Abstract: This paper proposes a task graph (TG) model to represent a single discrete step of a computational fluid dynamics (CFD) application. The TG model is then used to predict the performance of a set of task assignment heuristics developed based on the constraints inherent in the CFD problem. Two primitive assignments, the Largest Task First and the Minimum Task First, are systematically enhanced by the integration of the status of the processing units and communication costs. Evaluation is performed on a synthetic TG with tasks defined in terms of the number of gridpoints in predetermined grid zones. A realistic problem with eight million gridpoints is also used as a test case.