def sim(params,timerange):
k1,k2,N = params
Is what you want I think ..,.. if you added an extra param you would just add it after N ... but it would not be an optional argument
or maybe better
def sim(*params,**kwargs):
timerange = kwargs.get('timerange',default_timerange)
K1,K2,N = params #assuming you know you have exactly 3
#then call it like so
sim(k1,k2,N,timerange=(-100,100))