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Subject: proper orthogonal decomposition ×

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    A reduced-order modeling for efficient design study of artificial valve in enlarged ventricular outflow tracts
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Caiazzo, Alfonso; Guibert, Romain; Vignon-Clementel, Irene E.
    A computational approach is proposed for efficient design study of a reducer stent to be percutaneously implanted in enlarged right ventricular outflow tracts (RVOT). The need for such a device is driven by the absence of bovine or artificial valves which could be implanted in these RVOT to replace the absent or incompetent native valve, as is often the case over time after Tetralogy of Fallot repair. Hemodynamics are simulated in the stented RVOT via a reduce order model based on proper orthogonal decomposition (POD), while the artificial valve is modeled as a thin resistive surface. The reduced order model is obtained from the numerical solution on a reference device configuration, then varying the geometrical parameters (diameter) for design purposes. To validate the approach, forces exerted on the valve and on the reducer are monitored, varying with geometrical parameters, and compared with the results of full CFD simulations. Such an approach could also be useful for uncertainty quantification. Device design, percutaneous pulmonary valve replacement, proper orthogonal decomposition (POD), finite element method, blood flow CFD, repaired Tetralogy of Fallot.
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    A numerical investigation of velocity-pressure reduced order models for incompressible flows
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Caiazzo, Alfonso; Iliescu, Traian; John, Volker; Schyschlowa, Swetlana
    This report has two main goals. First, it numerically investigates three velocity-pressure reduced order models (ROMs) for incompressible flows. The proper orthogonal decomposition (POD) is used to generate the modes. One method computes the ROM pressure solely based on the velocity POD modes, whereas the other two ROMs use pressure modes as well. To the best of the authors knowledge, one of the latter methods is novel. The second goal is to numerically investigate the impact of the snapshot accuracy on the ROMs accuracy. Numerical studies are performed on a two-dimensional laminar flow past a circular obstacle. It turns out that, both in terms of accuracy and efficiency, the two ROMs that utilize pressure modes are clearly superior to the ROM that uses only velocity modes. The numerical results also show a strong correlation of the accuracy of the snap shots with the accuracy of the ROMs.