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Hi Pengyang,</div>
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<br>
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Thank you for your answer !</div>
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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.</div>
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Best regards,
<div>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 SONG Pengyang <peterspy@outlook.com><br>
<b>Sent:</b> Monday, June 14, 2021 8:05 PM<br>
<b>To:</b> mitgcm-support@mitgcm.org <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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<span lang="EN-US">Hi Zaher,</span></p>
<p class="x_MsoNormal" style="margin: 0cm; text-align: justify; font-size: 10.5pt; font-family: DengXian;">
<span lang="EN-US">I guess this is caused by the nonlinear advection.</span></p>
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<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>
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<span lang="EN-US">See table 2.2 of <a href="https://emea01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmitgcm.readthedocs.io%2Fen%2Flatest%2Falgorithm%2Fadv-schemes.html&data=04%7C01%7C%7C42d00df00bdd42e5d30508d92f56b9ca%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637592871798828243%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=WB62ocjMmFwpVSPIVCp788B28NFP3poOYCthFJhmDzY%3D&reserved=0" originalsrc="https://mitgcm.readthedocs.io/en/latest/algorithm/adv-schemes.html" shash="WveacikiQ5UFYzDHoUfs0tamEWCJgvFOPstgH392RD16aWGvgYh2fv5LwrVbLgc1Op33Qvtijz6layA1RrSLxXQ2gSbE0/ljlMBZDrg5VQHWXx7BXJDdF+l1L/1MDbUk5/7UC35MdXpuUuSAQ7bD7EG8rW7yq4bZdNheidgljXA=">
<span style="color:#954F72">2.17.1. Linear advection schemes — MITgcm checkpoint67y-20-gb7589390f documentation</span></a></span></p>
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<span lang="EN-US">Kind regards,</span></p>
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<span lang="EN-US">Pengyang</span></p>
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<span lang="EN-US"> </span></p>
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<span lang="EN-US" style="font-family:"Times New Roman",serif; color:black">----------------------------------------------------------------</span></p>
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<span lang="EN-US" style="font-family:"Times New Roman",serif; color:black">SONG Pengyang</span><span style="color:black">（宋朋洋）</span><span lang="EN-US" style="font-family:"Times New Roman",serif; color:black"></span></p>
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<span lang="EN-US" style="font-family:"Times New Roman",serif; color:black">PhD candidate in Paleoclimate Dynamics</span></p>
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<span lang="EN-US" style="font-family:"Times New Roman",serif; color:black">Department of Climate Sciences</span></p>
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<span lang="EN-US" style="font-family:"Times New Roman",serif; color:black">Alfred Wegener Institute,</span></p>
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</span><b>发送时间<span lang="EN-US">: </span></b><span lang="EN-US">2021</span>年<span lang="EN-US">6</span>月<span lang="EN-US">14</span>日<span lang="EN-US"> 18:00<br>
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Today's Topics:<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>
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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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