http://www.cscamm.umd.edu/~tadmor/centralstation
http://www.atmos.ucla.edu/~bstevens/MAMAOS/numerics.html
There are similarities with ENO/WENO algorithms at least for the reconstruction step (some of the later central-upwind papers use "Central Weno"). A nice review of ENO/WENO is:
http://techreports.larc.nasa.gov/icase/1997/icase-1997-65.pdf, "Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws", Chi-Wang SHu, November 1997, ICAS Report No. 97-65, NASA-CR/97-206253.
Culbert B. Laney, Computational Gasdynamics, 1998.
An excellent book recommended to me by Bill Dorland, and which covers a lot
of topics not really covered in Durran's book (such as elliptic solvers or
more details on spectral methods) is:
Chebyshev and Fourier Spectral Methods, John P. Boyd
available for free at:
http://www-personal.engin.umich.edu/~jpboyd/BOOK_Spectral2000.html
Trefethen numerical ODE/PDE Textbook online at Oxford.
Jim Stone
and others involved in the development of Zeus (a widely used MHD code
in Astrophysics), are working on a new higher-order Godunov code for
astrophysical MHD and have written a number of interesting articles.
Two interesting articles pointed out by Eliot Quataert:
An MHD review article by Axel Brandenburg:
http://xxx.lanl.gov/abs/astro-ph/0109497
Another useful article was a review by Ue-Li Pen from CITA:
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2003PASP..115..303T&db_key=AST&high=3c4f95876c07833
One comment: It's kind of interesting that this 3D MHD code is only
500 lines. It is even parallelized (though only with openMP) and uses
a "relaxed TVD" algorithm. The relaxed TVD algorithm avoids the need for a
Reimann solver, but does it necessarily assure positivity from advection?
(I suppose it should if it is called TVD?)
But this code is
written for a pretty simple limit and simple coordinate system. The
complexity of codes seems to grow exponentially with the number of features
in the code. The complexity of the code
quickly increases with unusual geometries (in fusion devices such as tokamaks,
a lot of effort goes into accurate evaluation of gradients along field lines,
sometimes by using field-aligned coordinates, because the thermal conduction
along field lines can be a million times faster than across field lines),
implicit methods to deal with irrelevant fast waves (fusion devices
are often at relatively low beta, or have low beta regions where there is
a very fast compresional Alfven wave that can be ordered out of the system,
or if non-ideal MHD effects such as the Hall terms are kept then there are
even faster waves...), i/o to set up a wide variety of problems, higher-order
differencing algorithms, more advanced parallelization, graphics and
diagnostics, and especially adaptive mesh refinement,..
Useful starting points:
the table of contents for the online book
online lecture notes
Lecture link to ODE
notes
Lecture link to PDE
notes
Gear's Backward Differentiation Formulas for integrating stiff
equations.