Particle-tracking models are often used for near field short-term subgrid transport of substances. The consistency demand at the discrete level does not show up so dominantly for these applications. This demand refers to the use of a numerical advection scheme for particles that is fully compatible with the local mass conserving advection properties of the underlying flow field at the discrete level of that field. A noncompatible scheme will produce both local convergence and local divergence of particles in different parts of the model area and thus erroneous advection results and erroneous concentration patterns. This compatibility in particle tracking is especially important if smooth distributions over larger areas are modelled for longer times. These applications did not occur that often in the past because they require many particles and thus much computation time. These applications occur more frequently nowadays especially for environmental assessment such as for the modelling of transport of fish larvae growing during their journey in the model to juvenile stages. The advection scheme that is developed in this paper is shown to be exactly compatible with hydrodynamic flow fields computed by mass conserving curvilinear grid models. It is not only exact, it is fortunately also very simple to implement and fast, allowing for modelling a huge amount of particles with moderate computation time. Copyright © 2012 John Wiley & Sons, Ltd.