When solving a FV formulation of a set of equations, a code I am currently working with has user defined normalization factors for scaling equations.  It normalizes time, number densities, potential, and fluxes, each with a different factor.  I have the impression that these are a legacy attempt at a rough diagonal preconditioner from before the code utilized external solvers and preconditioners.  Besides preconditioning matrices, are there any numerical reasons for normalizing unknowns in a FV problem?Edit: Bort brings up another reason in his answer that I had forgotten.  Formulating the problems in non-dimensional unknowns and non-dimensional parameters can allow simplification if certain physical quantities are small enough to be neglected.  While this is very useful in the formulation of the problem, the code I am working with does not make any decisions based on non-dimensional parameters.  It simply rescales unknowns by arbitrary, user-provided values while working with them.
Effect of Normalization in Unknowns
finite volume