A range of cosmological observations demonstrate an accelerated expansion of the universe, and the most likely explanation of this phenomenon is a cosmological constant. Given the importance of understanding the underlying physics, it is relevant to investigate alternative models. This article uses numerical simulations to test the consistency of one such alternative model. Specifically, this model has no cosmological constant; instead, the dark matter particles have an extra force proportional to the velocity squared, somewhat reminiscent of the magnetic force in electrodynamics. The constant strength of the force is the only free parameter. Because bottom-up structure formation creates cosmological structures whose internal velocity dispersions increase in time, this model may mimic the temporal evolution of the effect from a cosmological constant. It is shown that models with force linearly proportional to internal velocities, or models proportional to velocity to power 3 or more, cannot mimic the accelerated expansion induced by a cosmological constant. However, models proportional to velocity squared are still consistent with the temporal evolution of a universe with a cosmological model.