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

Thu Jun 17 16:44:45 EDT 2021

Hi Martin,

Thank you for your clarification!

Yes, exactly that's what I meant when I wrote no dissipation or diffusivity.

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.

Any help would be appreciated.

Best regards,
Zaher

________________________________
From: MITgcm-support <mitgcm-support-bounces at mitgcm.org> on behalf of Martin Losch <Martin.Losch at awi.de>
Sent: Wednesday, June 16, 2021 11:06 AM
To: MITgcm Support <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,

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 ¨D MITgcm checkpoint67y-20-gb7589390f documentation
> Kind regards,
> Pengyang
>
> ----------------------------------------------------------------
> SONG Pengyang£¨ËÎÅóÑó£©
> 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
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>    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>
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> 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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