Academic literature on the topic 'A posteriori local VF correction'

This paper presents a novel active contour model in a variational level set formulation for simultaneous segmentation and bias field estimation of medical images. An energy function is formulated based on improved Kullback-Leibler distance (KLD) with likelihood ratio. According to the additive model of images with intensity inhomogeneity, we characterize the statistics of image intensities belonging to each different object in local regions as Gaussian distributions with different means and variances. Then, we use the Gaussian distribution with bias field as a local region descriptor in level set formulation for segmentation and bias field correction of the images with inhomogeneous intensities. Therefore, image segmentation and bias field estimation are simultaneously achieved by minimizing the level set formulation. Experimental results demonstrate desirable performance of the proposed method for different medical images with weak boundaries and noise.

In 1977, Nourein (Intern. J. Comput. Math. 6:3, 1977) constructed a fourth-order iterative method for finding all zeros of a polynomial simultaneously. This method is also known as Ehrlich’s method with Newton’s correction because it is obtained by combining Ehrlich’s method (Commun. ACM 10:2, 1967) and the classical Newton’s method. The paper provides a detailed local convergence analysis of a well-known but not well-studied generalization of Nourein’s method for simultaneous finding of multiple polynomial zeros. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with verifiable initial condition and a posteriori error bound) for the classical Nourein’s method. Each of the new semilocal convergence results improves the result of Petković, Petković and Rančić (J. Comput. Appl. Math. 205:1, 2007) in several directions. The paper ends with several examples that show the applicability of our semilocal convergence theorems.

A large eddy simulation (LES) a posteriori study is conducted for a temporal mixing layer which initially contains different species in the lower and upper streams and in which the initial pressure is larger than the critical pressure of either species. A vorticity perturbation, initially imposed, promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid-scale (SGS) fluxes, a new SGS term denoted a ‘pressure correction’ (p correction) in the momentum equation. This additional term results from filtering the Navier–Stokes equations and represents the gradient of the difference between the filtered p and p computed from the filtered flow field. A previous a priori analysis, using a direct numerical simulation (DNS) database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of regions of high density-gradient magnitude that populated the entire flow; in that study, the appropriateness of several SGS-flux models was assessed, and a model for the p-correction term was proposed.In the present study, the constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid of, or including, the SGS p-correction term. A new p-correction model, different from that of the a priori study, is used, and the results of the two p-correction models are compared. The results reveal that the former is less computationally intensive and more accurate than the latter in reproducing global and structural features of the flow. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC) model, in conjunction with the Yoshizawa (YO) model for the trace, the gradient (GRC) model and the scale similarity (SSC) models, all exercised with the a priori study constant-coefficient values calibrated at the transitional state. Further, dynamic SGS-flux model LESs are performed with the p correction included in all cases. The dynamic models are the Smagorinsky (SMD) model, in conjunction with the YO model, the gradient (GRD) model and ‘mixed’ models using SMD in combination with GRC or SSC utilized with their theoretical coefficient values. The LES comparison is performed with the filtered-and-coarsened DNS (FC-DNS) which represents an ideal LES solution. The constant-coefficient models including the p correction (SMCP, GRCP and SSCP) are substantially superior to those devoid of it; the SSCP model produces the best agreement with the FC-DNS template. For duplicating the local flow structure, the predictive superiority of the dynamic mixed models is demonstrated over the SMD model; however, even better predictions in capturing vortical features are obtained with the GRD model. The GRD predictions improve when LES is initiated at a time past the initial range in which the p-correction term rivals in magnitude the leading-order term in the momentum equation. Finally, the ability of the LES to predict the FC-DNS irreversible entropy production is assessed. It is shown that the SSCP model is the best at recovering the domain-averaged irreversible entropy production. The sensitivity of the predictions to the initial conditions and grid size is also investigated.

Abstract. We present lower/middle tropospheric column-averaged CH4 mole fraction time series measured by nine globally distributed ground-based FTIR (Fourier transform infrared) remote sensing experiments of the Network for the Detection of Atmospheric Composition Change (NDACC). We show that these data are well representative of the tropospheric regional-scale CH4 signal, largely independent of the local surface small-scale signals, and only weakly dependent on upper tropospheric/lower stratospheric (UTLS) CH4 variations. In order to achieve the weak dependency on the UTLS, we use an a posteriori correction method. We estimate a typical precision for daily mean values of about 0.5% and a systematic error of about 2.5%. The theoretical assessments are complemented by an extensive empirical study. For this purpose, we use surface in situ CH4 measurements made within the Global Atmosphere Watch (GAW) network and compare them to the remote sensing data. We briefly discuss different filter methods for removing the local small-scale signals from the surface in situ data sets in order to obtain the in situ regional-scale signals. We find good agreement between the filtered in situ and the remote sensing data. The agreement is consistent for a variety of timescales that are interesting for CH4 source/sink research: day-to-day, monthly, and inter-annual. The comparison study confirms our theoretical estimations and proves that the NDACC FTIR measurements can provide valuable data for investigating the cycle of CH4.

Abstract. We present lower/middle tropospheric column-averaged CH4 mole fraction time series measured by nine globally distributed ground-based FTIR (Fourier Transform InfraRed) remote sensing experiments of the Network for the Detection of Atmospheric Composition Change (NDACC). We show that these data are well representative of the tropospheric regional-scale CH4 signal, largely independent of the local small-scale signals of the boundary layer, and only weakly dependent on upper tropospheric/lower stratospheric (UTLS) CH4 variations. In order to achieve the weak dependency on the UTLS, we use an a posteriori correction method. We estimate a typical precision for daily mean values of about 0.5% and a systematic error of about 2.5%. The theoretical assessments are complemented by an extensive empirical study. For this purpose, we use surface in-situ CH4 measurements made within the Global Atmosphere Watch (GAW) network and compare them to the remote sensing data. We briefly discuss different filter methods for removing the local small-scale signals from the surface in-situ datasets in order to obtain the in-situ regional-scale signals. We find good agreement between the filtered in-situ and the remote sensing data. The agreement is consistent for a variety of time scales that are interesting for CH4 source/sink research: day-to-day, monthly, and inter-annual. The comparison study confirms our theoretical estimations and proves that the NDACC FTIR measurements can provide valuable data for investigating the cycle of CH4.

Methane (CH4) is one of the most contributing anthropogenic greenhouse gases (GHGs) in terms of global warming. Industry is one of the largest anthropogenic sources of methane, which are currently only roughly estimated. New satellite hyperspectral imagers, such as PRISMA, open up daily temporal monitoring of industrial methane sources at a spatial resolution of 30 m. Here, we developed the Characterization of Effluents Leakages in Industrial Environment (CELINE) code to inverse images of the Korpezhe industrial site. In this code, the in-Scene Background Radiance (ISBR) method was combined with a standard Optimal Estimation (OE) approach. The ISBR-OE method avoids the use of a complete and time-consuming radiative transfer model. The ISBR-OEM developed here overcomes the underestimation issues of the linear method (LM) used in the literature for high concentration plumes and controls a posteriori uncertainty. For the Korpezhe site, using the ISBR-OEM instead of the LM -retrieved CH4 concentration map led to a bias correction on CH4 mass from 4 to 16% depending on the source strength. The most important CH4 source has an estimated flow rate ranging from 0.36 ± 0.3 kg·s−1 to 4 ± 1.76 kg·s−1 on nine dates. These local and variable sources contribute to the CH4 budget and can better constrain climate change models.

Shroud cavities in aero engines are typically formed by a labyrinth seal between the rotating turbine shroud and the stationary casing wall. To mitigate rub-in and reduce weight, the casing often features honeycomb structures above the rotor seal fins. In this paper, the aerodynamic performance of such honeycomb structures is experimentally investigated using a rotating test rig featuring both smooth and honeycomb-tapered casing walls. Measurements show that the discharge coefficient decreases for the honeycomb configuration while losses and subsequent windage heating of the flow increase. A variation in rotational speed reveals additional sensitivities to the local flow field in the swirl chamber. Numerical simulations are conducted and validated using the experiments. A good agreement between the prediction and measurements of the jet via the evolution of pressure across the sealing fins is identified. In contrast, the prediction of losses and integral parameters reveals larger deficits. Empirical correlations from available literature satisfactorily predict the leakage mass flow rate if rotation is low and if the casing is smooth. High rotation and the presence of honeycombs, however, prove challenging and reveal the potential for further improvements. We propose a simple a-posteriori correction that can capture the effect of honeycomb structures on seal discharge by accounting for changes in momentum and flow area.

AbstractCalculations of point defect energetics with Density Functional Theory (DFT) can provide valuable insight into several optoelectronic, thermodynamic, and kinetic properties. These calculations commonly use methods ranging from semi-local functionals with a-posteriori corrections to more computationally intensive hybrid functional approaches. For applications of DFT-based high-throughput computation for data-driven materials discovery, point defect properties are of interest, yet are currently excluded from available materials databases. This work presents a benchmark analysis of automated, semi-local point defect calculations with a-posteriori corrections, compared to 245 “gold standard” hybrid calculations previously published. We consider three different a-posteriori correction sets implemented in an automated workflow, and evaluate the qualitative and quantitative differences among four different categories of defect information: thermodynamic transition levels, formation energies, Fermi levels, and dopability limits. We highlight qualitative information that can be extracted from high-throughput calculations based on semi-local DFT methods, while also demonstrating the limits of quantitative accuracy.

Dans cette Thèse de Doctorat, nous nous intéressons à deux problématiques: (i) le développement de stratégies de stabilisation pour des méthodes de type discontinuous Galerkin (DG) appliquées à des écoulements shallow-water fortement non-linéaires, (ii) le développement d'une stratégie de modélisation et de simulation numérique des interactions non-linéaires entre les vagues et un objet flottant en surface, partiellement immergé. Les outils développés dans le cadre du premier axe de travail sont mis à profit et valorisés au cours de la deuxième partie.Les méthodes de discrétisation de type DG d'ordre élevé présentent en général des problèmes de robustesse en présence de singularités de la solution. Ces singularités peuvent être de plusieurs natures: discontinuité de la solution, discontinuité du gradient ou encore violation de la positivité de la hauteur d'eau pour des écoulements à surface libre. Nous introduisons dans la première partie de ce manuscript deux approches de type Finite-Volume Subcells permettant d'apporter une réponse à ces problèmes de robustesse. La première approche repose sur une correction a priori du schéma DG associée à un limiteur TVB et un limiteur de positivité. La seconde approche s'appuie quant à elle sur une correction a posteriori permettant d'identifier avec une meilleure précision les cellules incriminée, ainsi que sur les propriétés de robustesse inhérentes au schéma Volumes-Finis limite d'ordre un. Cette seconde approche permet d'assurer la robustesse du schéma DG initial en présence de discontinuité, ainsi que la positivité de la hauteur d'eau, tout en préservant une excellente qualité d'approximation, bénéficiant d'une résolution de l'ordre de la sous-maille. De façon préliminaire, cette seconde approche est également étendue au cas de la dimension deux d'espace horizontal. De nombreux cas-test permettent de valider cette approche.Dans la seconde partie, nous introduisons une nouvelle stratégie numérique conçue pour la modélisation et la simulation des interactions non linéaires entre les vagues en eau peu profonde et un objet flottant partiellement immergé. Au niveau continu, l'écoulement situé dans le domaine extérieur est globalement modélisé par les équations hyperboliques non-linéaires de Saint-Venant, tandis que la description de l'écoulement sous l'objet se réduit à une équation différentielle ordinaire non linéaire. Le couplage entre l'écoulement et l'objet est formulé comme un problème au bord, associé au calcul de l'évolution temporelle de la position des points d'interface air-eau-objet. Au niveau discret, la formulation proposée s'appuie sur une approximation DG d'ordre arbitraire, stabilisée à l'aide de la méthode de correction locale des sous-cellules (a posteriori) introduite dans la première partie. L'évolution temporelle de l'interface air-eau-objet est calculée à partir d'une description Arbitrary Lagrangian-Eulerian (ALE) et d'une transformation appropriée entre la configuration initiale et celle dépendant du temps. Pour n'importe quel ordre d'approximation polynomiale, l'algorithme résultant est capable de: (1) préserver la loi de conservation géométrique discrète (DGCL), (2) garantir la préservation de la positivité de la hauteur d'eau au niveau des sous-cellules, (3) préserver la classe des états stationnaires au repos (well-balancing), éventuellement en présence d'un objet partiellement immergé.Plusieurs validations numériques sont présentées, montrant le caractère opératoire de cette approche, et mettant en évidence que le modèle numérique proposé: (1) permet effectivement de modéliser les différents types d'interactions vague / objet flottants, (2) calcul efficacement l' évolution temporelle des points de contact air-eau-objet et redéfinit en conséquence le nouveau maillage grâce à la méthode ALE, (3) gère avec précision et robustesse les possibles singularités de l'écoulement, (4) préserve la haute résolution des schémas DG au niveau des sous-cellules
In this Ph.D., we investigate two main research problems: (i) the design of stabilization patches for higher-order discontinuous-Galerkin (DG) methods applied to highly nonlinear free-surface shallow-water flows, (ii) the construction of a new numerical approximation strategy for the simulation of nonlinear interactions between waves in a free-surface shallow flow and a partly immersed floating object. The stabilization methods developed in the first research line are used in the second part of this work.High-order discontinuous-Galerkin (DG) methods generally suffer from a lack of nonlinear stability in the presence of singularities in the solution. Such singularities may be of various kinds, involving discontinuities, rapidly varying gradients or the occurence of dry areas in the particular case of free-surface flows. In the first part of this work, we introduce two new stabilization methods based on the use of Finite-Volume Subcells in order to alleviate these robustness issues. The first method relies on an a priori limitation of the DG scheme, together with the use of a TVB slope-limiter and a PL. The second one is built upon an a posteriori correction strategy, allowing to surgically detect the incriminated local subcells, together with the robustness properties of the corresponding lowest-order Finite-Volume scheme. This last strategy allows to ensure the nonlinear stability of the DG scheme in the vicinity of discontinuities, as well as the positivity of the discrete water-height, while preserving the subcell resolution of the initial scheme. This second strategy is also preliminary investigated in the two dimensional horizontal case. An extensive set of test-cases assess the validity of this approach.In the second part, we introduce a new numerical strategy designed for the modeling and simulation of nonlinear interactions between surface waves in shallow-water and a partially immersed surface piercing object. At the continuous level, the flow located in the textit{exterior} domain is globally modeled with the nonlinear hyperbolic shallow-water equations, while the description of the flow beneath the object reduces to a nonlinear ordinary differential equation. The coupling between the flow and the object is formulated as a free-boundary problem, associated with the computation of the time evolution of the spatial locations of the air-water-body interface. At the discrete level, the proposed formulation relies on an arbitrary-order discontinuous Galerkin approximation, which is stabilized with the a posteriori Local Subcell Correction method through low-order finite volume scheme introduced in the first part. The time evolution of the air-water-body interface is computed from an Arbitrary-Lagrangian-Eulerian (ALE) description and a suitable smooth mapping between the original frame and the current configuration. For any order of polynomial approximation, the resulting algorithm is shown to: (1) preserves the Discrete Geometric Conservation Law, (2) ensures the preservation of the water-height positivity at the subcell level, (3) preserves the class of motionless steady states (well-balancing), possibly with the occurrence of a partially immersed object.Several numerical computations and test-cases are presented, highlighting that the proposed numerical model(1) effectively allows to model all types of wave / object interactions, (2) efficiently provides the time-evolution of the air-water-body contact points and accordingly redefine the new mesh-grid thanks to ALE method (3) accurately handles strong flow singularities without any robustness issues, (4) retains the highly accurate subcell resolution of discontinuous Galerkin schemes

Le but de cette étude est d'améliorer les performances, en termes d'espace mémoire et de temps de calcul, des simulations actuelles de l'Interaction mécanique Pastille-Gaine (IPG), phénomène complexe pouvant avoir lieu lors de fortes montées en puissance dans les réacteurs à eau sous pression. Parmi les méthodes de raffinement de maillage, méthodes permettant de simuler efficacement des singularités locales, une approche multi-grille locale a été choisie car elle présente l'intérêt de pouvoir utiliser le solveur en boîte noire tout en ayant un faible nombre de degrés de liberté à traiter par niveau. La méthode Local Defect Correction (LDC), adaptée à une discrétisation de type éléments finis, a tout d'abord été analysée et vérifiée en élasticité linéaire, sur des configurations issues de l'IPG, car son utilisation en mécanique des solides est peu répandue. Différentes stratégies concernant la mise en oeuvre pratique de l'algorithme multi-niveaux ont également été comparées. La combinaison de la méthode LDC et de l'estimateur d'erreur a posteriori de Zienkiewicz-Zhu, permettant d'automatiser la détection des zones à raffiner, a ensuite été testée. Les performances obtenues sur des cas bidimensionnels et tridimensionnels sont très satisfaisantes, l'algorithme proposé se montrant plus performant que des méthodes de raffinement h-adaptatives. Enfin, l'algorithme a été étendu à des problèmes mécaniques non linéaires. Les questions d'un raffinement espace/temps mais aussi de la transmission des conditions initiales lors du remaillage ont entre autres été abordées. Les premiers résultats obtenus sont encourageants et démontrent l'intérêt de la méthode LDC pour des calculs d'IPG
The aim of this study is to improve the performances, in terms of memory space and computational time, of the current modelling of the Pellet-Cladding mechanical Interaction (PCI),complex phenomenon which may occurs during high power rises in pressurised water reactors. Among the mesh refinement methods - methods dedicated to efficiently treat local singularities - a local multi-grid approach was selected because it enables the use of a black-box solver while dealing few degrees of freedom at each level. The Local Defect Correction (LDC) method, well suited to a finite element discretisation, was first analysed and checked in linear elasticity, on configurations resulting from the PCI, since its use in solid mechanics is little widespread. Various strategies concerning the implementation of the multilevel algorithm were also compared. Coupling the LDC method with the Zienkiewicz-Zhu a posteriori error estimator in orderto automatically detect the zones to be refined, was then tested. Performances obtained on two-dimensional and three-dimensional cases are very satisfactory, since the algorithm proposed is more efficient than h-adaptive refinement methods. Lastly, the LDC algorithm was extended to nonlinear mechanics. Space/time refinement as well as transmission of the initial conditions during the remeshing step were looked at. The first results obtained are encouraging and show the interest of using the LDC method for PCI modelling

Le but de cette étude est d'améliorer les performances, en termes d'espace mémoire et de temps de calcul, des simulations actuelles de l'Interaction mécanique Pastille-Gaine (IPG), phénomène complexe pouvant avoir lieu lors de fortes montées en puissance dans les réacteurs à eau sous pression. Parmi les méthodes de raffinement de maillage, méthodes permettant de simuler efficacement des singularités locales, une approche multi-grille locale a été choisie car elle présente l'intérêt de pouvoir utiliser le solveur en boîte noire tout en ayant un faible nombre de degrés de liberté à traiter par niveau. La méthode Local Defect Correction (LDC), adaptée à une discrétisation de type éléments finis, a tout d'abord été analysée et vérifiée en élasticité linéaire, sur des configurations issues de l'IPG, car son utilisation en mécanique des solides est peu répandue. Différentes stratégies concernant la mise en oeuvre pratique de l'algorithme multi-niveaux ont également été comparées. La combinaison de la méthode LDC et de l'estimateur d'erreur a posteriori de Zienkiewicz-Zhu, permettant d'automatiser la détection des zones à raffiner, a ensuite été testée. Les performances obtenues sur des cas bidimensionnels et tridimensionnels sont très satisfaisantes, l'algorithme proposé se montrant plus performant que des méthodes de raffinement h-adaptatives. Enfin, l'algorithme a été étendu à des problèmes mécaniques non linéaires. Les questions d'un raffinement espace/temps mais aussi de la transmission des conditions initiales lors du remaillage ont entre autres été abordées. Les premiers résultats obtenus sont encourageants et démontrent l'intérêt de la méthode LDC pour des calculs d'IPG.