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A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration, exploiting an arbitrary number of hierarchical fidelity levels, i.e., performance evaluations coming from different models, solvers, or discretizations, characterized by different accuracy. The method is intended to accurately predict the design performance while reducing the computational effort required by simulation-driven design (SDD) to achieve the global optimum. The overall MF prediction is evaluated as a low-fidelity trained surrogate corrected with the surrogates of the errors between consecutive fidelity levels. Surrogates are based on stochastic radial basis functions (SRBF) with least squares regression and in-the-loop optimization of hyperparameters to deal with noisy training data. The method adaptively queries new training data, selecting both the design points and the required fidelity level via an active learning approach. This is based on the lower confidence bounding method, which combines performance prediction and associated uncertainty to select the most promising design regions. The fidelity levels are selected considering the benefit-cost ratio associated with their use in the training. The method's performance is assessed and discussed using four analytical tests and three SDD problems based on computational fluid dynamics simulations, namely the shape optimization of a NACA hydrofoil, the DTMB 5415 destroyer, and a roll-on/roll-off passenger ferry. Fidelity levels are provided by both adaptive grid refinement and multi-grid resolution approaches. Under the assumption of a limited budget of function evaluations, the proposed MF method shows better performance in comparison with the model trained by high-fidelity evaluations only.

International audience; A generalized multi-fidelity (MF) metamodel of CFD (computational fluid dynamics) computations is presented for design-and operational-space exploration, based on machine learning from an arbitrary number of fidelity levels. The method is based on stochastic radial basis functions (RBF) with least squares regression and in-the-loop optimization of RBF parameters to deal with noisy data. The method is intended to accurately predict ship performance while reducing the computational effort required by simulation-based optimization (SBDO) and/or uncertainty quantification problems. The present formulation here exploits the potential of simulation methods that naturally produce results spanning a range of fidelity levels through adaptive grid refinement and/or multi-grid resolution (i.e. varying the grid resolution). The performance of the method is assessed for one analytical test and three SBDO problems based on CFD simulations, namely a NACA hydrofoil, the DTMB 5415 model, and a roll-on/roll-off passenger ferry in calm water. Under the assumption of a limited budget of function evaluations, the proposed MF method shows better performance in comparison with its single-fidelity counterpart. The method also shows very promising results in dealing with and learning from noisy CFD data.

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This paper presents an efficient screening tool, based on the 2D strip method and the CFD-based approach. The proposed method allows the study of the dynamics of the vortex-induced vibration (VIV) phenomenon with almost the same accuracy as a fully 3D Fluid-Structure interaction (FSI) model, but with a reduction in computational times by a factor of nearly 20 compared to the 3D approach. Such a large reduction makes the use of CFD-based analysis feasible on a workstation within a reasonable time frame and opens the possibility of CFD approaches in a subsea pipeline design process.

When cavitation occurs around hydrofoils it is the cause of noise radiation, vibration and erosion. Consequently numerical cavitation models have been developped and tested over the last decades (Schnerr and Sauer [1]). However, recent works show that numerical predictions for cavitating flow might be very sensitive to the spatial resolution of the mesh and require dicretization errors estimations (Negrato et al. [2], Asnaghi et al. [3]). The experimental and numerical approches joined in this work are the first step of the validation of the ISIS-CFD code for cavitating flows with fluid-structure interaction. Although, only results for a rigid profile in cavitating conditions are presented in this work. The test case is a NACA0015 profile in the cavitation tunnel located at the french Naval Academy Research Institute. On the numerical side, the ISIS-CFD code is used to solve the unsteady Reynolds Averaged Navier Stokes Equations (uRANSE). The two phases mixture dynamics are solved thanks to an interface capturing method and the Sauer cavitation model. The test case is first adressed using a two-dimensional computational domain. A set of unstructured grids is generated using Hexpress to perform a grids and time steps convergence study and obtain uncertainty estimations for both wetted and cavitating flow conditions. Then, the same study is done for an extended three-dimensional geometry taking into account the lateral walls of the tunnel and the convergent section located upstream of the test section. Influences of the turbulence quantities at the inflow and the cavitation model parameters are also assessed. The numerical results are compared with experimental effort measurements, high-speed camera signals and PIV acquisitions provided by Lelong [4]. From the verification and validation analysis a three dimensional grid and a set of computational parameters are chosen for future calculations with fluid-structure interaction and cavitation.

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International audience; Surrogate models are simplified models for the behaviour of a complex system, based on a limited number of operating points where the system behaviour is simulated accurately. In hydrofoil design for sailing yachts, surrogate models can be used both for automatic shape optimisation of the foil and for performance evaluation of the entire yacht in the context of a VPP, as a response surface. We present an adaptive method for the construction of surrogate models which can be used for both these objectives, with a simple change of parameters. A Gaussian process regression (GPR) is used for the data fitting, while the adaptive choice of sample points is based either on the GPR variance or on a combination with a cross-validation error estimation. A first test on analytical functions shows that the cross-validation approach is superior for response surface creation, while both adaptation methods are equally suited for shape optimisation. A second test on the shape optimisation of a two-dimensional hydrofoil indicates that for moderate immersion depths, the optimum shape is not sensible to the distance to the free surface.

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International audience; Most engineering design processes rely on physical or numerical experiments to evaluate the candidate design performances. When the design space is large or when the model response is complex, the possibly high computational expense poses a challenge since the number of simulations is usually limited by time or financial cost. This is even more of a challenge when performing global optimization as many evaluations are required. Hydrofoil optimisation for naval applications is typically facing these limitations. One way to address this limitation is to build a simplified model of the actual model from responses of experiments. Meta-modelling is the process of generating such models of models or meta-models. This process is also referred in engineering as surrogate modelling. Strategies involving surrogate models are used in a wide range of engineering fields to efficiently address computational cost limitations. Evaluations of a surrogate model are cheap and can be used for visualization, trade-off analysis and optimization. Nevertheless, building a surrogate requires evaluating the original model at specified design points and gathering the corresponding responses. The amount of points needed to approximate the behaviour of a numerical model depends on the complexity of the response, which is not necessarily known beforehand. The chosen sampling strategy plays an important role in the quality of the surrogate. Under-sampling might not allow capturing the complexity of the phenomenon and over-sampling could lead to expensive computation times. Adaptive sampling or response-adaptive design uses the responses to the simulation for adjusting the sampling design in a sequential way while the surrogate is being constructed. This allows for determining and minimizing the required number of points for efficient global surrogate construction. Hydrofoil optimisation can be performed in different ways. Hydrofoils can be either optimized independently from the rest of the ship they will be fitted to or, in a more robust way, by taking into account the whole ship and simulating its behaviour in a third party simulating code (VPP). We usually switch from one approach to another according to the design stage. Surrogate models can be used for both approaches but, if build in adaptive way, will be sampled quite differently. If the goal is response surface creation, exploration (sampling from areas of high uncertainty) will be favoured whereas exploitation (sampling areas likely to offer improvement over the current best observation) will lead to sampling areas close to the optimum. In this study we investigate the possibility of both creating responses surface and perform shape optimisation with the same tool. We chose Gaussian process regression (GPR), also known as Kriging, to create the surrogates. After defining an initial set of points using a traditional design of experiment method, the following points are chosen in a sequential and adaptive way. An appropriate acquisition function (infill sampling criterion) has been investigated to access the exploration/exploitation trade-off. The efficiency is tested on analytical function (Branin function) and then applied both to an optimisation and response surface creation of a 2D hydrofoil NACA profile.

An overview is presented of the activities conducted within the NATO STO Task Group AVT-204 to “Assess the Ability to Optimize Hull Forms of Sea Vehicles for the Best Per- formance in a Sea Environment.” The objective is the development of a greater understanding of the potential and limitations of the hydrodynamic optimization tools. These include low- and high-fidelity solvers, automatic shape modification methods, and multi-objective optimiza- tion algorithms, and are limited here to a deterministic application. The approach includes simulation-based design optimization methods from different research teams. Analysis tools include potential flow and Reynolds-averaged Navier-Stokes equation solvers. Design modifica- tion tools include global modification functions, control point based methods, and parametric modelling by hull sections and basic curves. Optimization algorithms include particle swarm optimization, sequential quadratic programming, genetic and evolutionary algorithms. The ap- plication is the hull-form and propeller optimization of the DTMB 5415 model for significant conditions, based on actual missions at sea.

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International audience; The flow around the well-known KRISO Very Large Crude Carrier no. 2 (KVLCC2) is characterised by boundary layer thickening, flow separation, and vortex creation on the aft body of the ship, leading to a very nonhomogeneous velocity field in the propeller plane (figure 1). It is known since the 1990s that the numerical simulation of such flows is highly sensitive to the treatment of the turbulence. For RANS equations, standard turbulence models perform poorly; measures like the anisotropic treatment of turbulence production are necessary in order to compute correctly the most famous aspect of the flow, the hook-shaped low-velocity zone in the main longitudinal vortex. The case is therefore justly famous as a test of turbulence models for marine flow simulation. The focus of most studies that use the KVLCC2, such as Larsson et al. [3], is the comparison of different flow solvers or different turbulence models. To keep such studies compact and accessible, comparisons are mostly done for a few physical features only. The propeller plane with its hook shape in the axial velocity is often studied. The objective of this paper, on the contrary, is to use a single numerical simulation of good quality to visualise the entire flow field around the aft body of the KVLCC2.We then attempt a physical analysis of this flow, searching explanations of less-studied features such as the outer boundary layer shape and the flow behind the propeller hub cap.We hope that better knowledge of the flow will allow, in the future, to understand more precisely the behaviour of different turbulence models, which may ultimately lead to better models. The paper starts with a definition of the test case and the computation (section 2). Then section 3 presents the visualisation and analysis of the numerical solution. To assess the validity of the analysis, selected aspects of the solution are compared with experiments in section 4. The conclusion (section 5) addresses the challenges for turbulence modelling which the KVLCC2 test case still presents.

International audience; The Proper Generalized Decomposition (PGD) method has been used to solve many kinds of problem in multi-dimensional spaces: quantum chemistry, kinetic theory description of complex uid and chemical master equations, etc...The interested reader can refer to [1] for a recent review in the context of computational rheology. The present work describes a first implementation of the PGD formulation into a general unstructured finite-volume unsteady Navier-Stokes solver dedicated to viscous ship hydrodynamics (ISIS-CFD [2]).

International audience; The accurate modeling of surface tension is an important prerequisite to correctly simulate the phenomena that take place in smaller scales. However, modeling surface tension for complex hydrodynamic flows, such as marine applications, poses several difficulties. More specifically the method has to deliver accurate curvature results for absurdly changing topological features of the free surface. As a result, the topological features of the free surface have to be dynamically recovered during the calculation. In this work, we present a surface tension (ST) method implemented in the VOF-RANS flow solver ISIS-CFD [1], that has the above features and present preliminary results obtained for a flat inclined plane cutting the free-surface in an asymmetric flow. In order to capture the geometry of free-surface, the method uses a marching cube algorithm (see for example [2]). The algorithm dynamically generates the grid of the volume fraction isosurface representing the free surface. The curvature is calculated by the generated grid, using a high-order differencing method based on least squares. The results obtained for the test case studied, demonstrate that the method can be used in practical cases to directly visualize complex three dimensional flow regimes and investigate the surface tension effects for smaller scales. For example, the figure below shows the unstructured surface grid generated for the ventilating air vortex emanating near the plate's (transparent plane) submerged leading edge corner and a detail of the free surface roll-up.REFERENCES[1] P. Queutey and M. Visonneau, “An interface capturing method for free-surface hydrodynamicflows”, Computers and Fluids, Vol. 36, pp. 1481−1510, (2007).[2] T.S. Newman, H. Yi, “A survey of the marching cubes algorithm”, Computers and Graphics,Vol. 30, pp. 854–879, (2006).

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International audience; This paper studies if adaptive grid refinement combined with finite-volume simulation of the incompressible RANS equations can be used to obtain grid-independent solutions of realistic flow problems. It is shown that grid adaptation based on metric tensors can generate series of meshes for grid convergence studies in a straightforward way. For a two-dimensional airfoil and the flow around a tanker ship, the grid convergence of the observed forces is sufficiently smooth for numerical uncertainty estimation. Grid refinement captures the details of the local flow in the wake, which is shown to be grid converged on reasonably-sized meshes. Thus, grid convergence studies using automatic refinement are suitable for high-Reynolds incompressible flows.

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International audience; This paper is devoted to the verification and validation exercises with the ISIS-CFD code conducted for the Tokyo 2015 workshop. In addition to numerical uncertainty estimation, we also address issues such as the effect of turbulence modelization, wall resolved versus wall modeled approach, propeller resolved versus propeller modeled approach for self-propulsion simulation, etc.

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One of the trends in computational fluid dynamics today is the use of the ever-increasing computational resources for the high-fidelity simulation of more and more complex flows. For example, simulations are performed for realistic geometries such as ships with their propellers and appendices. Flow separation, vortex shedding and breakup are simulated in detail. Finally, multiphysics computations such as fluid-structure interaction or the modelling of cavitation become more and more common.The results of such simulations depend heavily on the physical models being used, such as the turbulence model in the Reynolds-averaged Navier-Stokes (RANS) equations. In many cases, such models are being applied in situations which are far more complex than the ones for which they were developed and which may be outside their range of validity. Research of physical modelling for today's realistic simulations is therefore of prime importance.A complication for this study is the inevitable appearance of numerical errors. To accurately assess the precision of a physical model, we need to know a numerical solution in which the numerical errors are small with respect to the physical ones: a solution that is close to grid convergence. In simple cases, it may be possible for an experienced user to generate reasonable meshes by hand which provide sufficiently small numerical errors. However, for complex flows it is impossible to know beforehand what mesh size is needed where, in order to obtain grid convergence. Adaptive grid refinement is therefore the ideal technique to master the numerical error.In this paper, we pose the question whether grid refinement can be used in such a way as to guarantee that the solution of a complex flow problem is grid-independent. The work is based on the ISIS-CFD unstructured finite-volume incompressible RANS solver developed by ECN-CNRS [1], which contains an integrated anisotropic grid refinement technique [2]. As a reference, a two-dimensional airfoil flow is simulated on a series of ever finer adapted meshes; these results are compared with simulations on different fine meshes in order to understand if a converging series of adapted meshes truely leads to mesh-independence. The findings of this initial case will then be applied to the simulation of the three-dimensional vortical wakes behind ships in sideslip condition.

Submitted to Ocean Engineering on 15 July 2014

International audience; Fluid Structure Interaction (FSI) problems are commonly encountered in naval architecture. They can be solved with a monolithic or a partitioned approach [1]. The partitioned approach (or block-iterative method) consists in solving the fluid and the structure problems in a segregated way. Even if this can be done through a single solver, it is most commonly used in a co-simulation context and consequently it is especially well fitted to the resolution of complex FSI problems. Indeed, the co-simulation allows to use complex models for both the fluid and the structure without additional simplifications because each solvers can be numerically adapted to its problem.

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In this paper, a dynamic computation of the Groupama 3 foil is performed. Foils are thin profiles, placed under the hull of a ship, allowing it to provide a lifting force. This study is placed in the context of the 2013 America’s Cup, which will see the appearance of a new kind of high performance multihull. At high speeds, the foils are subject to intense hydrodynamic forces and to movement due to the sea. The deformations are then sizable and there is a risk of ventilation, cavitation or vibration that could lead to important modification of the hydrodynamic forces or to the destruction of the foil. It is therefore necessary to quantify correctly its deformation and its response to dynamical efforts. The foil/water interaction is a strongly coupled problem, due to the thickness of the object. In this paper, the problem is solved using a segregated approach. The main problems resulting of such a method are the numerical stability and remeshing. These problems are detailed and some results presented. As a first test case, the simulation of a vortex excited elastic plate proposed by Hüb- ner is presented. This case is very demanding in terms of coupling stability and mesh deformation. Then, the foil of Groupama 3 is modelled in a simplified form without hull and free surface, and then in a more realistic conditions with free surface and waves.

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For the simulation of water flow with waves, grid refinement must be anisotropic to limit the total grid size. For these flows, the grid has to be refined at the water surface, to resolve the conservation law which indicates the surface position, and below the surface to resolve the water flow. A combined criterion is presented, based on the free-surface position and on the Hessian of the pressure. It is shown that this criterion creates suitable grids for two- and three-dimensional flows.

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The Gothenburg 2010 Workshop on Numerical Hydrodynamics gathered 33 groups with computations for one or more of 18 test cases. All results were collected and discussed at a meeting in Gothenburg in December 2010. In the present paper some representative examples from the workshop are presented. The complete results are found in the workshop Proceedings.

International audience; Ce papier présente les résultats numériques obtenus par le code de calcul ISIS-CFD pour un bateau amarré dans des vagues. Le cas choisi est celui d'un transporteur de gaz naturel liquéfié (LNG Carrier) en faible profondeur. Les amarres sont modélisées par quatre ressorts. En tenant compte des amarres, les forces exercées sur le bateau sont plus faibles que si le bateau était libre et sans amarres. Le mouvement de cavalement présente une double période alors que les mouvements de pilonnement et de tangage sont réguliers.

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