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En la actualidad las más avanzadas técnicas para diseño naval ya no se restringen sólo a proyectos de alto coste; si no que también ahora son de aplicación en el campo de las embarcaciones de recreo y turísticas, dando con ello un valor añadido al proyecto final. La utilización de un código CFD para el mayor conocimiento del comportamiento hidrodinámico de las embarcaciones de recreo y turísticas es de una gran utilidad debido a las complejidades que en el diseño de estas se presentan. Estas herramientas nos van a proporcionar una serie de datos como sustentación lateral en las embarcaciones de vela o interacción entre cascos en catamaranes con deriva lateral, que de otra forma nunca pudieran conocerse. Los resultados hidrodinámicos obtenidos nos sirven para comparar las diferentes alternativas, y para además obtener unos valores que directamente son usados para la predicción de velocidad de la embarcación, que más tarde se verán refrendadas por las pruebas de mar. La utilización de técnicas CFD, basadas en el método de los elementos finitos, para la resolución de las ecuaciones de Reynolds (RANSE), incluyendo efectos de superficie libre, hace que todo esto sea posible. En este trabajo se presentan diversos resultados de aplicación del código CFD SHYNE a varias embarcaciones deportivas y de recreo. SHYNE está basado en la técnica del Cálculo Finitesimal para la integración de las ecuaciones de Reynolds.

In this paper, a second order SL-PFEM scheme for solving the incompressible Navier-Stokes equations is presented. This scheme is based on the second order velocity Verlet algorithm, which uses an explicit integration for the particle’s trajectory and an implicit integration for the velocity. The algorithm is completed with a predictor-multicorrector scheme for the integration of the velocity correction using the Finite Element Method. A second order projector based on least squares is used to transfer the intrinsic variables information from the particles onto the background mesh, while a second order interpolation scheme is used to transfer the accelerations from the mesh to the particles. Convergence analyses are carried out to assess the second order convergence.

The objective of the project that is presented at the IV Prize Duran i Farell Award for Research and Technology is the development of a new computational code based on the finite element method for the fluid-dynamics analysis of vessels. The code allows to accurately reproduce the model basin tests (MBT) usually used for the experimental evaluation of the hydrodynamic resistance of ships. The new code, called Tdyn, is a much more economical and precise alternative to model basin tests, by allowing the analysis of the behavior of vessels in real scale, thus eliminating the usual scale errors in the experimental tests. Tdyn incorporates new mathematical models and advanced finite elements methods that have led to numerous international publications. Tdyn was jointly developed by researchers from the Technical University of Catalonia (UPC) of the Department of Strength of Materials and Structural Engineering of the Barcelona School of Civil Engineering and of the Department of Nautical Engineering and Science of the Faculty of Nautical Studies of Barcelona in the framework of several European and national projects carried out in collaboration with the research center CIMNE and the company Compass IS, as well as other prestigious companies in the naval architecture sector. Tdyn was applied to the design of several America’s Cup yachts (in particular, of the ALINGHI team, winner of the 2003 edition). Tdyn is currently commercialized worldwide through Compass IS, a spin-off of the UPC.

En los últimos años CIMNE ha desarrollado en colaboración con la empresa COMPASS Ingeniería y Sistemas, S.A. (www.compassis.com) un nuevo código de cálculo basado en el método de los elementos finitos para el estudio fluido-dinámico de embarcaciones. El código permite reproducir de forma virtual con fidelidad el denominado “Canal de Ensayos Hidrodinámicos” (CEH) utilizado regularmente para la evaluación experimental de la resistencia hidrodinámica de barcos. El nuevo código, denominado TDYN, es una alternativa a mucho más económica y precisa a los ensayos en el CEH, al permitir analizar el comportamiento de barcos en el agua a escala real, eliminando así los errores de escala usuales en los ensayos experimentales. TDYN incorpora nuevos modelos matemáticos y métodos de elementos finitos avanzados que han llevado a término numerosas publicaciones internacionales. TDYN se desarrolló conjuntamente por investigadores de la Universidad Politécnica de Catalunya (UPC) del Depto. De Resistencia de Materiales y Estructuras de la Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos de Barcelona y del Departamento de Ciencia e Ingenieros Náuticas de la Facultad de Náutica de Barcelona en el marco de diversos proyectos europeos y nacionales llevados a término en colaboración con CIMNE y la empresa COMPASS, además de otras empresas de prestigio en el sector naval. TDYN se aplicó al diseño de diversos veleros de la Copa América (en particular por el equipo del barco ALINGHI ganador de la edición de 2003). TDNY lo comercializa actualmente en todo el mundo la empresa COMPASS, una spin-off de la UPC. &nbsp

We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented.

One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. A relevant aspect of LES theory, which we will consider in our work, is the close relationship between the mathematical properties of LES models and the numerical methods used for their implementation. In last years it is more and more common the idea in the scientific community, especially in the numerical community, that turbulence models and stabilization techniques play a very similar role. Methodologies used to simulate turbulent flows, RANS or LES approaches, are based on the same concept: unability to simulate a turbulent flow using a finite discretization in time and space. Turbulence models introduce additional information (impossible to be captured by the approximation technique used in the simulation) to obtain physically coherent solutions. On the other side, numerical methods used for the integration of partial differential equations (PDE) need to be modified in order to able to reproduce solutions that present very high localized gradients. These modifications, known as stabilization techniques, make possible to capture these sharp and localized changes of the solution. According with previous paragraphs, the following natural question appears: Is it possible to reinterpret stabilization methods as turbulence models? This question suggests a possible principle of duality between turbulence modelling and numerical stabilization. More than to share certain properties, actually, it is suggested that the numerical stabilization can be understood as turbulence. The opposite will occur if turbulence models are only necessary due to discretization limitations instead of a need for reproducing the physical behaviour of the flow. Finally: can turbulence models be understood as a component of a general stabilization method?

A stabilized semi-implicit fractional step algorithm based on the finite element method for solving ship wave problems using unstructured meshes is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus procedure. This allows us to obtain a stabilized numerical solution scheme. Some particular aspects of the problem solution, such as the mesh updating procedure and the transom stern treatment, are presented. Examples of the efficiency of the semi-implicit algorithm for the analysis of ship hydrodynamics problems are presented.

En este trabajo se presenta una metodología basada en el método de los elementos finitos para el análisis de problemas de flujo incompresible en fluidodinámica naval. Esta metodología se basa en la obtención de unas nuevas ecuaciones diferenciales, basadas en criterios discretos, alternativas a las tradicionales ecuaciones de Navier-Stokes. El punto más novedoso del presente trabajo es la aplicación del método de análisis de flujo incomprensible mencionado a problemas navales.

A stabilized semi-implicit fractional step finite element method (FEM) for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus (FIC) procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented.

We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The standard Eulerian formulation is described first. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the finite calculus (FIC) method. A simple extension of the fluid flow equations to an arbitrary Lagrangian–Eulerian (ALE) frame adequate for treating fluid–structure interaction problems is briefly presented. A fully Lagrangian formulation called the particle finite element method (PFEM) is also described. The PFEM is particularly attractive for fluid–structure interaction problems involving large motions of the free surface and breaking waves. Examples of application of the Eulerian, the ALE and the fully lagrangian PFEM formulations are presented.

We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.

A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous fluid and the free surface are derived at a differential level via a finite increment calculus procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented.

Brash ice is the accumulation of floating ice made up of blocks no larger than two meters across. Navigation in brash ice is becoming more usual as new navigation routes are being opened in the Artic regions. This navigation brings new concerns regarding the interaction of ice blocks with the ship. This work presents recent advances towards the development of a computational model for simulation of this navigation condition including the interaction among the ship and the ice blocks. The computational tool developed in this work is based on the coupling of a Semi-Lagrangian Particle Finite Element Method (SL-PFEM) with a multi rigid-body dynamics tool. The Particle Finite Element Method (Idelsohn et al. 2004)is a versatile framework for the analysis of fluid-structure interaction problems. The PFEM combines Lagrangian particle-based techniques with the advantage of the integral formulation of the Finite Element Method (FEM). It has been shown (Idelsohn et al. 2014 andNadukandi et al. 2017) to successfully simulate a wide variety of complex engineering problems, e.g. free-surface/multi-fluid flows with violent interface motions, multi-fluid mixing and buoyancy-driven segregation problems etc. The latest development within the framework of the PFEM is the X-IVAS (eXplicit Integration along the Velocity and Acceleration Streamlines) scheme. It is a semi-implicit scheme built over a Semi-Lagrangian (SL) formulation of the PFEM. In this work, the SL-PFEM model has been coupled with a multibody dynamics solver, able to handle the interactions between thousands of bodies, representing the different ice blocks. The interaction between the fluid flow and the ice blocks is taking into account by enriching the finite element space at the boundaries of the different blocks. This work is part of the research project NICESHIP sponsored by the U.S. Office of Naval Research under Grant N62909-16-1-2236.

Brash ice is the accumulation of floating ice made up of blocks no larger than two meters across. Navigation in brash ice is becoming more usual as new navigation routes are being opened in the Artic regions. This navigation brings new concerns regarding the interaction of ice blocks with the ship. This work presents recent advances towards the development of a computational model for simulation of this navigation condition including the interaction among the ship and the ice blocks. The computational tool developed in this work is based on the coupling of a Semi-Lagrangian Particle Finite Element Method (SL-PFEM) with a multi rigid-body dynamics tool. The Particle Finite Element Method(Idelsohn et al. 2004)is a versatile framework for the analysis of fluid-structure interaction problems. The PFEM combines Lagrangian particle-based techniques with the advantage of the integral formulation of the Finite Element Method (FEM). It has been shown (Idelsohn et al. 2014 andNadukandi et al. 2017) to successfully simulate a wide variety of complex engineering problems, e.g. free-surface/multi-fluid flows with violent interface motions, multi-fluid mixing and buoyancy-driven segregation problems etc. The latest development within the framework of the PFEM is the X-IVAS (eXplicit Integration along the Velocity and Acceleration Streamlines) scheme. It is a semi-implicit scheme built over a Semi-Lagrangian (SL) formulation of the PFEM. In this work, the SL-PFEM model has been coupled with a multibody dynamics solver, able to handle the interactions between thousands of bodies, representing the different ice blocks. The interaction between the fluid flow and the ice blocks is taking into account by enriching the finite element space at the boundaries of the different blocks. This work is part of the research project NICESHIP sponsored by the U.S. Office of Naval Research under Grant N62909-16-1-2236.

This paper presents advances in recent work of the authors to derive a fractional step scheme based on the stabilized finite element method that allows overcoming the above mentioned problem, resulting in a efficient time accurate scheme. The starting point is the modified governing differential equations for the incompressible turbulent viscous flow and the free surface condition incorporating the necessary stabilization terms via a finite calculus (FIC) procedure developed by the authors . This technique is based on writting the different balance equations over a domain of finite size and retaining higher order terms. These terms incorporate the ingredients for the necessary stabilization of any transient and steady state numerical solution already at the differential equations level. The resulting stabilized equations are integrated in space using the standard finite element method, and in time using an implicit and uncoupled second order fractional step method.

The complexity of the dynamic response of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these devices. This presentation introducesa new time-domain model for solving the dynamics of moored floating marine devices, specifically offshore wind turbines, subjected to non-linear environmental loads. Different application examples are presented,including aGVA, and the OC3 and OC4platforms.&nbsp

This presentation shows the recent work of the CIMNE in the maritime transport field. It was given at the Conference on Computation and Big Data in Transport (CM3-2017) held in November 22 – 23, 2017.

We present three new stabilized finite element (FE) based Petrov–Galerkin methods for the convection–diffusion–reaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e. g.M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the CDR problem. The structure of the method in 1d is identical to the consistent approximate upwind (CAU) Petrov–Galerkin method [68] except for the definitions of the stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [141] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i. e.second order accuracy for smooth/regular regimes and good shock-capturing in non-regular regimes. The design procedure in 1d embarks on the problem of circumventing the Gibbs phenomenon observed in L2 projections. Next, we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1d this scheme is identical to the alphainterpolation method [140] and in 2d choosing the value 0.5 for both the parameters, we recover the generalized fourth-order compact Padé approximation [81, 168] (therein using the parameter gamma = 2). We follow [10] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [10]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2d. A Petrov–Galerkin formulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the l1 Euclidean norm is done and the pollution effect is found to be small. Finally, we present a collection of stabilized FE methods derived via first-order and second-order FIC procedures for the Stokes problem. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method [93], the Pressure Gradient Projection (PGP) method [35] and the orthogonal sub-scales (OSS) method [34] are recovered from the general iii residual-based FIC stabilized form. A new family of Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are nonlinear and residual-based, i. e.the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of these stabilization techniques are discussed and several examples of application are presented.

Aula FNB-CIMNE was created on 2002 through an agreement between the Faculty of Nautical Studies of Barcelona (FNB) and the International Center for Numerical Methods in Engineering (CIMNE) aiming to promote the development and application of computational methods for the solution of naval & maritime engineering problems.

This presentation shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver developed for this purpose, uses a potential flow approach along with a stream-line integration of the free surface. The presentation focuses on the free surface-structure algorithm that has been developed to allow the simulation of the complex and highly dynamic behavior of the seals in the interface between the air cushion, and the water. The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken’s method. Several validations against experimental results have been carried out to demonstrate the developed algorithm.

Wave-structure interaction is a topic of great interest in naval and offshore engineering. This interest is growing in the last years due to the boost given by the development of the marine renewable energy field. In this context the development of an efficient time-domain coupled waves-structure solver is a main request from the industry. Up to date the numerical seakeeping simulation has been mostly carried out using the frequency domain. The reason might be that the computational cost of time domain simulations were too high and computational time was too large. Moreover assumptions like linear waves and the harmonic nature of water waves made the frequency domain to be the right choice. However nowadays computing capabilities make possible to carry out numerical simulations in the time domain in a reasonable time, with the advantage of making easier the introduction of non-linearities into the algorithm and therefore coupling with other phenomena. This presentation showsthe work of the authors in developing a time-domain unstructured Finite Element Method (FEM) algorithm for analysis of coupled wave-structure interaction. For this purpose, a new diffraction-radiation solver using the FEM was developed. The solver has been implemented in GPU, using CUDA architecture. The speed-up obtained ranges from 5 to 10 times compare to the implementation in a standard CPU with a conjugate gradient and ILU preconditioner. The seakeeping analysis tool has been integrated within a coupled waves-structure analysis tool. The coupling algorithm is based on a partitioned iterative algorithm, using an interpolation library able to communicate pressure forces and displacements of the structure at memory level. Furthermore, an innovative wetting and drying scheme able to improve the evaluation of the water action on the structure. The accuracy of the new seakeeping formulation for analysis of waves and floating structures interaction has been verified in different validation cases and practical applications.&nbsp

A new Petrov–Galerkin (PG) method involving two parameters, namelyα1andα2, is presented, which yields the following schemes on rectangular meshes: (i) a compact stencil obtained by the linear interpolation of the Galerkin FEM and the classical central finite difference method (FDM), should the parameters be equal, that is,α1 = α2 = α; and (ii) the nonstandard compact stencil presented in (Int. J. Numer. Meth. Engng2011; 86:18–46) for the Helmholtz equation if the parameters are distinct, that is,α1 ≠ α2. The nonstandard compact stencil is obtained by taking the linear interpolation of the diffusive terms (specified byα1) and the mass terms (specified byα2) that appear in the stencils obtained by the standard Galerkin FEM and the classical central FDM, respectively. On square meshes, these two schemes were shown to provide solutions to the Helmholtz equation that have a dispersion accuracy of fourth and sixth order, respectively (Int. J. Numer. Meth. Engng2011; 86:18–46). The objective of this paper is to study the performance of this PG method for the Helmholtz equation using nonuniform meshes and the treatment of natural boundary conditions.

A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies the characteristic layers which are found only in higher dimensions. This is done by matching the width of the characteristic layers to the width of the parabolic layers found for a fictitious 1D reaction–diffusion problem. The nondimensional element number is then defined using this fictitious reaction coefficient, the diffusion coefficient and an appropriate element size. Next, we introduce anisotropic element length vectorsliand the stabilization parametersαi,βiare calculated along theseli. Except for the modification to include the new dimensionless number that quantifies the characteristic layers, the definitions ofαi,βiare a direct extension of their counterparts in 1D. Usingαi,βiandli, objective characteristic tensors associated with the HRPG method are defined. The numerical artifacts across the characteristic layers are manifested as the Gibbs phenomenon. Hence, we treat them just like the artifacts formed across the parabolic layers in the reaction-dominant case. Several 2D examples are presented that support the design objective—stabilization with high-resolution

We propose a fourth‐order compact scheme on structured meshes for the Helmholtz equation given byR(φ):=f(x)+Δφ+ξ2φ=0. The scheme consists of taking the alpha‐interpolation of the Galerkin finite element method and the classical central finite difference method. In 1D, this scheme is identical to the alpha‐interpolation method (J. Comput. Appl. Math.1982;8(1):15–19) and in 2D making the choice α=0.5 we recover the generalized fourth‐order compact Padé approximation (J. Comput. Phys.1995;119:252–270;Comput. Meth. Appl. Mech. Engrg1998;163:343–358) (therein using the parameter γ=2). We follow (SIAM Rev.2000;42(3):451–484;Comput. Meth. Appl. Mech. Engrg1995;128:325–359) for the analysis of this scheme and its performance on square meshes is compared with that of the quasi‐stabilized FEM (Comput. Meth. Appl. Mech. Engrg1995;128:325–359). In particular, we show that the relative phase error of the numerical solution and the local truncation error of this scheme for plane wave solutions diminish at the rateO((ξℓ)4), where ξ, ℓ represent the wavenumber and the mesh size, respectively. An expression for the parameter α is given that minimizes the maximum relative phase error in a sense that will be explained in Section 4.5. Convergence studies of the error in theL2norm, theH1semi‐norm and thel∞Euclidean norm are done and the pollution effect is found to be small. Copyright © 2010 John Wiley & Sons, Ltd.

We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi /partial t + upartial phi /partial x - kpartial^2 phi /partial x^2 +s phi -f where k; s > o =0. The structure of the method in 1D is identical to the consistent approximate upwind Petrov– Galerkin (CAU/PG) method [A.C. Galeão, E.G. Dutra do Carmo, A consistent approximate upwind Petrov– Galerkin method for the convection-dominated problems, Comput. Methods Appl. Mech. Engrg. 68 (1988) 83–95] except for the definitions of the stabilization parameters. Such a structure may also be attained via the finite-calculus (FIC) procedure [E. Oñate, Derivation of stabilized equations for numerical solution of advective–diffusive transport and fluid flow problems, Comput. Methods Appl. Mech. Engrg. 151 (1998) 233–265; E. Oñate, J. Miquel, G. Hauke, Stabilized formulation for the advection–diffusion– absorption equation using finite-calculus and linear finite elements, Comput. Methods Appl. Mech. Engrg. 195 (2006) 3926–3946] by an appropriate definition of the characteristic length. The prefix ‘high-resolution’ is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in nonregular regimes. The design procedure embarks on the problem of circumventing the Gibbs phenomenon observed in L2-projections. Next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. It is shown that the method indeed reproduces stabilized high-resolution numerical solutions for a wide range of values of u; k; s and f . Finally, some remarks are made on the extension of the HRPG method to multidimensions.

In this work we will be based on two experimental-based statistical techniques, which allow us to determine approximately the residual resistance coefficient of the sailboat and the viscous coefficient and wave resistance coefficient in the case of merchants. For the calculation of the residual resistance in sailboats the most used method is the Delft series, and for the calculation of the residual resistance in merchants the most widespread method is that of Holtrop and Mennen. Both methods used experimental data to adjust a function, the results obtained with the functions are quite reliable, but it is difficult to improve the model since the statistical adjustment is complicated. For this reason, in this work we try to overcome that limitation and develop a tool that is capable of performing the same calculations, with the same or better reliability and also that allows to be constantly improved with experimental data. The tool used is the neural network.

This chapter presents an overview of some computational methods for analysis of ship hydrodynamics problems. Attention is focused on the description of a stabilized finite element formulation derived via a finite calculus procedure. Both arbitrary Lagrangian-Eulerian (ALE) and fully Lagrangian forms are presented. Details of the treatment of the free-surface waves and the interaction between the ship structure and the sea water are also given. Examples of application to a variety of ship hydrodynamics problems are shown.

In the present work a novel approach has been developed for the resolution of this problem of analysis of the movement of roll of a ship. The methodology used for this is based on the modification of the differential equations of the fluid dynamics (RANSE equations), including the movement of the free surface, by applying the finite calculus method. The modified equations are solved using an implicit predictor-corrector scheme and the finite element method (FEM). This resolution scheme is considered optimal for these types of problems, both in accuracy and in calculation time. As an example, it should be noted that for typical problems (more than 1,000,000 finite elements) less than 4 hours of CPU are required to solve several cycles of ship movement (Pentium IV). This allows the analysis of an array of tests in a few days or even hours, having a computer network or sufficient computing power.

El método Level Set utilizado en un amplio espectro de problemas de distinta índole, como la simulación de interfaces entre fluidos, el tratamiento de imágenes, la combustión,…tiene como principal objetivo la simulación numérica de la evolución de interfaces entre distintas regiones en contacto. El presente estudio es una revisión y aportación de nuevas propuestas para el método Level Set, en particular para su aplicación a la interfaz entre fluidos. Este método formulado independiente del tipo de método utilizado para la integración numérica de las ecuaciones en derivadas parciales que gobiernan el fenómeno a simular, disfruta de gran aceptación en el mundo de las diferencias finitas y existe abundante literatura al respecto. En este estudio se ha considerado la combinación del método Level Set y el método de Elementos Finitos no tan usual como en el caso anterior, dotando a este estudio de cierta singularidad. El estudio se ha organizado en 9 secciones o capítulos. En capítulos del 1 al 5 se presenta una introducción teórica al método Level Set con todo el rigor matemático. Se introducen también las últimas ideas desarrolladas en este campo. A lo largo de estos capítulos se propone a modo de ejemplo la aplicación del método Level Set a la interfaz entre dos fluidos. Los capítulos 6 y 7 se presentan los detalles computacionales de este método, así como los detalles de los algoritmos necesarios para la aplicación del método de Level Set. También se hace una revisión de la discretización por el método de los Elementos Finitos estabilizados de la ecuación de transporte, necesaria para la aplicación del método. Los capítulos 8 y 9 recogen varios resultados y conclusiones de la aplicación de este método a distintos ejemplos en dos y tres dimensiones, algunos de ellos presentes en gran parte de la literatura existente.

A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented. &nbsp

A stabilized semi-implicit frictional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized equations are derived at a differential level via a finite element calculus procedure. A new mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. One example of the efficiency of the stabilized semi-implicit algorithm for the coupled solution of fluid-structure interaction problems is presented.

The BAJEL project consists on the validation and final development of a comprehensive computer system to support the hydrodynamic design of ships. It aims at contributingto the optimal design of the new generations of ships, specially passenger vessels, improving their navigation conditions. This project is developed as a result of the joint work of a center specialized inComputational Analysis (CIMNE) and two Hydrodynamic Research Centers (ETSIN and Canal de El Pardo) within the framework of the industrial reality represented by the company BAZAN. This work presents the objectives of the project, describing the computer tools that have served as the basis and starting point for it. It also presents the achievements that in this field have achieved in recent years the member of the research teams. Finally, different results of studies carried out on real geometries of ships with special dedication to high-speed passenger ships are included.

El “Innovative Naval Prototype Transformable Craft” (T-Craft) es un nuevo concepto de buque desarrollado por la marina de los Estados Unidos de América para la conexión de una base en alta mar con tierra. El TCraft puede operar en múltiple modos, usándose para conectar una base intermedia de soporte con la principal, y luego ser utilizado como conexión de alta velocidad con la costa, transportando vehículos y otros equipos y carga pesada hasta la playa. El T-Craft se ha concebido como un buque de efecto superficie (Surface-Effect Ship, SES) con un colchón de aire activo entre dos cascos rígidos, que permite al buque operar a desplazamiento completo, con soporte parcial del colchón o con el colchón plenamente activo. Este artículo presenta el trabajo reciente de los autores en el desarrollo de un modelo de evaluación del comportamiento en la mar y la maniobrabilidad del T-Craft, incluyendo la interacción del faldón. Este modelo está basado en la resolución de las ecuaciones de flujo potencial en el dominio del tiempo, mediante el método de los elementos finitos, integrando la superficie libre a lo largo de las líneas de corriente. Este artículo revisa el algoritmo de interacción fluido estructura desarrollado para la simulación de la compleja dinámica de los sellos, en la interfaz entre el colchón de aire y el agua. El algoritmo se basa, por una parte, en un algoritmo explícito alternado que permite la comunicación entre los solvers fluido-dinámico y estructural mediante TCP-IP sockets, intercambiando fuerzas de presión y desplazamientos en los sellos durante la ejecución, y por otra parte, en un innovador esquema de secado-mojado que permite predecir la interacción del agua con los sellos. Se incluyen varios casos de aplicación de la metodología desarrollada sobre el modelo l XR-1B.