The field of computational fluid dynamics (CFD) is dedicated to solving the Navier-Stokes equations (or some simplification of them). A subset of CFD, ocean and atmospheric models numerically solve the same equations for realistic applications. What are the differences and trade-offs between the general CFD approaches and the applied realistic cases?

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    $\begingroup$ Ocean and atmospheric models that solve Navier-Stokes are a subset of all CFD methods. As it's written, this question seems a bit like asking "What are the differences and trade-offs between mountain bikes and bikes?" Do you mean to ask what assumptions or specializations are needed in ocean and atmospheric models? This seems to be what @Jed is answering below. $\endgroup$ Oct 1, 2014 at 17:40
  • $\begingroup$ Thanks. I tried to edit the question accordingly. In my experience, most people that do ocean and atmospheric modeling would not describe themselves as doing CFD. $\endgroup$
    – arkaia
    Oct 1, 2014 at 17:54
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    $\begingroup$ I guess I'm still not quite sure about the question. What would you consider a "general" CFD approach. Once you start discretizing the NS equations for CFD you're making choices that decrease generality so all CFD methods are in some way specialized for their intended applications. It makes much more sense to me to discuss the choices that are made (and why) in geophysical fluid dynamics (GFD) models. E.g. rotating reference frames, stratified flows, turbulence models. Those choices are different than e.g. CFD for shocks in transonic flows. $\endgroup$ Oct 1, 2014 at 18:13
  • $\begingroup$ I think the question you mention about the choices in GFD models is also relevant and it might be worth posting it. As I see it, what I am asking is well answered by @Jed_Brown $\endgroup$
    – arkaia
    Oct 1, 2014 at 18:31
  • $\begingroup$ For some background you can take a look at WRF's documentation. E.g., see www2.mmm.ucar.edu/wrf/users/docs/arw_v3.pdf $\endgroup$
    – stali
    Oct 1, 2014 at 22:31

3 Answers 3


Atmosphere and ocean have highly-stratified flows in which the Coriolis force is a major source of dynamics. Maintaining geostrophic balance is extremely important and many numerical schemes are intended to be exactly compatible (at least in the absence of topography) to avoid radiating energy in gravity waves. Due to the stratification, limiting vertical numerical diffusion is extremely important and special grids are often used (especially in the ocean) for that purpose. Many methods are effectively 2.5-dimensional formulations.

For climate simulation over long time periods, conservation of energy and other fluxes (like salt) are often considered to be critical for statistically meaningful results. Methods that are less accurate and have certain numerical artifacts may be chosen in order to avoid damping out the dynamics. Note that long-term dynamics may not homogenize at continental scales averaged over multiple decades.

Industrial CFD solvers tend to be used for flows that are more isotropic (genuinely 3D) and often neglect Coriolis. They often have stronger forcing and thus less critical energy conservation requirements. It is common to deal with strong shocks, in which case nonlinear spatial discretizations must be used, despite being more dissipative.

Because lab experiments can actually be performed for most industrial applications, the software experiences more validation. Weather models also have constant validation, but climate models are almost impossible to validate due to the time scales involved and unavoidable over-fitting.

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    $\begingroup$ Though it should be noted that climate models do receive validation through two approaches: (i) comparison with past climate, for example over the past 150 years where we do have fairly accurate data, (ii) by comparing among different climate models that are independently developed. That's not the same standard as applied to CFD codes, but it's far better than any ordinary code written by scientists for scientists :-) $\endgroup$ Oct 1, 2014 at 10:52
  • $\begingroup$ @WolfgangBangerth It is still over-fitting. The models depend on a plethora of tunable parameters. Changing resolution, time steps, or other components of a model require "recalibration". Recalibration is an extremely labor-intensive and subjective process (many person-years). It is just not possible to have today's world-class scientists ignore the last 50 years of observations while spending years calibrating a model in order to avoid over-fitting in a (risky) attempt to reproduce recent climate history. $\endgroup$
    – Jed Brown
    Oct 4, 2014 at 23:51
  • $\begingroup$ I don't disagree. Climate codes are delicate creatures. I just wanted to point out that your answer seems to imply that climate codes receive basically no validation. This isn't true. (It's also something we are obligated to stress to the general public -- see youtube.com/watch?v=ud7fHTswj5k). $\endgroup$ Oct 6, 2014 at 15:34
  • $\begingroup$ In comparison to engineering or weather forecasting, which have many independent realizations, climate has essentially one realization that we know suffers from over-fitting. When I put on my Applied Mathematics hat, I recall that verification is supposed to precede validation and that validation is an ongoing process rather than a task that can be completed. But climate models are not convergent in space or time, so it's hard to talk about verification, and we only have one realization. $\endgroup$
    – Jed Brown
    Oct 6, 2014 at 18:12
  • $\begingroup$ While we as a community agree about certain causal relationships and general trends, we cannot agree about whether the sign of 30-year average surface temperature across North America is something that can be predicted. Indeed, results of the recent CESM Large Ensemble Project suggest that it may not be. Consequently, we don't know whether quantitative regional policy questions are well-posed, let alone whether today's models can be trusted to give meaningful answers. This is not to denigrate the field or reduce confidence in the broader interpretation. The problem is hard. $\endgroup$
    – Jed Brown
    Oct 6, 2014 at 18:20

Jed Brown described the traditional approach used in the mesoscale and larger scale models. Actually, in microscale many atmospheric models are very close to to traditional CFD codes, use similar finite volume discretizations, similar 3D grids where vertical is treated similarly as horizontal, and so on. Depending on the resolutions even features like buildings are resolved with the same approaches known from engineering CFD, like the immersed boundary methods or body fitted grids.

You can encounter all the discretization techniques you know from the engineering CFD, like finite differences, finite volumes, pseudo-spectral and even finite elements. The same pressure correction (fractional-step) methods are often used to solve the incompressible Navier-Stokes equations (with the Boussinesq or anelastic terms for buoyancy).

Of course, different parametrization for the heat and momentum fluxes near the surface are commonly used, taking into account the specifics of the land-surface interactions like the Monin-Obukhov similarity or other semi-empirical relations.

The whole method of large-eddy simulation (LES), now very popular in engineering, actually originates in boundary layer meteorology. I would even say that many atmospheric modelers at this scale wouldn't hesitate at all to call their work CFD.

In many (but not all) applications you also have to add the Coriolis force. The schemes do not have to be well-balanced however, it is just one additional volume force. If you also compute the processes like cloud formation, precipitation and radiation, things get more complicated, but the same holds for engineering models which solve reaction kinetics, combustion and similar.

This class of models also includes those accounting for the ocean-atmosphere interactions you asked for, see for example https://ams.confex.com/ams/pdfpapers/172658.pdf


Difference between weather prediction software and "casual CFD solver" is how weather prediction works with transition of water. Water is being treated as second component, so model becomes 3 dimensional with 2 components.

Second (not the least important) is that weather (and other convection) models work directly with $\omega$ from $d \omega/dt = (\omega \nabla) u + \nu \nabla^2 \omega$.

  • $\begingroup$ Various models work with various things. If you mean vorticity by omega than some weather models do use it, some don't. $\endgroup$ Jun 27, 2017 at 12:03

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