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Publication# Hydrocontest – Computational Fluid Dynamics of Hydrofoils

Résumé

HYDROcontest is a challenge open to students from 13 universities from all over the world. The aim of the competition is to design the motorboat that best fulfills the tradeoff between high speed and low energy consumption. In order to optimize the shape of the hydrofoils sustaining the boat, suitable Computational Fluid Dynamics models and parallel simulations were employed. The variational multiscale (VMS) model proposed by Bazilevs et al. (2009) was linearized by means of a Newton method, discretized in time through a fully-implicit scheme, transformed into a dimensionless form and implemented in C++, using the Finite Elements library LifeV.

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We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum balance equation for the mixture (fluid and sediments).
The model proposed here couples the Navier-Stokes equations, with a
volume-of-fluid (VOF) approach for the tracking of the free surfaces between the liquid
and the air, plus a nonlinear advection equation for the sediments (for the transport, deposition, and resuspension of sediments).
The numerical algorithm relies on a splitting approach to decouple diffusion and advection phenomena such that we are left with a Stokes operator, an advection operator, and deposition/resuspension operators.
For the space discretization, a two-grid method couples a finite element discretization for the resolution of the Stokes problem, and a finer structured grid of small cells for the discretization of the advection operator and the sediment deposition/resuspension operator.
SLIC, redistribution, and decompression algorithms are used for post-processing to limit numerical diffusion and correct the numerical compression of the volume fraction of liquid.
The numerical model is validated through numerical experiments.
We validate and benchmark the model with deposition effects only for some specific experiments, in particular erosion experiments. Then, we validate and benchmark the model in which we introduce resuspension effects. After that, we discuss the limitations of the underlying physical models.
Finally, we consider a one-dimensional diffusion-convection equation and study an error indicator for the design of adaptive algorithms. First, we consider a finite element backward scheme, and then, a splitting scheme that separates the diffusion and the convection parts of the equation.

This project is developed within the scope of HydroContest which is an inter-school competition for the design of a racing boat with a high focus on energetic efficiency; the goal is to maximize the speed of the boat under the constraint of a limited power source. Hydrofoils are especially interesting since they offer an important reduction of drag at high speeds while remaining cost efficient. Within the contest, this project aims at delivering a prediction tool for the hydrofoil performance using numerical simulations of the incompressible Navier-Stokes equations approximated by the means of the Finite Element method with suitable stabilization techniques, such as the Variational Multiscale Method; we consider P1 Finite Elements with a second order BDF time discretization scheme. An automated meshing script was developed to handle arbitrary foil geometries and angles of attack. The numerical simulations were conducted using the LifeV Finite Element Library in a parallel setting. Satisfactory results have been obtained using this approach for Reynolds numbers up to 1 million.

2014Medicine is one of the branches of scientific research in which numerical simulation can give a great support. In particular, a well mature branch like computational fluid dynamics (CFD) can provide a substantial help for the understanding of several pathologies of the cardiovascular system. The local behavior of blood flow may affect substantially the on-rise of such pathologies: a remarkable instance is atherosclerosis, which is unfortunately largely widespread in Western Countries. An accurate fluid dynamics analysis can better enlight these mechanisms, and CFD becomes necessary since physical data from

`in vivo'' measures are troublesome to obtain. Moreover, allowing completely controlled simulations, CFD can eventually provide a useful paradigm for clinical practice, for instance suggesting optimal strategy for a surgeric operation. par However, the study of biological systems is a difficult task not only from the numerical viewpoint, but also in the modeling phase. Indeed, different systems interact each other at mechanical or biochemical level. Therefore, making a hierarchy of simplifications in the models considered is almost always mandatory. These notes illustrate some specific features of the blood flow problem, in the case of `

large'' vessels, where the atherosclerotic plaques are localized. In particular, the interaction between blood and compliant vessel walls is of upmost interest. The purpose is to review shortly the existing literature on the field (limitedly to the most genuine mathematical aspects) and mention a first contribution from our side to the modeling of blood-wall interaction and its numerical simulation.