Digital modelling of circuits with diode (i.e. guitar distortion)
One possible tool is Wave Digital Filter analysis which is a type of physical modeling that represents signals as travelling waves. It can also be extended to non-linear elements such as diodes.

However, for distortion unit, you could instead of trying to digitalize the analog circuit try to extract a waveshaper from its behaviour. Common waveshapers are 3rd order polynomial and atan function.

EDIT : here is an intersting paper about wave digital domain modeling of guitar distortion

EDIT2 : and here a DAFx lecture about existing methods for non linearities in virtual analog