Numerical simulations for computational hemodynamics in clinical settings require a combination of many ingredients, mathematical models, solvers and patient-specific data. The sensitivity of the solutions to these factors may be critical, particularly when we have a partial or noisy knowledge of data. Uncertainty quantification is crucial to assess the reliability of the results. We present here an extensive sensitivity analysis in aortic flow simulations, to quantify the dependence of clinically relevant quantities to the patient-specific geometry and the inflow boundary conditions. Geometry and inflow conditions are generally believed to have a major impact on numerical simulations. We resort to a global sensitivity analysis, (i.e., not restricted to a linearization around a working point), based on polynomial chaos expansion (PCE) and the associated Sobol' indices. We regard the geometry and the inflow conditions as the realization of a parametric stochastic process. To construct a physically consistent stochastic process for the geometry, we use a set of longitudinal-in-time images of a patient with an abdominal aortic aneurysm (AAA) to parametrize geometrical variations. Aortic flow is highly disturbed during systole. This leads to high computational costs, even amplified in a sensitivity analysis -when many simulations are needed. To mitigate this, we consider here a large Eddy simulation (LES) model. Our model depends in particular on a user-defined parameter called filter radius. We borrowed the tools of the global sensitivity analysis to assess the sensitivity of the solution to this parameter too. The targeted quantities of interest (QoI) include: the total kinetic energy (TKE), the time-average wall shear stress (TAWSS), and the oscillatory shear index (OSI). The results show that these indexes are mostly sensitive to the geometry. Also, we find that the sensitivity may be different during different instants of the heartbeat and in different regions of the domain of interest. This analysis helps to assess the reliability of in silico tools for clinical applications.

This paper studies Kalman filtering applied to Reynolds-Averaged Navier–Stokes (RANS) equations for turbulent flow. The integration of the Kalman estimator is extended to an implicit segregated method and to the thermodynamic analysis of turbulent flow, adding a sub-stepping procedure that ensures mass conservation at each time step and the compatibility among the unknowns involved. The accuracy of the algorithm is verified with respect to the heated lid-driven cavity benchmark, incorporating also temperature observations, comparing the augmented prediction of the Kalman filter with the Computational Fluid-Dynamic solution found on a fine grid.