I am solving compressible inviscid two-fluid flows. To set initial conditions, I nondimensionalized the variables. When I used nondimensionalized initial conditions, I got results in shorter time than I used usual initial conditions. I wonder that the nondimensionalization help reducing computational time as well.

Why do you use the nondimensionalized initial conditions?

I have very little experience in compressible cases and I just think that the nondimensionaliyation in compressible flows, like what we do in preconditioning procedure, mostly relates to convergence problem in low M number. this is just a guess and I am not quite sure whether this is the answer of your question or not.

It also has something to do with the digits that are kept for every variable. It is almost the same difference as using single-precision or double-precision. With the latter convergence comes quicker (in less iterations). For example, if a temperature is 1000. degrees in single precision only 4 digits after the "." are kept.

If you are interested in observing the relation of preconditioning and rate of converged solution in low mach number compressible flow I refer you to paper by Asouti et al under the title of ' low Mach number preconditioning for 2d and 3d upwind flow solution schemes on unstructured grids' Just google it. you'll find freely!