Collaborative Research: Efficient Modeling of Incompressible Fluid Dynamics at Moderate Reynolds Numbers by Deconvolution LES Filters Analysis and Applications to Hemodynamics

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Computational fluid dynamics has emerged as a powerful tool to study the physiopathology of the cardiovascular system and for patient-specific Surgical Planning (SP) for cardiovascular diseases. Recently, clinical trials - the standard procedure for understanding diseases and assessing the impact of therapies and devices in the clinical practice - have been supported by a massive use of numerical simulations to improve the knowledge extracted from measured data, leading to Computer Aided Clinical Trials (CACT). For a large variety of pathologies involving the aorta - the major artery of the circulation - this requires to work with turbulent flows. While Direct Numerical Simulation in this context can be appropriate for a proof of concept, for the large number of patients involved in CACT and SP we need different numerical tools to provide the appropriate trade-off between accuracy and reliability needed by clinical applications and computational efficiency needed by tight deadlines. As CACT and SP are new emerging concepts in cardiovascular mathematics, an appropriate numerical modeling of turbulent physiological flows for clinical applications is now an unmet need that we intend to solve in this proposal.A possible way to limit the computational costs associated with Direct Numerical Simulations without sacrificing accuracy is to solve the flow average and model properly the effects of the small scales (not directly solved) at the medium and large scales (solved). We intend to investigate carefully new cutting-edge methods for disturbed flows based on Large Eddy Simulation (LES) Deconvolution filtering techniques with the ultimate goal of enabling practical use of numerical tools to improve knowledge extraction and clinical practice through CACT and SP. The main objective of this research is the development and the analysis of a robust and accurate LES based approach requiring no or minimal user's set-up for realistic incompressible flow problems with application to computational hemodynamics. We articulate the project in the following points: (a) Sensitivity analysis of key parameters involved in the method to understand their impact on the solution, leading to an automated parameter set-up through physical and numerical arguments. (b) Development and analysis of high-order in time methods, particularly for the computation of the pressure, with consequent improvement of the mass conservation properties. (c) Analysis of the impact of our LES approach on non-Dirichlet boundary conditions and the possible backflow stabilizing effects. We plan to test the method on both academic and real bioengineering problems. Finally, we plan to deliver a finite element open source library incorporating the findings of our research, available for CACT and SP.