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We introduce a novel loosely coupled-type algorithm for fluid-structure interaction between blood flow and vascular walls. This algorithm successfully deals with the difficulties associated with the " added mass effect " , which is known to be the cause of numerical instabilities in fluid-structure interaction problems involving fluid and structure of(More)
We present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. Arterial walls are modeled by a linearly viscoelastic, cylindrical Koiter shell model capturing both radial and longitudinal displacement. Fluid flow is modeled by the(More)
— In this article, we address the numerical solution of a non-smooth eigenvalue problem, which has implications in plasticity theory and image processing. The smallest eigenvalue of the non-smooth operator under consideration is shown to be the same for all bounded, sufficiently smooth, domains in two space dimensions. Piecewise linear finite elements are(More)
A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in microvessels. The biconcave RBC shape in static plasma and tank-treading behavior of single cell in shear flows have been successfully captured in this model. The behavior of the RBC in a Poiseuille flow and the(More)
The main goal of this article is to review various results and methods concerning the numerical simulation of Bingham visco-plastic flow; these results have been obtained from the early 1970s to now. We consider first the case of flow in cylindrical pipes and then flow in multi-dimensional cavities. The methods to be discussed include classical ones relying(More)
We describe in this report the numerical analysis of a particular class of nonlinear Dirichlet problems. We consider an equivalent variational inequality formulation on which the problems of existence, uniqueness and approximation are easier to discuss. We prove in particular the convergence of an approximation by piecewise linear finite elements. Finally,(More)
We present a new time-splitting scheme for the numerical simulation of fluid-structure interaction between blood flow and vascular walls. This scheme deals in a successful way with the problem of the added mass effect. The scheme is modular and it embodies the stability properties of implicit schemes at the low computational cost of loosely coupled ones.