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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 study the flow of an incompressible viscous fluid through a long tube with compliant walls. The flow is governed by a given time dependent pressure head difference. The Navier-Stokes equations for an incompressible viscous fluid are used to model the flow, and the Navier equations for a curved, linearly elastic membrane to model the wall. Employing the(More)
Fluid-structure interaction describing wave propagation in arteries driven by the pulsatile blood flow is a complex problem. Whenever possible, simplified models are called for. One-dimensional models are typically used in arterial sections that can be approximated by the cylindrical geometry allowing axially symmetric flows. Although a good first(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.
Effective equations describing the flow of a viscous incompressible fluid through a long elastic tube (Reçu le jour mois année, accepté après révision le jour mois année) Abstract. We study the flow of a viscous incompressible fluid through a long and narrow elastic tube whose walls are modeled by the Navier equations for a curved, linearly elastic(More)
We prove the existence of a solution of a free boundary problem for the tran-sonic small-disturbance equation. The free boundary is the position of a tran-sonic shock dividing two regions of smooth flow. Assuming inviscid, irrotational flow, as modeled by the transonic small-disturbance equation, the equation is hy-perbolic upstream where the flow is(More)
The focus of this work is on modeling blood flow in medium-to-large systemic arteries assuming cylindrical geometry, axially symmetric flow, and viscoelasticity of arterial walls. The aim was to develop a reduced model that would capture certain physical phenomena that have been neglected in the derivation of the standard axially symmetric one-dimensional(More)
We prove the existence of a solution to the weak regular reflection problem for the unsteady transonic small disturbance (UTSD) model for shock reflection by a wedge. In weak regular reflection, the state immediately behind the reflected shock is supersonic and constant. The flow becomes subsonic further downstream ; the equation in self-similar coordinates(More)