ADER-WENO finite volume
Garch et al. (EuroVis 2012) cites Dumbser et al. (JCP 2007) for its finite volume WENO advection. Having looked into it (briefly) I think it builds a 1D WENO stencil as a pre-process to determine the volume in cell, then flux through the face.
Github has this: https://github.com/tbenthompson/rupturotops
for ADER-WENO.
For advection-diffusion in general, I think this is a nice explanation. ftp://www.geosci.usyd.edu.au/pub/dietmar/GEOS3104/Pracs/Prac5/AdvectionDiffusionWithMatlab.pdf
Edit:
Finally figured out what “ADER” means: Arbitrary DERivative in space and time from
http://physics.nd.edu/assets/139422/2014_web_reu_research_papers.pdf
Edit 2:
The author in the previous PDF had a related paper at arvxiv.
http://arxiv.org/pdf/1401.6448v1.pdf
Edit 3:
From the github:
Using pyweno for reconstruction of uniform grids.
https://github.com/memmett/PyWENO