Efficient modeling of incompressible flows with moderate large Reynolds numbers using a deconvolution-based Leray model: analysis, uncertainty quantification and application in aortic dissections

Abstract

Progressive false lumen aneurysmal degeneration in the acute uncomplicated type B aortic dissection is a complex process with a combination of mechanical and biological etiologies. Patient-specific Computational Fluid Dynamics (CFD) provides spatial and temporal hemodynamic quantities that facilitate understanding of this disease progression. However, due to the moderate large Reynolds number and complex geometries, Direct Numerical Simulation (DNS) could be intimidatingly computational expensive. As a Large Eddy Simulation (LES) model, the Leray model solves the flow structure at large scales while models the effect of the small-scale flows using a deconvolution-based differential filter, whose efficiency and accuracy make it a promising candidate for the hemodynamic problem in human aortas. In order to evaluate the robustness of the model prediction, Uncertainty Quantification (UQ) and sensitivity analysis are necessary for understanding the effects of the model parameter and patients' data. The goal of this work is to develop and analyze the deconvolution-based Leray model for the incompressible flow problem in the hemodynamics of aortic dissections, to quantify the model uncertainty, and to apply the model to investigate the prognostic factors for the late complication of the originally uncomplicated type B aortic dissection in order to facilitate the decision of the less invasive early surgical intervention. The specific aims are: Aim 1, development and implementation of the deconvolution-based Leray model using the Finite Element Method. Aim 2, analysis of using the Leray model for suppressing the backflow instability, a common numerical instability in hemodynamic simulations. Aim 3, sensitivity analysis and uncertainty quantification of the influence of the Leray model parameter and patients' data. Aim 4, investigation of the hemodynamic indication factors of early surgical intervention for the acute uncomplicated type B aortic dissection by correlating the hemodynamic factors and false lumen degeneration in time.