Does anybody know of books that discuss the implementaion of precondtioning? particularly for runge - kutta schemes. online references would be good too. thanks.

Clifford,

Since you are already at Penn State, I suggest you go to the engineering library (if you haven't already) and look up the PhD theses by the following people...

Jonathan Weiss (He implemented preconditioning for R-K, went to Fluent and extended his work there, then went to Computational Dynamic North America)

Philip E. O. Buelow (preconditioning for high grid aspect ratios, stability analyses for implicit and explicit (R-K) schemes, Boundary condition implementation with preconditioning)

Yun-Ho Choi (earlier implementation of preconditioning for inviscid and viscous flows)

These are all students of Professor Charles Merkle who used to be at Penn State, but is now at University of Tennessee Space Institute. He has been doing work with preconditioning for over 12 years now. Other names to search for would be papers by Dr. Sankaran Venkateswaran (also one of Merkle's former students), Professor Bram van Leer (at Univ. of Michigan) and his students (W-Z Lee, John Lynn, Dohyung Lee) as they mainly use Runge-Kutta schemes.

Hope this helps.

Philip E. O. Buelow