The numerical simulation of hemodynamics is increasingly recognized as a valuable analysis tool for the bioengineering laboratories who design implantable vascular grafts, and it is thought to become in a not so far future a complement to the physician’s analysis for the choice of interventional methods to restore a proper irrigation in diseased arteries [1]. The detailed numerical results obtained from 3d unsteady simulations permit to verify the hypotheses formulated by physiologists concerning the evolution of arterial disease and to quantify the risks associated to medical intervention. These objectives require an accurate representation of the major physiological parameters, much more complex than that encountered in standard CFD analysis of pipe flows, which makes the computation of blood flows in compliant vessels extremely challenging to the CFD and CSM communities. A comprehensive methodology for the adaptation of existing numerical schemes to this advanced modelling issues was conducted, for the behaviour laws of the fluid and walls on the one hand, and for the unsteady boundary conditions on the other hand. The complex nature of the mathematical model formed by the coupled fluid and structural mechanics equations, completed by highly unsteady boundary conditions, led to a choice of fully time-implicit algorithms with problem matching subiterations. These algorithms are successfully applied to different 3D, unsteady haemodynamics problems in a coronary artery. The complex, patients’ dependent geometry of a stenosed artery was reconstructed in CAD format from medical imaging. The accuracy of the numerical procedure is discussed, and this methodology can open the way for the validation of physiological criteria for the design of medical apparatus and the choice of interventional methods adapted to each individual patient’s situation.

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