Portail HAL Ensta
Not a member yet
11080 research outputs found
Sort by
Construction of polynomial particular solutions of linear constant-coefficient partial differential equations
No full textInternational audienceThis paper introduces general methodologies for constructing closed-form solutions to linear constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in two and three spatial dimensions. Polynomial solutions have recently regained significance in the development of numerical techniques for evaluating volume integral operators and also have potential applications in certain kinds of Trefftz finite element methods. The equations covered in this work include the isotropic and anisotropic Poisson, Helmholtz, Stokes, linearized Navier-Stokes, stationary advection-diffusion, elastostatic equations, as well as the time-harmonic elastodynamic and Maxwell equations. Several solutions to complex PDE systems are obtained by a potential representation and rely on the Helmholtz or Poisson solvers. Some of the cases addressed, namely Stokes flow, Maxwell’s equations and linearized Navier-Stokes equations, naturally incorporate divergence constraints on the solution. This article provides a generic pattern whereby solutions are constructed by leveraging solutions of the lowest-order part of the partial differential operator (PDO). With the exception of anisotropic material tensors, no matrix inversion or linear system solution is required to compute the solutions. This work is accompanied by a freely-available Julia library, ElementaryPDESolutions.jl, which implements the proposed methodology in an efficient and user-friendly format
How does sailor morphology affect Olympic windfoil performance?
No full textInternational audienceThe Olympic windfoiling class consists of a windsurfing board that flies above the water with a hydrofoil. The sail is held by the sailor whose weight and position are key in the balance with aerodynamic and hydrodynamic forces. Therefore, understanding performance relative to sailor morphology is crucial. Windfoil performance is complex to model due to factors like aero-hydrodynamics, cavitation [1], and/or free surface effects [2] and fluid-structure interactions [3]. To assess the performance of a windfoil, the use of a Velocity Prediction Program (VPP) is a conventional approach [4] for sailing boats.This work presents the development of a 5DOF VPP tailored to windfoiling, optimizing sail angle, sailor position, and kinematic orientation. A simplified biomechanical model of the sailor is included to evaluate the impact of the sailor’s morphology on performance. The numerical flow model uses the Vortex Lattice Method (VLM), without considering structural effects, to minimize calculation costs.The results show that the VPP converges to different optimal positions and orientations for sailors with different morphologies. This work is part of the project ”Du Carbone à l’Or Olympique” and is funded by the Agence Nationale de La Recherche (ANR) through grant n°ANR-19- STHP-0002
Heat and momentum losses in H 2 –O2 –N 2/Ar detonations: on the existence of set-valued solutions with detailed thermochemistry
No full textInternational audienceThe effect of heat and momentum losses on the steady solutions admitted by the reactive Euler equations with sink/source terms is examined for stoichiometric hydrogen–oxygen mixtures. Varying degrees of nitrogen and argon dilution are considered in order to access a wide range of effective activation energies, E a,eff / R u T 0 , when using detailed thermochemistry. The main results of the study are discussed via detonation velocity-friction coefficient ( D – c f ) curves. The influence of the mixture composition is assessed, and classical scaling for the prediction of the velocity deficits, D ( c f,crit ) / D CJ , as a function of the effective activation energy, E a,eff / R u T 0 , is revisited. Notably, a map outlining the regions where set-valued solutions exist in the E a,eff / R u T 0 -- α space is provided, with α denoting the momentum–heat loss similarity factor, a free parameter in the current study
Guided modes in a hexagonal periodic graph like domain
No full textInternational audienceThis paper deals with the existence of guided waves and edge states in particular two-dimensional media obtained by perturbing a reference periodic medium with honeycomb symmetry. This reference medium is a thin periodic domain (the thickness is denoted δ > 0) with an hexagonal structure, which is close to an honeycomb quantum graph. In a first step, we show the existence of Dirac points (conical crossings) at arbitrarily large frequencies if δ is chosen small enough. We then perturbe the domain by cutting the perfectly periodic medium along the so-called zigzag direction, and we consider either Dirichlet or Neumann boundary conditions on the cut edge. In the two cases, we prove the existence of edges modes as well as their robustness with respect to some perturbations, namely the location of the cut and the thickness of the perturbed edge. In particular, we show that different locations of the cut lead to almost-non dispersive edge states, the number of locations increasing with the frequency. All the results are obtained via asymptotic analysis and semi-explicit computations done on the limit quantum graph. Numerical simulations illustrate the theoretical results
Développement d'une méthode DEM polyédrique pour la simulation de la relocalisation du combustible nucléaire lors d'un APRP
No full textNational audienceLors d’un Accident de Perte de Réfrigérant Primaire (APRP), les crayons combustibles sont soumis à des sollicitations thérmo-mécaniques intenses. Celles-ci peuvent provoquer un ballonnement ponctuel de la gaine dans lequel le combustible, présent dans un état fragmenté, peut se relocaliser radialement et axialement et induire un état de température élevé conduisant à la rupture de la gaine, donc de la première barrière de sûreté. Des recherches visent à étudier cet effet grâce à des modèles numériques avancés. Ici, on propose d’assimiler le combustible fragmenté à un milieu granulaire et de mettre en œuvre une modélisation par éléments discrets de la relocalisation des fragments. L’objectif final étant de prendre en compte l’interaction entre fragments et gaz de fission ainsi que la rupture de la gaine et l’expulsion des fragments, un premier objectif est de reprendre la méthode des éléments discrets (DEM) disponible dans le code Europlexus, et de l’étendre à des géométries polyédriques, en s’inspirant d’une méthode utilisée dans le code Rockable basée sur des sphéro-polyèdres
Frequency-Fresnel Domain Equalization for Underwater Acoustic OCDM Systems
No full textInternational audienceOrthogonal Chirp Division Multiplexing (OCDM) is a promising multi-carrier modulation for Underwater Acoustic (UWA) systems, as several low complexity OCDM receivers capable of exploiting the channel diversity have already been proposed. However, OCDM receivers are often designed and studied over time-invariant channels. This paper proposes a hybrid Frequency-Fresnel domain equalizer to enhance the system performance over the doubly selective UWA channel. Our method first estimates the Channel Impulse Response (CIR) using pilot blocks and the Least Square (LS) criterion. The CIR is then sparsified by removing coefficients below a threshold, and the receiver performs equalization in the frequency domain. To address residual InterSymbol Interference (ISI) in doubly selective UWA channels, we propose to equalize again the obtained symbols in the Fresnel domain and perform jointly phase synchronization. Simulations both on synthetic channels and a real underwater channel show that the proposed algorithm improves significantly the BER performance compared to existing methods.</div
Characterization of the interface fracture energy dependency on mixed mode fracture between rigid fiber and soft matrix
No full textInternational audienceAn enhanced version of the Rubber Cord Adhesion Inflation Test (RCAIT) has been designed to experimentally assess the internal pressure and cable tension applied to the specimen needed to propagate a crack along the matrix/reinforcement interface. To calculate the critical strain energy release rate, we develop a semi-analytical model describing the deformation of a hyperelastic tube under loading conditions that reflect the ones applied experimentally. A more comprehensive numerical model of the test is also proposed to investigate the influence of loading conditions on rubber deformation near the crack tip. Comparison of different experimental data sets with the theoretical/numerical data demonstrates that the new experimental setup allows for a reliable determination of the rubber/cord interface failure envelope under combined loading conditions
An HLS algorithm for the direct synthesis of complex control flow graphs into finite state machines with implicit datapath
No full textInternational audienceIn this paper, we introduce an efficient algorithm for automating the direct transformation of a control flow graph (CFG) into a synthesizable finite-state machine with implicit datapath (FSMD). In our opinion, this transformation has not received sufficient attention: although the passage of a CFG to FSMD is mentioned in many textbooks on digital system design, and presented as trivial, to our knowledge it has never been explicitly formulated nor automated. Our experience shows, moreover, that this process is trickier than claimed. We believe our algorithm can become a key transformation for high-level synthesis (HLS) of control-dominated applications presenting a low level of instruction-level parallelism. Our paper presents the algorithm in detailed procedural form. Experimental measurements carried out on synthetic benchmarks shows its effectiveness.</div
A Likelihood-Based Triangulation Method for Uncertainties in Through-Water Depth Mapping
No full textInternational audienceCoastal environments, which are crucial for economic and strategic reasons, heavily rely on accurate bathymetry for safe navigation and resource monitoring. Recent advancements in through-water photogrammetry have shown promise in mapping shallow waters efficiently. However, robust uncertainty modeling methods for these techniques, especially in challenging coastal environments, are lacking. This study introduces a novel likelihood-based approach for through-water photogrammetry, focusing on uncertainties associated with camera pose—a key factor affecting depth mapping accuracy. Our methodology incorporates probabilistic modeling and stereo-photogrammetric triangulation to provide realistic estimates of uncertainty in Water Column Depth (WCD) and Water–Air Interface (WAI) height. Using simulated scenarios for both drone and airborne surveys, we demonstrate that viewing geometry and camera pose quality significantly influence resulting uncertainties, often overshadowing the impact of depth itself. Our results reveal the superior performance of the likelihood ratio statistic in scenarios involving high attitude noise, high flight altitude, and complex viewing geometries. Notably, drone-based applications show particular promise, achieving decimeter-level WCD precision and WAI height estimations comparable to high-quality GNSS measurements when using large samples. These findings highlight the potential of drone-based surveys in producing more accurate bathymetric charts for shallow coastal waters. This research contributes to the refinement of uncertainty quantification in bathymetric charting and sets a foundation for future advancements in through-water surveying methodologies
Nonlinear normal modes as invariant manifolds for model order reduction
No full textInternational audienceThis chapter introduces the nonlinear normal modes (NNMs) for vibrating systems as invariant manifolds of the phase space, and their use for model order reduction of nonlinear structures. NNMs are defined as the continuation of the linear normal modes by enforcing tangency to a subset of master eigenspaces for small amplitudes. Conservative and damped dynamics are considered, as well as forced systems where the NNMs are time-dependent. A systematic procedure using the parametrisation method for invariant manifolds, is devised for their computation, directly operating from the physical space, and up to arbitrary order of expansions. Applications to academic examples are shown to highlight the ability of the method to deal with hardening/softening behaviour, the presence of a folding manifold, and superharmonic resonance. In each case, reduced-order models with minimal dimensions and excellent accuracy, are derived