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 > _______________________________________________ > fipy mailing list > fipy@nist.gov > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] _______________________________________________ fipy mailing list fipy@nist.gov http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
