A numerical method operating within a processor-based environment for predicting the fill pattern and coating pressure distribution for a substrate in a computer simulation of an in-mold coating flow within a two-dimensional flow domain having a plurality of possible inlet nodes for injection, which includes the steps of initializing pressure and thickness change of the substrate for at least one of the inlet nodes, determining which of the inlet nodes are newly filled nodes and new flow front nodes, calculating pressure for the newly filled nodes; updating thickness and coating volume of the substrate, checking if pressure and time step have converged, and updating pressure and time step and returning to the pressure calculation step if pressure and time step calculations have not converged, and determining whether the substrate is filled, and updating filling time and returning to the determining step if the substrate is not filled.