Daniel is much better versed in the nuances of FV schemes than I am, but I did 
want to question one assertion you made: 

> On Oct 16, 2017, at 6:16 PM, F Hssn <fhs...@gmail.com> wrote:
> If you wish to use an unstructured Delaunay mesh, it has
> to be isotropic (equilateral triangles) or near-isotropic otherwise
> the control volume calculation will result in overlaps and the
> conservation property will be violated (the solution would more likely
> be incorrect).

CC-FVM is a direct discretization of the divergence theorem. As such, I'm 
pretty sure it is guaranteed to be conservative.

Non-orthogonality will lead to fluxes being wrong, but they will still be 
conservative (whatever they flux out of one cell, they deposit in the neighbor).

> On Oct 17, 2017, at 4:07 PM, F Hssn <fhs...@gmail.com> wrote:
>> What is an anisotropic mesh?
> By anisotropic, I mean the mesh having low-quality triangles (skinny
> triangles, as opposed to equilateral triangles), strategically
> oriented so they reduce the number of vertices required but do not
> negatively affect the resolution of the functions or solutions
> involved (e.g., the interpolation error does not increase compared to
> an isotropic mesh where all triangles are equilateral or
> near-equilateral).
> bamg is a good anisotropic mesh generator and its user manual [1]
> contains examples of anisotropic meshes (e.g., Fig 12 on page 14).
> I should point out that when I say anisotropic quad-tree based
> axis-aligned mesh, I really mean quasi-ansiotropy, since an
> axis-aligned mesh can only orient skinny triangles along x or y axis.
> If your solution has an interface layer that is oriented in neither,
> e.g., if it's at a 45 degree angle, an axis-aligned mesh would not be
> able to make use of anisotropy and would end up using way more
> vertices instead (for constructing small rectangles along the layer).
> (An illustration of an axis-aligned mesh: 
> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fimgur.com%2F15pyjHG&data=02%7C01%7Cjonathan.guyer%40nist.gov%7C0cd9082479634078c46808d5159ac7e0%7C2ab5d82fd8fa4797a93e054655c61dec%7C1%7C0%7C636438676887192908&sdata=SdR7MZg8rnTndTHH5p%2Fqxxni8s4KPo1KQLubiNVAMQg%3D&reserved=0)
> [1] 
> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.ljll.math.upmc.fr%2Fhecht%2Fftp%2Fbamg%2Fbamg.pdf&data=02%7C01%7Cjonathan.guyer%40nist.gov%7C0cd9082479634078c46808d5159ac7e0%7C2ab5d82fd8fa4797a93e054655c61dec%7C1%7C1%7C636438676887192908&sdata=ATMC%2FZGC9k5g%2FIs%2BqED%2F1sFbMIp90LK84urX3Py6RS4%3D&reserved=0
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