implementing preconditioning

clifford bradford

Hello, I'm interested in implementing preconditioning to a time iterative code that I'm have. the code is 4 step R-K scheme with the choice of 1st order Riemann, Kinetic, or limited or unlimited 2nd order upwind schemes (MUSCL). I've been reading papers on preconditioning and I've noticed that for the most part the authors write the preconditioned Euler equations in primitive variable (non conservative) form. I had been of the impression that to implement preconditioning for steady state solutions one simply multiplied the residual by the preconditioning matrix at each time step, but after reading these papers I'm not sure how to proceed. Does anyone out there have succesful experience in writing preconditioned codes and can give me advice. particularly is the preconditioning applied at each R-K step, is it applied to artificial dissipation terms, how do you deal with it at the boundaries, what are the special treatment for the N-S equations (including turbulence), and what are the most efficient ways of coding (I'm working with f77 for the moment but f90 or C tips would be relevant too). Also If anyone has good online references to preconditioning links I'd appreciate it.