Variable accretion has been well studied in the evolved stages of low-mass star formation. However, the accretion history in the initial phases of star formation is still a seldom studied topic. The outflows and jets emerging from protostellar objects could shed some light on their accretion history. We consider the recently studied case of W43-MM1, a protocluster containing 46 outflows driven by 27 protostellar cores. The outflow kinematics of the individual cores and associated knots in W43-MM1 indicate episodic protostellar ejection. We take the observed parameters of an individual core system (core #8) and perform 3D hydrodynamic simulations of such a system, including episodic changes in the velocity of the outflow. The simulations consist of a collimated jet emerging from a core, taking into account one- and two-velocity modes in the variation of the ejection velocity of the jet. In addition, we investigated the effect of including the precession of the jet in the one- and two-velocity-mode models. From the simulations, we constructed position–velocity diagrams and compared them with the observations. We find that including a second mode in the ejection velocity, as well as the precession, are required to explain the positions of the outflow knots and other position–velocity features observed in core #8 in W43-MM1.