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Subject: backflow stabilization ×

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    A Stokes-consistent backflow stabilization for physiological flows
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Bertoglio, Cristobal; Caiazzo, Alfonso
    In computational fluid dynamics incoming flow at open boundaries, or emphbackflow, often yields to unphysical instabilities for high Reynolds numbers. It is widely accepted that this is due to the incoming energy arising from the convection term, which cannot be empha priori controlled when the velocity field is unknown at the boundary. In order to improve the robustness of the numerical simulations, we propose a stabilized formulation based on a penalization of the residual of a weak Stokes problem on the open boundary, whose viscous part controls the incoming convective energy, while the inertial term contributes to the kinetic energy. We also present different strategies for the approximation of the boundary pressure gradient, which is needed for defining the stabilization term. The method has the advantage that it does not require neither artificial modifications or extensions of the computational domain. Moreover, it is consistent with the Womersley solution. We illustrate our approach on numerical examples
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    A tangential regularization method for backflow stabilization in hemodynamics
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bertoglio, Cristóbal; Caiazzo, Alfonso
    In computational simulations of fluid flows, instabilities at the Neumann boundaries may appear during backflow regime. It is widely accepted that this is due to the incoming energy at the boundary, coming from the convection term, which cannot be controlled when the velocity field is unknown. We propose a stabilized formulation based on a local regularization of the fluid velocity along the tangential directions on the Neumann boundaries. The stabilization term is proportional to the amount of backflow, and does not require any further assumption on the velocity profile. The perfomance of the method is assessed on a twoand three-dimensional Womersley flows, as well as considering a hemodynamic physiological regime in a patient-specific aortic geometry.
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    Benchmark problems for numerical treatment of backflow at open boundaries
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Bertoglio, Cristóbal; Bazilevs, Yuri; Caiazzo, Alfonso; Braack, Malte; Esmaily-Moghadam, Mahdi; Gravemeier, Volker; Marsden, Alison L.; Pironneau, Olivier; Vignon-Clementel, Irene E.
    In computational fluid dynamics, incoming velocity at open boundaries, or backflow, often yields to unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been proposed in the literature. However, these approaches have not yet been compared in detail in terms of accuracy in different physiological regimes, in particular due to the difficulty to generate stable reference solutions apart from analytical forms. In this work, we present a set of benchmark problems in order to compare different methods in different backflow regimes (with a full reversal flow and with propagating vortices after a stenosis). The examples are implemented in FreeFem++ and the source code is openly available, making them a solid basis for future method developments.