In a previous communication, we have proposed a numerical framework for the prediction of in vitro hemolysis indices in the preselection and optimization of medical devices. This numerical methodology is based on a novel interpretation of Giersiepen-Wurzinger blood damage correlation as a volume integration of a damage function over the computational domain. We now propose an improvement of this approach based on a hyperbolic equation of blood damage that is asymptotically consistent. Consequently, while the proposed correction has yet to be proven experimentally, it has the potential to numerically predict more realistic red blood cell destruction in the case of in vitro experiments. We also investigate the appropriate computation of the shear stress scalar of the damage fraction model. Finally, we assess the validity of this consistent approach with an analytical example and with some 3D examples.

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SUMMARYA space-time finite element method for the incompressible Navier-Stokes equations in a bounded domain in R d (with d=2 or 3) is presented. The method is based on the time-discontinuous Galerkin method with the use of simplex-type meshes together with the requirement that the space-time finite element discretization for the velocity and the pressure satisfy the inf-sup stability condition of Brezzi and Babuška. The finite element discretization for the pressure consists of piecewise linear functions, while piecewise linear functions enriched with a bubble function are used for the velocity. The stability proof and numerical results for some two-dimensional problems are presented.

SUMMARYThe behaviour and accuracy of the stable mixed space-time ÿnite element methods for the incompressible Navier-Stokes equations in a two-dimensional bounded domain are investigated in this work. The mixed method is based on the recently developed space-time mini element, which consists of piecewise linear functions for the pressure and of piecewise linear functions enriched with a bubble function for the velocity. This element is stable in the sense that the underlying pair of discrete spaces for velocity and pressure satisÿes the so-called 'inf-sup' condition. We assess the behaviour and accuracy of the underlying mixed approximation when compared with the stabilized Galerkin/least-squares space-time method for some two-dimensional problems. Both methods are based on the time-discontinuous Galerkin method with the use of simplex-type meshes.

Dà epartement de mathà ematiques et de gà enie industriel; à Ecole Polytechnique de Montrà eal; C.P. 6079; succ. Centre-ville; Montrà eal (Quà ebec) Canada, H3C 3A7 SUMMARY A semi-discrete ÿnite element methodology for the modelling of transient free surface ows in the context of Eulerian interface capturing is proposed. The focus of this study is put on the choice of an appropriate time integration strategy for the accurate modelling of the dynamics of free surfaces and of interfacial physics. It is composed of an adaptive time integration scheme for the Navier-Stokes equations, and of the implicit midpoint rule for the transport equation of the Eulerian marker variable. The adaptive scheme allows the automatic determination of a time-step size that follows the physics of the problem under study, which facilitates the accurate modelling of sti free surface ows. It is shown that the implicit midpoint rule reduces mass loss for each uid. Various free surface ow problems are studied to verify and validate the proposed time integration strategy.