The complexities in the flow pattern in a cavo-pulmonary vascular system-after application of the Fontan procedure in the vicinity of the superior vena cava, inferior vena cava, and the confluence at the T-junction-are analysed. A characteristic-based split (CBS) finite element scheme involving the artificial compressibility approach is employed to compute the resulting flow. Benchmarking of the CBS scheme is carried out using standard problems and with the flow features observed in an experimental model with the help of a dye visualization technique in model scale. The transient flow variations in a total cavo-pulmonary connection (TCPC) under pulsatile conditions are investigated and compared with flow visualization studies. In addition to such qualitative flow investigations, quantitative analysis of energy loss and haemodynamic stresses have also been performed. The comparisons show good agreement between the numerical and experimental flow patterns. The numerically predicted shear stress values indicate that the pulsatile flow condition is likely to be more severe than steady flow, with regard to the long-term health of the surgically corrected TCPC. Copyright © 2008 John Wiley & Sons, Ltd.