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Abstract: We consider the incompressible Navier–Stokes problem with flow rate boundary conditions. This problem has been investigated in [J. Heywood, R. Rannacher, S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier–Stokes equations, Int. J. Numer. Methods Fluids 22 (1996) 325–352; L. Formaggia, J. F. Gerbeau, F. Nobile, A. Quarteroni, Numerical treatment of defective boundary conditions for the Navier–Stokes equation, SIAM J. Numer. Anal. 40(1) (2002) 376–401; A. Veneziani, C. Vergara, Flow rate defective boundary conditions in haemodynamics simulations, Int. J. Numer. Methods Fluids 47 (2005) 803–816]. In the latter two papers, a feasible numerical formulation of this problem, based on a Lagrange multiplier approach has been investigated. This approach has the drawback of high computational costs. In this paper, we propose an approximate formulation of this problem, yielding a strong reduction of the computational costs. The error analysis shows that the error introduced by this approximate formulation is confined in a small region of the boundary. This is confirmed by the numerical simulations. [Copyright &y& Elsevier]

Abstract: In this work, we propose a Robin–Robin preconditioner combined with Krylov iterations for the solution of the interface system arising in fluid–structure interaction (FSI) problems. It can be seen as a partitioned FSI procedure and in this respect it generalizes the ideas introduced in [S. Badia, F. Nobile, C. Vergara, J. Comput. Phys. 227 (2008) 7027–7051]. We analyze the convergence of GMRES iterations with the Robin–Robin preconditioner on a model problem and compare its efficiency with some existing algorithms. The method is shown to be very efficient for many challenging fluid–structure interaction problems, such as those characterized by a large added-mass effect or by enclosed fluids. In particular, the possibility to solve balloon-type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches. [Copyright &y& Elsevier]

Two crucial factors for accurate numerical simulations of cardiac electromechanics, which are also essential to reproduce the synchronous activity of the heart, are: (i) accounting for the interaction between the heart and the circulatory system that determines pressures and volumes loads in the heart chambers; (ii) reconstructing the muscular fiber architecture that drives the electrophysiology signal and the myocardium contraction. In this work, we present a 3D biventricular electromechanical model coupled with a 0D closed-loop model of the whole cardiovascular system that addresses the two former crucial factors. With this aim, we introduce a boundary condition for the mechanical problem that accounts for the neglected part of the domain located on top of the biventricular basal plane and that is consistent with the principles of momentum and energy conservation. We also discuss in detail the coupling conditions behind the 3D and the 0D models. We perform electromechanical simulations in physiological conditions using the 3D–0D model and we show that our results match the experimental data of relevant mechanical biomarkers available in the literature. Furthermore, we investigate different arrangements in cross-fibers active contraction. We prove that an active tension along the sheet direction counteracts the myofiber contraction, while the one along the sheet-normal direction enhances the cardiac work. Finally, several myofiber architectures are analyzed. We show that a different fiber field in the septal area and in the transmural wall affects the pumping functionality of the left ventricle. • 3D electromechanical biventricular model coupled with a 0D hemodynamic closed-loop model. • A novel effective mechanical boundary condition for the biventricular basal plane. • Numerical results on a realistic biventricular model matching the experimental data. • Study of different configurations in cross-fibers active contraction. • Evaluation of the impact of different myofibers architectures on biventricular electromechanics. [ABSTRACT FROM AUTHOR]