Multimode interference (MMI) devices have been developed for a large number of optoelectronic applications. Frequency domain methods have been widely used to simulate the behavior of this class of device at fixed operating wavelengths. However time domain models are becoming more popular in photonic simulation as bandwidths increase and account needs to be taken of material properties such as nonlinearity. By making physically consistent approximations, the time-domain beam propagation method provides simulation without incurring the large memory and computational penalties of other time domain numerical methods. In this paper we will compare these various approaches in the context of simulating MMI devices, provide guidelines for the selection of one approach in preference to the other and discuss the limitations and errors introduced by some of the common approximations made.