The present invention is a method and system for simulating fluid flow in a cavity, having relevance to the modeling of viscous flows within thin cavities of complex shapes in which heat exchange with the cavity walls may be a governing factor, as in injection molding of plastic parts. Its automated discretization scheme, in which the model cavity is partitioned into macrocells, each macrocell having substantial contact areas with the model cavity walls, eliminates the need for time consuming and expensive manual model configuration required by some modeling methods. Because of the simplicity of the discretization, models based on the invention are less demanding on computer resources then conventional finite element methods, and execute more quickly. A key innovation of the method is a function characterizing the shape of a macrocell that appears in a coefficient in equations governing the flow. As a consequence of the improvements offered by the invention, molds for complex parts can be fabricated more rapidly, with the resulting parts having high quality.