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International audience; The increasing number of frail elderly people in our aging society is becoming problematic: about 11% of community-dwelling older persons are frail and another 42% are pre-frail. Consequently, a major challenge in the coming years will be to test people over the age of 60 years to detect pre-frailty at the earliest stage and to return them to robustness using the targeted interventions that are becoming increasingly available. This challenge requires individual longitudinal monitoring (ILM) or follow-up of community-dwelling older persons using quantitative approaches. This paper briefly describes an effort to tackle this challenge. Extending the detection of the pre-frail stages to other population groups is also suggested. Appropriate algorithms have been used to begin the tracing of faint physiological signals in order to detect transitions from robustness to pre-frailty states and from pre-frailty to frailty states. It is hoped that these studies will allow older adults to receive preventive treatment at the correct institutions and by the appropriate professionals as early as possible, which will prevent loss of autonomy. Altogether, ILM is conceived as an emerging property of databases ("digital twins") and not the reverse. Furthermore, ILM should facilitate a coordinated set of actions by the caregivers, which is a complex challenge in itself. This approach should be gradually extended to all ages, because frailty has no age, as is testified by overwork, burnout, and post-traumatic syndrome.

The mechanical behavior at contact points in high-voltage electrical cable conductors is simulated to find where damage may occur. The presented approach is based on a numerical model that is referred to as the wire model. The critical zones are detected by simulating the mechanical behavior of a cable conductor section with a large number of contacts. For the wire model, a relevant regularized contact law that improves convergence of the contact algorithm compared to the standard contact law is implemented. This model is validated by making comparisons with experimental results available in the literature for various conductors. However, this approach employs a costly finite element method. In order to reduce the evaluation cost and allow sensitivity analysis of the input parameters, a surrogate model is proposed to replace the initial wire model. The surrogate model approximates the input–output relationship of the costly wire model. The choice of the sampling method that allows selection of the best fitting surrogate model for this application is discussed, but comparisons show little influence on the obtained scores. The robustness of the obtained result depends mostly on the chosen surrogate model, where the scores obtained with random forest and neural network are better than the scores obtained with linear and polynomial regression. The application is the French high-voltage network, but the work is relevant for any other network.

The granulation process using rotary drums technology, is an essential unit operation to form good quality granules in many industries such as food processing, pharmaceutical, petrochemical and mineral processing. The main objective of this work is to study and analyze, by CFD approach, the dynamics of solid fertilizer granules and the fluid phase, within an industrial inclined rotary drum granulator. Particularly, we studied the impact of the rotational speed, and angle of inclination of the equipment on the particles size distribution (PSD) within the solid phase. The three-dimensional CFD model that we are adapting is based on an Euler-Euler multiphase flow approach coupled with the kinetic theory of granular flow (KTGF), the appropriate model and numerical schemes were selected based on previous studies ( Zheng et al. (2019) ). As could be proved by experiments and simulation results, the particles size distribution depends on the rotational speed and show regime transition along the rotary drum. Our study demonstrates the capability of multiphase CFD model to predict the solid and fluid flow behaviors, and analyze the PSD of fertilizer granules inside the inclined rotary drum granulator.

This work focuses on the study of the phenomenon of vortex-induced vibrations in overhead lines under the effect of weak winds. Full three-dimensional simulation is not feasible because of the high length to width aspect ratios of the overhead lines. Thus a quasi-3D method based on strip theory is adopted in this work. This method decouples the system of interactions between the overhead line and the wind into a series of sub-systems. The fluid flow in each sub-system is represented as a series of independent rigid oscillating cylinder flows that are only coupled through the transmission line model. To avoid the use of a moving mesh for the fluid domain, a moving reference frame approach is employed. In this approach, the coordinate axes of the flow simulation are attached to the oscillating cylinder and an acceleration term in the flow equations accounts for the cable motion. Moreover, in order to take into account the turbulent effect in the flow, turbulence models, including RANS, LES and DES, are evaluated for the present application involving flows in the sub-critical regime. Finally, numerical test cases are performed in order to validate the turbulence models and the moving reference frame approach, then cable dynamics test cases are conducted to validate the quasi-3D method.

Slamming, the violent impact between a liquid and solid, has been known to be important for a long time in the ship hydrodynamics community. More recently, applications ranging from the transport of liquefied natural gas (LNG) in LNG carriers to the harvesting of wave energy with oscillating wave surge converters have led to renewed interest in the topic. The main reason for this renewed interest is that the extreme impact pressures generated during slamming can affect the integrity of the structures involved. Slamming fluid mechanics is challenging to describe, as much from an experimental viewpoint as from a numerical viewpoint, because of the large span of spatial and temporal scales involved. Even the physical mechanisms of slamming are challenging: What physical phenomena must be included in slamming models? An important issue deals with the practical modeling of slamming: Are there any simple models available? Are numerical models viable? What are the consequences for the design of structures? This article describes the loading processes involved in slamming, offers state-of-the-art results, and highlights unresolved issues worthy of further research.

An alternative to the stiffened-gas equation of state is proposed that corrects for unphysical behavior, namely the returning of negative pressure values for densities lower than the reference density. The question of generalizing a given isentropic equation of state is first addressed. Then, a regularized stiffened-gas equation of state is derived, which is the main goal of this work. Finally, the use of the new equation of state is briefly illustrated for a classical computational fluid dynamics benchmark concerning the evaluation of liquid impact on a wall.

Use of empirical correlations for state variables allows for more accurate physical representation than simplistic approaches offer. The simplistic approaches include the ideal or stiffened gas laws, both of which can have major shortcomings. This is particularly important when dealing with cases that are near saturation or where liquid compressibility is important. Hence, two new state variable libraries have been developed. The first is called Quicksteam, which is for water and steam, and the second is called Quickmethane, which is for methane liquid and vapour. Well established correlations of experimental data have been used to create the libraries. The libraries are coupled to a multi-phase flow solver and run as part of a fluid dynamics simulation. The calculations are quick and robust when the values remain within the limits of the correlations. Several test cases have been carried out to demonstrate the quality and validity of the results. The test cases include phase change, with gas and liquid compressibility. Results are compared with data from another simulation code that uses steam tables and also with experimental data. The libraries are developed with 3 applications in mind; the first is simulation of blast wave attenuation in aqueous foams, the second is wave impact on tank walls of liquefied natural gas carriers and the third is thermohydraulics. These libraries also have many other potential applications.

Summary The Lagrangian approach is usually used for the simulation of flow with strong shock waves. Moreover, this approach is particularly well suited to treatment of material interfaces in the case of multi-material flows. Unfortunately, this formulation leads to very large deformations in the mesh [1]. The Arbitrary Lagrangian Eulerian (ALE) method overcomes this drawback by using a mesh regularization that is based on an analysis of cell geometry, e.g. [2]. The regularization step may be considered as a method used to correct the non-convex and potentially tangled cells that constitute the mesh. In this paper we present a new approach to mesh regularization. Instead of using a purely geometric criterion we propose that the mesh evolution is computed based on the flow vorticity. This approach is called the L.E.L. method (Large Eddy Limitation) and it is aimed here to be used in Finite Volume direct ALE methods. The L.E.L. method is general, which means that it is not restricted to applications in the Finite Volume framework dedicated to fluid flow simulation; for instance, it could also be naturally applied to the Finite Element framework. This article is protected by copyright. All rights reserved.

A new two-dimensional interface reconstruction method that ensures continuity of the interface and preserves volume fractions is presented here. It is made of two steps, first, the minimization of a cost functional based on volume fractions least square errors by using dynamic programming, a fast and efficient scheme well known in image processing, and then a local correction phase. In each cell, the interface is made of two line segments joining two edges. This new interface reconstruction method, called Dynamic Programming Interface Reconstruction has been coupled with various advection schemes, among them the Lagrange + remap scheme. With a reasonable computational cost, it has been observed in various test cases that Dynamic Programming Interface Reconstruction is more accurate and less diffusive compared with other existing classical reconstruction methods. Copyright (C) 2017 John Wiley and Sons, Ltd.

Gas–liquid density ratio (DR) is a key dimensionless number in sloshing assessment methodologies of membrane containment systems for LNG tanks of floating structures. Earlier studies on the effect of DR were mainly statistical and effects of DR were usually mixed with those of gas compressibility and ullage gas pressure but attributed only to DR. In an attempt to separately study such effects, Karimi et al. (2015) [11] studied the effects of DR far from impact zones (global effects of gas–liquid density ratio) which proved to be small in the studied range of DR (0.0002 to 0.0060). The effects of DR near impact zones and before detection of any compressibility effects are referred to as local effects and correspond to modifications of wave shape before impact. They were treated in Karimi et al. (2016). This paper studies the influence of ullage gas at the same scale as well as scaling of sloshing loads at different scales. The test setups were similar to those presented in Karimi et al. (2015) [11] and Karimi et al. (2016) and consisted of three 2D model tanks as transverse slices of tank 2 (out of 4) of a membrane LNG carrier with total capacity of 152000 m3 at scales 1:10, 1:20 and 1:40. All model tests were performed at a fill level corresponding to 20% of the tank heights. Water as liquid and different ullage gases of helium (He), air, two mixtures of sulfur hexafluoride (SF6) and nitrogen (N2), and pure SF6, all at atmospheric pressure with a range of DRs from 0.0002 to 0.0060 were used. Synchronized High-speed video cameras (@4000 fps) and arrays of piezo-electric PCB pressure sensors (@40 kHz) monitored and measured impacts on the tank walls. The study was mainly based on the definition of Impact ID based on impact coincidence. The results are presented at 4 main stages. First, in the same way that sloshing loads measured in irregular model tests are treated in the current methodologies, the measured pressure peaks are studied as statistical samples. Next by the notion of impact ID, the effect of change of ullage gas at the same scale is verified. Thirdly with the same notion of impact ID, impacts are tracked down through three scales to verify scaling. At last dominant impact IDs are introduced. It is shown that the most severe impacts are generated by only a few dominant IDs.

Mathematical modelling and numerical simulations are widely used in the petrochemical industries for operator training, design, and process optimization. However, there is a lack of rigorous numerical modelling and simulations in the phosphate fertilizer industry. There exist many challenges in the production systems of phosphate fertilizers including (i) multiphase flows in the system involving liquids, solids or gases, (ii) particles with different size distributions, and (iii) dynamic variations in the physical properties including rheology and thermodynamic behavior. In the current study, using well-established techniques from computational fluid dynamics, we develop a model for the numerical simulation of multiphase flows in a conditioner operation unit used in the phosphate fertilizers facilities. The proposed model deals with the first step in the process, consisting on the preneutralizer, and it uses the Reynolds-averaged Navier-Stokes equations for modeling turbulent flow in the system. The preneutralization consist on a partial reaction between ammonia and phosphoric acid. Numerical results are presented for several scenarios and we particularly show the importance of the baffles on eliminating vortices, and also their effect on the different hydrodynamic performance criteria. This approach can be used to describe the behavior of reaction systems within this type of industrial plants and the analysis of the other sub-process of the fertilizer plant is an ongoing work.

International audience

Asset management is a major challenge for RTE (Reseau de Transport d’Electricite), the French TSO (Transmission System Operator) since electrical grid component maintenance and renewal represent important economic issues. Thus, improved assessment of their lifetime could lead RTE to substantial savings while assuring a high quality of service. To tackle this issue, RTE has gathered large amounts of data (monitoring, material failures, asset database …) and at the same time has tried to understand the phenomena of equipment ageing that could eventually lead to failure. RTE has chosen to take advantage of these two information sources when developing a hybrid model. This model combines data analysis of the gathered data sets and numerical simulation applied to the physical modelling of the phenomena involved in the accelerated ageing of equipment. To illustrate this approach, we are going to present a complete run of the hybrid computation to estimate lifespan of overhead line conductors due to aeolian vibrations. Aeolian vibrations, which are a type of vortex induced vibration, are a well-known phenomenon in the overhead lines (OHL) community. These vibrations are caused by the interaction between conductors and low-speed winds (velocities ranging from 1 m/s to 7 m/s). They induce one of the main causes of conductors damage: fretting fatigue in the clamp/conductor system. In this hybrid computation, damage due to fretting fatigue is evaluated using a mechanical multiscale approach where representative loading and loading scenarios are obtained using machine learning techniques.

Numerical simulation of two-phase flows based on the two-fluid six-equation model is the focus of this work. This approach is widely used in thermo-hydraulics for many industrial applications, particularly nuclear power plant safety analysis. A semi-implicit numerical method that has been successfully adopted in several industrial thermo-hydraulic codes, because of its efficiency and robustness, has been extended. In this paper, the governing equations are solved on unstructured grids with collocated variables to accommodate complicated geometries, and a deferred-correction method is used to deal with the non-orthogonality of unstructured grids. In addition, the numerical method is conservative, meaning that it is capable of capturing a shock wave exactly in single-phase flows, and ensuring the conservation of physically conservative quantities of a two-phase flow mixture. Numerical benchmarks and industrial test cases are performed in order to validate the numerical method and to evaluate its behavior with respect to different physical configurations.

A methodology is developed for the prediction of fretting fatigue phenomenon that results in crack initiation in strands of overhead power line conductors. A numerical approach based on finite element analysis is used to obtain the local stress and strain fields for application of crack initiation criteria in the high cycle fatigue regime. Solutions for the stress field in the stabilised state, where further loading cycles no longer introduce changes to the plastic deformation, are obtained using the stationary incremental method. Cases where convergence does not occur due to significant ratcheting are disregarded as low cycle fatigue. Post-treatment analysis that includes localised averaging is used to implement a fatigue criteria that estimates the crack initiation risk. Validation of this approach is made by comparing with results obtained from experimental measurements made on a simplified clamp wire configuration. Analyses of a simplified three-dimensional configuration with fretting is presented for a range of loading parameters and qualitative trends are established, which will prove invaluable for lifespan assessment of overhead power lines.

Most current numerical simulations on sloshing impact loads do not take into account the possibility of evaporation and condensation of the fluid. Our goal is to develop a numerical model able to simulate a wave impact with phase change in order to evaluate the influence of phase change on sloshing impact loads. The proposed model describes compressible multiphase flows with separate phases and non-equilibrium interfacial phase change. In this paper, the liquid–vapor interface is discretized using the interface reconstruction scheme of Braeunig et al., 2009. Implementation of a phase change model in such a framework is presented. In particular, the agreement of the model with the Second Law of Thermodynamics is discussed. The discretized model is first tested using simple return to equilibrium test cases. Then the model is applied to the one-dimensional piston problem that models the behavior of a compressed gas pocket during a breaking wave impact.

In this Note we give a simple volume formulation of capillary force. This formulation is not conservative but less singular than that of Lafaurie et al., (1994). Moreover our formulation allows to recover immediately Laplace’s law.

Gas–liquid density ratio ( D R ) is a key dimensionless number in sloshing assessment methodologies of membrane containment systems for LNG tanks of floating structures. Earlier studies on the effect of D R were mainly statistical and effects of D R were usually mixed with those of gas compressibility and ullage gas pressure but attributed only to D R . In an attempt to separately study such effects, part I of this work studied the effects of D R far from impact zones (global effects of gas–liquid density ratio) which proved to be small in the studied range of D R (0.0002 to 0.0060). The effects of D R near impact zones and in the instants prior to the detection of any compressibility effects are referred to as local effects and are treated in the current paper (part II). The test setup was identical to the one presented in Part I and consisted of two 2D model tanks representing transverse slices of tank 2 (out of 4) of a membrane LNG carrier with total capacity of 152000 m3 at scales 1:20 and 1:40. Both model tests were performed at 20% fill level of the tank heights. Water was the main liquid that was used. In some tests at scale 1:20 a solution of sodium polytungstate (SPT) was also used which had a higher density compared to water. Different ullage gases of helium (He), air, two mixtures of sulfur hexafluoride (SF6) and nitrogen (N2), and pure SF6, all at atmospheric pressure with a range of D R s from 0.0002 to 0.0060 were utilized. Synchronized high-speed video cameras (@4000 fps) and arrays of piezo-electric PCB (112A21 and 112M361) pressure sensors (@40 kHz) monitored and measured impacts on the tank walls. In Part II of the study short and more regular tank motions which generated highly repeatable single impact waves (SIW) were used instead of long irregular tank motions which were considered in part I. By comparing the single impact waves (SIW) generated by identical tank motions but with different D R s, it was observed that D R clearly modifies wave shapes prior to the moment of wave breaking. Larger D R s tend to slow down the wave front and delay breaking. It was also observed that larger D R s slightly slow down wave trough runup as well. Those effects would also lead to a mild shift of impact types by changing the D R (for example Flip-through to slosh or large gas-pocket to small gas-pocket impacts). By comparing single impact waves (SIW) generated by identical tank motions and the same D R but with different gas and liquid densities it was shown that keeping the same D R is essentially needed to keep the same impact geometry as recommended by the existing sloshing assessment methodologies. Free surface instabilities were also very similar for those waves generated with the same tank motions and similar DR but with different gases and liquids. Considering the reduction of wave kinetic energy by heavier 1 ullage gases as a relevant source of the statistical reduction of impact pressures and having in mind the mild shift of wave impact types caused by the change of D R it is still to be studied further why the heavier gas leads to smaller statistical pressures.

International audience

Our aim is to simulate numerically the impact of a breaking wave on a wall when phase change between liquid and gas happens (Ancellin et al. Proceedings of the 26th International Offshore and Polar Engineering Conference 886–893, 2016 [2]). We thus need to model two compressible phases separated by a sharp interface allowing mass exchange. It leads us to extend the Euler conservation equations to a hyperbolic system of balance laws including nonequilibrium phase change. For real fluids, when the value of the latent heat is high, there might be no solution to the Riemann problem. However we are able to discretize it in the finite volume framework using the Roe-type scheme of Ghidaglia et al. (Eur J Mech B/Fluids 20:841–867, 2001 [4]), the numerical diffusion playing the stabilizing role of the thermal diffusion.

Les travaux présentés dans cet article s’inscrivent dans un projet de R&D mis en place par RTE (Réseau de Transport d’Electricité) et visant à évaluer le vieillissement des conducteurs électriques de lignes aériennes par des outils de simulation numérique. Après avoir rappelé la géométrie de tels conducteurs et l’utilisation qui en est faite, le principal risque d’endommagement de ces derniers est présenté. Il s’agit du phénomène de fretting-fatigue intervenant à proximité des systèmes de fixation des conducteurs au niveau des pylônes, pouvant produire la rupture de brins les constituant. Ainsi, une méthodologie originale est proposée de façon à évaluer, par l’intermédiaire d’un modèle éléments finis, la durée de vie des conducteurs vis-à-vis de ce risque. Cette méthodologie est ensuite appliquée sur un cas-test dont les données proviennent de la littérature. Enfin, des perspectives sont données concernant le modèle numérique employé et l’intégration de la démarche dans le projet de R&D concerné.

We build an extension of the FVCF-ENIP multi-material solver for the computation of low Mach number fluid flows. The loss of accuracy generally noticed for Godunov type solvers when the Mach number goes to zero is handled through the renormalization of the viscosity matrix of the numerical flux. An implicit scheme is proposed in order to achieve numerical stability with reasonable CFL numbers. Its linear unconditional stability is proved in the case of a one-dimensional isentropic Euler system. Various numerical tests attest the efficiency of the method.

International audience; In this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable $\theta$), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific upwinding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity $u_{\theta}$.

The purpose of this paper is to show that the cell-centered upwind Finite Volume scheme applied to general hyperbolic systems of m conservation laws approximates smooth solutions to the continuous problem at order one in space and time. As it is now well understood, there is a lack of consistency for order one upwind Finite Volume schemes: the truncation error does not tend to zero as the time step and the grid size tend to zero. Here, following our previous papers on scalar equations, we construct a corrector that allows us to prove the expected error estimate for nonlinear systems of equations in one dimension.

Mitigation of blast waves by aqueous foams is an important technological issue. Despite many theoretical and experimental works on the subject, it has not been possible until now to have simple analytical expressions or abaci giving the pressure as a function of the distance to the charge, of its strength and of the characteristics of the foam. This naturally leads to attempts at using numerical simulations to obtain the desired results. The flow in an aqueous foam is complex as three fluids (air, steam and water) and phase transitions are involved, and moreover, the geometry of the free surfaces between these fluids is quite complicated. In this work, our aim is to build a code to handle this question. We rely on the classical averaged model for multifluid flow, which allows bypassing the local geometrical complexity of the flow at the cost of new variables, the volumetric rate of presence of each fluid. Since our goal is to simulate blast waves from a point, we shall safely assume that the flow has spherical symmetry. Hence, the models derived will be one dimensional. In this paper, we shall introduce closed systems of equations and describe their discretization via a finite volume method, the efficiency of which has already been demonstrated in the context of thermohydraulics. We restrict ourselves to the one-dimensional Cartesian case. Numerical benchmarks are provided in order to check the correct behavior of the code in terms of numerics and physics (e.g. phase transition). In the companion paper, D’Alesio et al. [29] , we extend the code to the spherical case and give simulation results in the case of strong shock waves propagating in foams.

International audience; The article discusses a two-fluid model. The fluids are described by their densities ρ±, velocities u± and the proportions α± in every point of space, α++α−=1. The underlying physical space is the 3-dimensional torus. The equations are ∂∂t(α±ρ±)+div(α±ρ±u±)=0, ∂∂t(α±ρ±u±)+div(α±ρ±u±⊗u±)+α±∇p=2μ±div(α±D(u±))+σ±α±ρ±∇Δ(α±ρ±), p=ργ. The constants μ±,σ± are the viscosity and surface tension coefficients. The article consists of two parts; in the first part the authors describe the theory of linearization of the equations. One of the conclusions of this part of their investigation is the following statement. Theorem. The region α−≥0 is invariant if and only if the fluid + is compressible. The second part concerns constructing global weak solutions for the nonlinear equations. The global weak solutions are constructed via a compactness argument. The compactness is established by proving a priori estimates using the conserved and monotonic quantities of the system. In addition to the standard mass, momentum and energy, the authors derive a new monotonic quantity with u±+ν∇R±R± where R±=α±ρ±. To construct approximate solutions, the authors add the following force to the momentum equations: εR±∇Δ2k+1R±−ε∇logR±−η(Δ2lu+u), where k,l are large integers and ε,η are parameters to be taken to zero to obtain the weak solution of the original system.

The wavemaker theory for a single layer fluid is a classical chapter of books on water waves. Indeed, linear waves with a desired amplitude, wave length, and frequency can be generated with the horizontal motion of a vertical plate, which is estimated from the wavemaker theory. However, there is much less work on the wavemaker theory when two fluids are superposed. Here we consider a variant of the classical wavemaker theory, which consists in a semi-infinite container with two layers of fluid of finite depths, bounded above by a rigid roof and on one vertical side by a piston. The lower fluid is incompressible (typically a liquid) and the upper fluid is a lighter gas (or liquid), which is considered to be incompressible as well. When the piston is set in motion, waves are created at the interface between the liquid and the gas. Resulting wave profiles and velocity fields based on linearized theory will be shown and compared to the classical one fluid wavemaker theory and to numerical simulations of wave generation with two layers of fluid. Two approaches will be presented, a stationary one, which is the equivalent to the wavemaker theory encountered in books in the case of a single layer, and the initial value problem that takes into account the transient motion from water and wavemaker at rest. The effects of both the density ratio, as well as the effects of the rigid roof are analyzed.Copyright © 2015 by ASME

This paper presents a general method for imposing boundary conditions in the context of hyperbolic systems of conservation laws. This method is particularly well suited for approximations in the framework of Finite Volume Methods in the sense that it computes directly the normal flux at the boundary. We generalize our approach to nonconservative hyperbolic systems and discuss both the characteristic and the noncharacteristic cases. We present several applications to models occurring in Computational Fluid Mechanics like the Euler equations for compressible inviscid fluids with real equation of state, shallow water equations, magnetohydrodynamics equations and two fluid models.

Offshore oil facilities are complex systems that involve elaborate physics combined with stochastic aspects related, for instance, to failure risk or price variation. Although there exist many dedicated software tools to simulate flows typically encountered in oil exploitations, there is still no tool that combines physical (mostly engineering fluid mechanics) and risk simulation. Such a tool could be useful to engineers or decision makers for specification, design and study of offshore oil facilities. We present a first step towards the creation of such a tool. Our current simulator is based on new Modelica components to simulate fluid flows and on stochastic simulation at a higher level, for modeling risk and costs. Modelica components implement physical models for single and two-phase flows in some typical devices of an offshore field. The risk simulation uses Markov chains and statistical indicators to assess performance and resilience of the system over several months or years of operation.

The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier–Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright © 2001 John Wiley & Sons, Ltd.

Coleman, Marcus & Mizel studied the thermodynamical equilibrium of second–order materials, i.e. materials for which the free–energy density depends not only on the concentration but also on its first and second gradients. They showed that in certain regimes such materials must exhibit equilibrium states that are non–uniform by proving that space–periodic solutions can have lower energy than space–uniform solutions. A dynamical systems approach is used here and it is shown that there is a critical value of the mean concentration. When the mean concentration crosses this critical value, the uniform state can lose its minimizing character and periodic or quasi–periodic states can have lower energy. Mathematically speaking, the presence of that critical value corresponds to a 1:1 resonance. The reversible 1:1 resonance has been studied extensively by Iooss & Peroueme, who showed that a reversible system having a 1:1 resonance singularity can be approximated as closely as desired by an integrable vector field. On this integrable field, all bounded solutions can be easily found and they are described by two integrals. However, in the present application, a zero eigenvalue is present in addition to the double imaginary eigenvalues. Bounded solutions are then described by three integrals. Moreover, since the average concentration must remain constant, a non–local constraint is added, which changes the results significantly. Finally, a selection principle for second–order materials stemming from energy considerations is introduced. The energy of all bounded solutions is compared with the energy of the uniform state. In some cases, non–uniform solutions have a lower energy and lead to non–uniform equilibrium states. More precisely, it is shown that space–periodic or space–quasi–periodic states are minima. Quite surprisingly, it may occur that non–uniform states appear by dilution, i.e. by decreasing the concentration.

Resume Dans ce travail, nous proposons une nouvelle technique pour discretiser les operateurs de diffusion dans le cadre des methodes de volumes finis. La methode consiste a associer a une approximation volumes finis sur un maillage donne, une representation elements finis sur le meme maillage et a mettre en œuvre une operation inverse. Nous presentons, a titre d'exemple, les resultats d'essais numeriques pour un probleme non lineaire, bidimensionnel sur un maillage non structure.

Resume La propagation unidirectionnelle d’ondes de faible amplitude et de grande longueur d’onde est decrite, dans de nombreux systemes physiques, par l’equation de Korteweg-de Vries. L’objet de ce travail est de proposer un probleme mixte bien pose lorsque le domaine spacial est borne. Plus precisement, nous etablissons l’existence de solutions locales en temps pour des donnees initiales dans l’espace de Sobolev ainsi que l’existence de solutions globales pour des donnees initiales petites dans cet espace.

By deriving Pohojaev-type identities we prove that nonelliptic nonlinear Schrodinger equations do not admit localized travelling wave solutions. Similary, we prove that the Davey-Stewartson hyperbolic-elliptic systems do not support travelling wave solutions except for a specific range of the parameters that comprises the DS II focusing case (where the existence of lumps is well known).

This note is a continuation of a previous article which appeared in this journal (1988, 74, 369-390). In the previous work we showed that a weak dissipation is suffiient to impose a finite dimensional behavior for Korteweg de Vries equations with (space) periodic boundary conditions. More precisely, it was shown that all the trajectories are captured. by a finite dimensional attractor. However, we were only able to show that the convergence of the trajectories holds good in the sense of weak topology. The goal of this note is to show that in fact this convergence holds true in the sense of strong topology.

277 Bethuel, F. and J.-M. Ghidaglia, Weak limits of solutions to the steady incompressible two-dimensional Euler equation in a bounded domain, Asymptotic Analysis 8 (1994) 277-291. In this work we show that any sequence u' of smooth solutions to the steady incompressible two-dimensional Euler equation in a bounded domain D, which converges weakly in L2(D) as !: goes to zero, converges to a weak solution of this equation provided curlu' remains bounded in LI(D).

We derive an Implicit Explicit finite volume scheme for the computation of radiation hydrodynamics. The convective part is handled through a classical upwind method while the reactive and diffusive parts are discretized thanks to a centered scheme. These results are compared to semi-analytic solutions obtained by Lowrie and Edwards [10].