Astrid Decoene

ASYMPTOTIC DERIVATION OF THE SECTION-AVERAGED SHALLOW WATER EQUATIONS FOR NATURAL RIVER HYDRAULICS

The section-averaged shallow water model usually applied in river and open channel hydraulics is derived by an asymptotic analysis that accounts for terms up to second order in the vertical/longitudinal length ratio, starting from the three-dimensional Reynolds-averaged Navier–Stokes equations for incompressible free surface flows. The derivation is carried out under quite general assumptions on the geometry of the channel, thus allowing for the application of the resulting equations to natural rivers with arbitrarily shaped cross sections. As a result of the derivation, a generalized friction term is obtained, that does not rely on local uniformity assumptions and that can be computed directly from three-dimensional turbulence models, without need for local uniformity assumptions. The modified equations including the novel friction term are compared to the classical Saint Venant equations in the case of steady state open channel flows, where analytic solutions are available, showing that the solutions resulting from the modified equation set are much closer to the three-dimensional solutions than those of the classical equation set. Furthermore, it is shown that the proposed formulation yields results that are very similar to those obtained with empirical friction closures widely applied in computational hydraulics. The generalized friction term derived therefore justifies a posteriori these empirical closures, while allowing to avoid the assumptions on local flow uniformity on which these closures rely.

Moving meshes with freefem

Abstract - The Arbitrary Lagrangian-Eulerian framework allows to compute free surface flows with the Finite Element functions defined on a fittedmesh which follows the globalmotion of the fluid domain. We describe here how freefem++ can be used to implement this method, and we provide two and three dimensional illustrations in the context of water waves.

Estimating absolute aortic pressure using MRI and a one-dimensional model

Aortic blood pressure is a strong indicator to cardiovascular diseases and morbidity. Clinically, pressure measurements are done by inserting a catheter in the aorta. However, imaging techniques have been used to avoid the invasive procedure of catheterization. In this paper, we combined MRI measurements to a one-dimensional model in order to simulate blood flow in an aortic segment. Absolute pressure was estimated in the aorta by using MRI measured flow as boundary conditions and MRI measured compliance as a pressure law for solving the model. Model computed pressure was compared to catheter measured pressure in an aortic phantom. Furthermore, aortic pressure was estimated in vivo in three healthy volunteers.

Local error analysis for the Stokes equations with a punctual source term

The solution of the Stokes problem with a punctual force in source term is not

Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model

H^1 \times \mathbb {L}^2

Sigma transformation and ALE formulation for three‐dimensional free surface flows

H1×L2 and therefore the approximation by a finite element method is suboptimal. In the case of Poisson problem with a Dirac mass in the right-hand side, an optimal convergence for the Lagrange finite elements has been shown on a subdomain which excludes the singularity in

3D Free Surface Flows Simulations Using a Multilayer Saint-Venant Model. Comparisons with Navier-Stokes Solutions

\mathbb {L}^2