[MITgcm-support] advection scheme 33

Wed Sep 4 11:53:56 EDT 2019

Hi guys,

I would like to share some figures regarding the advection schemes from my previous practice.

I've injected a passive tracer (with a minimum value of 1 and a maximum value of 3) into a barotropic
nondivergent flow (5.5km resolution) and observed its evolution subjected to the advection process
only (I turned off the explicit lateral diffusion).  I selected nine advection schemes:
  code 2: centered 2nd order
  code 3: 3rd order upwind
  code 4: centered 4th order
  code 20: 2nd order DST (Lax-Wendroff)
  code 77: non-linear flux limiter
  code 30: 3rd order DST
  code 33: 3rd order DST with flux limiter
  code 7: 7th order one step method with monotonicity preserving
  code 80: 2nd order Prather scheme

The tracer is expected to conserve its extrema (min value of 1 and max value of 3) during integration.
Due to spurious numerical diffusion induced by every discretized advection scheme, this is not the case.
The temporal evolutions of tracer extrema look like:

We can also estimate the spurious domain-averaged numerical diffusivity as:

Results are:

Conclusions:
1. 2nd and 4th order centered schemes and 2nd DST generate very large spurious extrema
    while keep a very tiny numerical diffusivity;
2. advection scheme 33 (3rd-order DST with limiter) do not generate spurious extrema but
    has a relatively large numerical diffusivity (up to 25 m^2/s).  Limiter prevents false extrema
    but induces larger spurious diffusivity.
3. 2nd Prather scheme generates very small false extrema while keep a very-low numerical
    diffusivity (~5 m^/2), a very good choice suggested by Hill et al. (2012, OM).

Hope the figures can be seen correctly and hope this helps.

------------------
 Best regards 

Yu-Kun Qian (钱钰坤) 
Center for Monsoon and Environment Research 
 Department of Atmospheric Sciences
School of Environmental Science and Engineering 
 Sun Yat-sen University 
No. 135 Xingang West Road, Haizhu District 
Guangzhou, 510275, P.R. China 
Tel; 020-84115227 
Email: qianyk at mail3.sysu.edu.cn      

------------------ Original ------------------
From:  "Edward W Doddridge"<ewd at mit.edu>;
Date:  Wed, Sep 4, 2019 10:22 PM
To:  "mitgcm-support at mitgcm.org"<mitgcm-support at mitgcm.org>; 

Subject:  Re: [MITgcm-support] advection scheme 33

 Hello Yangxin, 

 Regarding your first point, there is a section in the manual devoted to advection schemes: https://mitgcm.readthedocs.io/en/latest/algorithm/adv-schemes.html

 If you found that section insufficient, it would be good to know why. That way we can work towards improving it.

 Cheers,
 Ed

 Edward  Doddridge
 Postdoctoral researcher
  Earth,  Atmospheric and Planetary Sciences
  Massachusetts  Institute of Technology

  www.doddridge.me

  On 3 Sep 2019, at 14:22, Yangxin He <y67he at uwaterloo.ca> wrote:

   Hi there,

 I am running a simple 2d oceanic model with tides sloshing up and down a slope, so internal tides are generated. Part of my data file looks like

   implicitDiffusion=.TRUE.,
   implicitViscosity=.TRUE.,
  #change advection shceme
   tempAdvScheme=33,

   staggerTimeStep=.TRUE.,

 The simulation is fine. Two quick questions, 
 1) I am certainly not an expert in coding, but I think it will be a good idea that I can at least have some idea of what I am using. Where can I find out more information about this advection scheme  33? There does not seem much in the manual. 
 2) In one of my previous threads here
 http://mailman.mitgcm.org/pipermail/mitgcm-support/2019-July/012095.html

 Jody mentioned adv33 will allow the lateral diffusion set to 0, i.e. diffKhT=0. I tried it, it did work. But why?

 Thanks

 Yangxin

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