The US weather model uses an uncommon (?) discretization called 'Finite Volume on Cubed Sphere'. To avoid the singularities that occur at the poles when using lat/lon discretization, they instead project the globe onto a cube. More pictures are on the noaa website.

cubed sphere

This discretization allows for mesh adaptation through stretching and nested grids: refined grids

What is the rationale behind choosing this cubed sphere projection over e.g. an icosahedral grid? Is this type of mesh used in other fields?


1 Answer 1


This kind of mesh is used quite frequently in fields where the goal is to simulate a thin spherical shell and if the goal is to use quadrilateral cells (or hexahedral if the third dimension/depth/height is relevant). Atmospheric modelers use it for the atmosphere, but it is also frequently used in simulating convection in the Earth mantle, for example. (You can't see the coarse mesh, but this simulation uses something similar to the cubed sphere mesh extruded into the depth of the Earth: https://www.youtube.com/watch?v=j63MkEc0RRw .)

If your code is based on triangles, then starting with a icosahedron would work just as well. Using quadrilateral meshes like for the cubed sphere has the advantage that one can use 6 nicely structured rectangular meshes for which the transformation from reference cell to real cell is easy to write down -- in essence, one works on 6 rectangles subdivided into orthogonal meshes. Whether you like quadrilateral or triangular meshes better is large a matter of choice and taste.

  • $\begingroup$ Thanks for the answer! Is there any other name for this mesh? $\endgroup$
    – guest
    Commented Jul 1, 2021 at 1:23
  • 1
    $\begingroup$ I think that cubed sphere is the most common name. $\endgroup$
    – nicoguaro
    Commented Jul 1, 2021 at 1:38
  • $\begingroup$ Thanks, nicoguaro. Found an article that introduces the concept. sciencedirect.com/science/article/pii/S0021999196900479 $\endgroup$
    – guest
    Commented Jul 1, 2021 at 1:58
  • $\begingroup$ In case anyone is interested, here is a comparison with hex meshing, which the author claims to be 4x faster than the cubed sphere. cliffmass.blogspot.com/2016/03/… $\endgroup$
    – guest
    Commented Jul 1, 2021 at 2:11
  • $\begingroup$ I am certain that the concept is older than that 1996 article. But it's nice to see shallow water equations added to the list of applications I mention above. $\endgroup$ Commented Jul 1, 2021 at 4:11

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