regards,</span></p>
<p class="MsoNormal"><span lang="EN-US">Pengyang</span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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Today's Topics:<br>
<br>
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>
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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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