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

[SONG Pengyang]

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<https://mitgcm.readthedocs.io/en/latest/algorithm/adv-schemes.html>
Kind regards,
Pengyang

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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<mailto: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<mailto:mitgcm-support at mitgcm.org>
主题: MITgcm-support Digest, Vol 216, Issue 4

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Today's Topics:

   1. Conservation of total energy for Internal Wave    Simulation
      (Adham El Zaher)


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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
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