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Publication# Numerical simulation of a sailing boat

Résumé

In this work, various aspects concerning the numerical simulation of a sailing boat are investigated. The attention is focused on simulation of the free-surface, the fluid-structure interaction (FSI) between wind and sails, and the dynamics of the whole boat. Some preliminary work on shape optimization is also presented. Free-surface simulations are carried out both on classical academic benchmark problems and for the prediction of the wave pattern around racing yachts. The comparison with experimental results and numerical data obtained with other CFD codes has proven the validity of the proposed set-up. In this framework, the Level Set method has been implemented and validated as a possible solution to the problem of interface diffusion arising in planing conditions with the standard Volume of Fluid approach. The FSI problem governing the interaction between wind and sails is solved via a strongly coupled segregated approach based on the standard Dirichlet-Neumann coupling. The structural solution is based on a MITC4 finite-element shell code. The fluid and structural meshes are non-conforming and the exchange of information at the interface is obtained via radial basis functions (RBF) interpolation. The fluid mesh motion is accomplished either through the mapping generated using the radial basis functions or via a method based on the inverse distance weighting (IDW) interpolations. The attention is paid to the methodological aspects of this complex problem and to the analysis of the numerical results. The fluid-structure interaction simulations of one and two sail configurations, with different trimmings, are presented; both steady and transient simulations are performed. The results obtained are very encouraging and show the potential of the proposed model. The dynamic motion of the Series 60 hull and the Alinghi’s AC 32 monohull complete of bulb, keel and sails have also been investigated. For the latter in particular, the free sink, trim and roll case has proven to be particularly interesting, with the boat rolling considerably on the side due to the aerodynamic loads exerted by the wind on the sails. Here, the whole boat has been considered as a rigid body but the integration of the FSI module for the sails into the full boat dynamic system is already under development. Finally, a preliminary analysis of shape optimization techniques applied to sailing boat elements have been investigated: in particular the attention has been focused on the drag minimization of (pseudo) bulb geometries under the constraint of fixed volume/fixed righting moment. The shape parametrization have been achieved either using directly the surface element nodes or via the Free Form Deformation (FFD) technique while the optimization algorithm has been based either on the solution of the adjoint Navier-Stokes equations or via pseudo finite-difference algorithms. The algorithm and developments mentioned have been implemented in a common open-source framework, the library OpenFOAM®.

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Mathematical and numerical aspects of free surface flows are investigated. On one hand, the mathematical analysis of some free surface flows is considered. A model problem in one space dimension is first investigated. The Burgers equation with diffusion has to be solved on a space interval with one free extremity. This extremity is unknown and moves in time. An ordinary differential equation for the position of the free extremity of the interval is added in order to close the mathematical problem. Local existence in time and uniqueness results are proved for the problem with given domain, then for the free surface problem. A priori and a posteriori error estimates are obtained for the semi-discretization in space. The stability and the convergence of an Eulerian time splitting scheme are investigated. The same methodology is then used to study free surface flows in two space dimensions. The incompressible unsteady Navier-Stokes equations with Neumann boundary conditions on the whole boundary are considered. The whole boundary is assumed to be the free surface. An additional equation is used to describe the moving domain. Local existence in time and uniqueness results are obtained. On the other hand, a model for free surface flows in two and three space dimensions is investigated. The liquid is assumed to be surrounded by a compressible gas. The incompressible unsteady Navier-Stokes equations are assumed to hold in the liquid region. A volume-of-fluid method is used to describe the motion of the liquid domain. The velocity in the gas is disregarded and the pressure is computed by the ideal gas law in each gas bubble trapped by the liquid. A numbering algorithm is presented to recognize the bubbles of gas. Gas pressure is applied as a normal force on the liquid-gas interface. Surface tension effects are also taken into account for the simulation of bubbles or droplets flows. A method for the computation of the curvature is presented. Convergence and accuracy of the approximation of the curvature are discussed. A time splitting scheme is used to decouple the various physical phenomena. Numerical simulations are made in the frame of mould filling to show that the influence of gas on the free surface cannot be neglected. Curvature-driven flows are also considered.

Two major lines of investigation have been pursued in this thesis: (1) More efficient, robust and realistic numerical techniques are designed for the simulation of complex turbulent fluid flows; (2) A new algorithm and its analysis is performed in the context of multiphasic fluid flow, for a cohesive fine-grained sediment (fluid mud) transport in estuaries. Estuaries exist between marine and freshwater system where waters of different physical, chemical and biological composition meet, combine and disperse primarily due to tidal influences. In the present thesis, the behavior of cohesive sediment in estuaries is reviewed based on the existing literature. Basic theories and recent developments are introduced to describe the formation of fluid mud from a very dilute suspension and its motion down a natural river bed with complex bathymetry. The present work contributes to the numerical simulation of complex turbulent multiphasic fluid flows encountered in estuarine channels, with the aim of the better understanding of the underlying physical processes as well as predicting realistically the cohesive sediment transport and bed morphology in such a zone. The model is based on the mass preserving method by using the so-called Raviart-Thomas finite element on the unstructured mesh in the horizontal plane. In the vertical, the computational domain is divided into number of layers at predefined heights and the method uses a conventional conforming P1 finite element scheme, with the advantage that the lowermost and uppermost layers variable height allow a faithful representation of the time-varying bed and free surface, respectively. Concerning the modeling of turbulence, the research effort focuses on the turbulence two-equation k - ε closure for the vertical parameterization of eddy viscosity. More precisely, a robust up-to-date algorithm is used for this issue. The new methodology is developed with the aim to account for more general relevant effects in the closure. The proposed model offers the capability to cope with the stiffness problem introduced by the large difference between the solid phase flow time scale and the hydrodynamic one, by using a sub-cycling strategy, whereas the splitting scheme is adopted with the aim of stability and the positivity of the relevant turbulent variables. The flexibility of the model and its performance are evaluated on several free-surface flow configurations with increasing complexity : homogeneous unsteady non-uniform flows in plane open channel flows, U-shaped (193°) curved open channel flow. Concerning the cohesive sediment transport, most of the existing models in the literature assume the analogous transport characteristics with that of the coarse sediment and adopt the relevant developed sediment transport for the latter to treat the former. Moreover, these existing models do not account for the consolidation of the mud-bed. The present research effort focused on a novel methodology based on the realistic empirical relationships, which accounts for the mutually exclusive processes for re-suspension and/or erosion and deposition of fine sediment, whereas only a limited range of bed shear stresses is allowed for simultaneous erosion and deposition to occur. Hence, on this basis, the new model investigated the bed morphology evolution by taking into account of the fluidization and/or consolidation of the fluid mud, which was handled by modeling the bed in three layers: (i) the mud-bed layer, (ii) the partially consolidated bed and (iii) the fully consolidated bed. The prediction of deposition/re-suspension using these two different methods lead to a non negligible difference in the results. Therefore, investigation of the true mechanism of erosion/deposition processes for cohesive sediments and their implementation in the numerical model is very important. This suggests that a realistic prediction must account for the fresh mud-bed re-suspension once deposited, as well as the consolidation and/or fluidization of the mud-bed deposits. Finally, the capability and improvements of the model are demonstrated, and its predicting performance is successfully evaluated by applying it to the simulation of the Po River Estuary (PRE) in Italy, which is the main source of river water discharge into the Northern Adriatic Sea. The analysis showed that the consolidation/fluidization process at the bed may have important influence on the prediction of bed morphology evolution. The three-layer approach used in this thesis is a first attempt to model these processes in detail within a numerical model.

Adelmo Cristiano Innocenza Malossi

The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned solution of geometrical multiscale problems made of different heterogeneous compartments that are implicitly coupled with each others. The driving motivation is the awareness that cardiovascular dynamics are governed by the global interplay between the compartments in the network. Thus, numerical simulations of stand-alone local components of the circulatory system cannot always predict effectively the physiological or pathological states of the patients, since they do not account for the interaction with the missing elements in the network. As a matter of fact, the geometrical multiscale method provides an automatic way to determine the boundary (more precisely, the interface) data for the specific problem of interest in absence of clinical measures and it also offers a platform where to study the interaction between local changes (due, for instance, to pathologies or surgical interventions) and the global systemic dynamics. To set up the framework an abstract setting is devised; the local specific mathematical equations (partial differential equations, differential algebraic equations, etc.) and the numerical approximation (finite elements, finite differences, etc.) of the heterogeneous compartments are hidden behind generic operators. Consequently, the resulting global interface problem is formulated and solved in a completely transparent way. The coupling between models of different dimensional scale (three-dimensional, one-dimensional, etc.) and type (Navier-Stokes, fluid-structure interaction, etc.) is addressed writing the interface equations in terms of scalar quantities, i.e., area, flow rate, and mean (total) normal stress. In the resulting flexible framework the heterogeneous models are treated as black boxes, each one equipped with a specific number of compatible interfaces such that (i) the arrangement of the compartments in the network can be easily manipulated, thus allowing a high level of customization in the design and optimization of the global geometrical multiscale model, (ii) the parallelization of the solution of the different compartments is straightforward, leading to the opportunity to make use of the latest high-performance computing facilities, and (iii) new models can be easily added and connected to the existing ones. The methodology and the algorithms devised throughout the work are tested over several applications, ranging from simple benchmark examples to more complex cardiovascular networks. In addition, two real clinical problems are addressed: the simulation of a patient-specific left ventricle affected by myocardial infarction and the study of the optimal position for the anastomosis of a left ventricle assist device cannula.