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:
Trefethen numerical ODE/PDE Textbook online at Oxford.
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:
Another useful article was a review by Ue-Li Pen from CITA:
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.