Molecular dynamics is a simulation technique used to predict the physical properties of systems based on their chemical structure and evolution of their atomic constituents. For these predictions to be reliable, it is critical that the simulation has reached convergence, whereby representative sampling of the phase space has been gathered. We show that the commonly used root mean square deviation is an unsuitable convergence descriptor for systems featuring surfaces and interfaces. We then present an effective criterion, embodied in the analysis tool DynDen, based on convergence of the linear partial density of all components in the simulation. With a varierty of examples we demonstrate the usage of DynDen for the accessment of convergence, as well as for identification of slow dynamical processes, which can be easily missed with conventional analysis.