We present a multilayer Saint-Venant system for the simulation of 3D free surface flows with friction and viscosity effects. A vertical discretization of a Navier-Stokes system approximation deduced from a precise analysis of the shallow water assumption leads to a set of coupled Saint-Venant-type systems. The idea is to obtain an accurate description of the vertical profile of the horizontal velocity while preserving the robustness and the computational efficiency of the usual Saint-Venant system.For each time-dependent layer, a Saint-Venant-type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. The free surface is directly deduced from the sum of layers water depth.We validate the model with some numerical academic and realistic examples. We present comparisons with simulations computed with the hydrostatic Navier-Stokes solver of the Telemac-3D code developed by Electricite de France. Copyright (C) 2007 John Wiley & Sons, Ltd.

We introduce a monotonic and conservative numerical scheme for the resolution of the linear advection problem set on a moving domain. The scheme is based on an extension to moving domains of the Multidimensional Upwind Residual Distributive (MURD) approach. The properties ensured by the residual distribution schemes set on fixed domains are not altered by the domain movement, except for the conservation of the advected quantity. We introduce in this paper an additional condition which ensures the conservation properties of the MURD scheme on amoving domain. Several numerical tests have been performed, providing satisfying results in terms of conservation of the advected quantity.

We present a multilayer Saint-Venant system for the simulation of 3D free surface flows. A precise analysis of the shallow water assumption leads to a set of coupled Saint-Venant type systems. For each time dependent layer, a Saint-Venant type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. We validate the model by comparisons with Navier-Stokes solutions.

The purpose of this work is to use a variational method to identify some of the parameters of one-dimensional models for blood flow in arteries. These parameters can be fit to approach as much as possible some data coming from experimental measurements or from numerical simulations performed using more complex models. A nonlinear least squares approach to parameter estimation was taken, based on the optimization of a cost function. The resolution of such an optimization problem generally requires the efficient and accurate computation of the gradient of the cost function with respect to the parameters. This gradient is computed analytically when the one-dimensional hyperbolic model is discretized with a second order Taylor-Galerkin scheme. An adjoint approach was used. Some preliminary numerical tests are shown. In these simulations, we mainly focused on determining a parameter that is linked to the mechanical properties of the arterial walls, the compliance. The synthetic data we used to estimate the parameter were obtained from a numerical computation performed with a more accurate model: a three-dimensional fluid-structure interaction model. The first results seem to be promising. In particular, it is worth noticing that the estimated compliance which gives the best fit is quite different from the values that are commonly used in practice.