Fast and Stable Schemes for Phase Fields Models

We propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to semi-implicit schemes for which the linear part is simplified using sparse pre-conditioners. The new methods allow to significant obtain a gain of CPU time. The numerical illustrations we give concern applications on pattern dynamics and on image processing (inpainting, segmentation) in two and three dimension cases

High-temperature oxidation resistance of chromium-based coatings deposited by DLI-MOCVD for enhanced protection of the inner surface of long tubes

For nuclear safety issues, there is an international effort to develop innovative “Enhanced Accident Tolerant Fuels” (EATF) materials. EATF cladding tubes are of particular interest because they constitute the first barrier against radioactive fission species dispersal in case of accidental scenario such as LOCA (LOss of Coolant Accident). Actual nuclear fuel claddings are made from Zr-based alloys and to increase safety margins, both mechanical strength and resistance to high-temperature oxidation have to be improved. Several alternatives using high-temperature oxidation resistant coatings for outer-wall protection have been proposed worldwide but there is currently no solution for the inner-wall protection. In order to resist to high temperature steam environment upon LOCA transients, internal Cr-based coatings deposited by DLI-MOCVD (Direct Liquid Injection of MetalOrganic precursors) were investigated. These hard metallurgical coatings could also be used in high-temperature corrosive environments as those encountered in aeronautics and other industries to protect 3D complex components. Thanks to a suitable chemistry of the liquid Cr precursor, bis(ethylbenzene)chromium, different coatings were deposited including: metal Cr, chromium carbides CrxCy and mixed carbides CrxSizCy. The high-temperature behavior of these Cr-based coatings under oxidizing atmospheres has been studied using several techniques and various oxidation tests including pure steam environment followed by water quenching down to room temperature to be representative of LOCA situations. Amorphous CrxCy coatings showed the most promising properties. For instance compared to uncoated substrate, they shift the catastrophic oxidation towards higher temperatures and delay the complete oxidation of the substrate at 1473K of >2h. The results are discussed in terms of oxidation mechanisms and protection of the fuel claddings inner surface deduced from fine characterizations of the samples before and after oxidation tests

Male-induced early puberty correlates with the maturation of arcuate nucleus kisspeptin neurons in does

In goats, early exposure of spring-born females to sexually active bucks induces an early puberty onset assessed by the first ovulation. This effect is found when females are continuously exposed well before the male breeding season starting in September. The first aim of this study was to evaluate whether a shortened exposure of females to males could also lead to early puberty. We assessed the onset of puberty in Alpine does isolated from bucks (ISOL), exposed to wethers (CAS), exposed to intact bucks from the end of June (INT1), or mid-August (INT2). Intact bucks became sexually active in mid-September. At the beginning of October, 100% of INT1 and 90% of INT2 exposed does ovulated, in contrast to the ISOL (0%) and CAS (20%) groups. This demonstrated that contact with males that become sexually active is the main factor prompting precocious puberty in females. Furthermore, a reduced male exposure during a short window before the breeding season is sufficient to induce this phenomenon. The second aim was to investigate the neuroendocrine changes induced by male exposure. We found a significant increase in kisspeptin immunoreactivity (fiber density and number of cell bodies) in the caudal part of the arcuate nucleus of INT1 and INT2 exposed females. Thus, our results suggest that sensory stimuli from sexually active bucks (e.g., chemosignals) may trigger an early maturation of the ARC kisspeptin neuronal network leading to gonadotropin-releasing hormone secretion and first ovulation

Schémas compacts hermitiens sur la Sphère : applications en climatologie et océanographie numérique

The problem to obtain accurate simulations of the atmospheric and oceanic equations has become essential in recent years for a proper understanding of the climate change. The full mathematical model to simulate is rather complex. It consists of the coupling of several equations involving fluid dynamics and thermodynamics. In the 19th century, Adhémar Barré de Saint-Venant first formulated the equations describing the dynamic of a fluid subject to gravity and bottom topography. This system is Shallow Water equations. The goal of this thesis is to develop and analyze a numerical scheme to solve the shallow water equation on a rotating sphere. First, a mathematical analsysis of finite difference operators that will be used on the sphere is presented. These schemes are then used to solve various equations in a spehreical setting, in particular the advection equation, the wave equation and the Burgers equation. Stability, accuracy and conservation properties are studied. In a second part, I consider in detail the Cubed-Sphere grid. This particular spherical grid has the mesh topology of a cube. Another interpretation makes use of great circles, this allows to obtain spherical discret operators gradient, divergence and curl of a preved third order. These operators are numercially of 4th order. Numerial results are show in particular for the SW equations an acurracy similar to the one of conservative schemes of 4th order published recentlyL’enjeu de la simulation de la dynamique atmosphérique et océanographique a pris ces dernières années une importance accrue avec la question du réchauffement climatique. Le modèle à simuler est complexe. Il combine les équations de la mécanique des fluides avec celles de la thermodynamique. Au 19ème siècle, le mathématicien Adhémar Barré de Saint-Venant formule un système d’équations aux dérivées partielles décrivant les mouvements d’un fluide soumis à la gravité et de faible épaisseur. Il s’agit des équations Shallow Water. L’objectif de cette thèse est de développer et d’analyser un algorithme de résolution des équations Shallow Water sur une sphère en rotation. Dans un premier temps, j’étudie différents aspects mathématiques des opérateurs aux différences finis utilisés par la suite en géométrie sphérique. Les schémas aux différences obtenus sont utilisés pour résoudre l’équation de transport, l’équation des ondes et l’équation de Burgers. Les propriétés de stabilité précision et conservation sont analysées. Dans un second temps, la grille Cubed-Sphere est introduite et analysée. La structure de ce maillage est analogue à celle d’un cube. L'interprétation de la Cubed-Sphere à l’aide de grands cercles permet de construire des opérateurs sphériques discrets gradient, divergence et vorticité d'ordre au moins égal à 3 (en pratique d'ordre 4). La troisième partie de la thèse est dédiée à différents tests pour le système d’équations Shallow Water ainsi que pour l’équation d’advection. Les résultats démontrent une précision proche de celle obtenue par les algorithmes conservatifs d'ordre 4 les plus récent

Hermitian compact schemes on the sphere : applications in numerical climatology and oceanography

L’enjeu de la simulation de la dynamique atmosphérique et océanographique a pris ces dernières années une importance accrue avec la question du réchauffement climatique. Le modèle à simuler est complexe. Il combine les équations de la mécanique des fluides avec celles de la thermodynamique. Au 19ème siècle, le mathématicien Adhémar Barré de Saint-Venant formule un système d’équations aux dérivées partielles décrivant les mouvements d’un fluide soumis à la gravité et de faible épaisseur. Il s’agit des équations Shallow Water. L’objectif de cette thèse est de développer et d’analyser un algorithme de résolution des équations Shallow Water sur une sphère en rotation. Dans un premier temps, j’étudie différents aspects mathématiques des opérateurs aux différences finis utilisés par la suite en géométrie sphérique. Les schémas aux différences obtenus sont utilisés pour résoudre l’équation de transport, l’équation des ondes et l’équation de Burgers. Les propriétés de stabilité précision et conservation sont analysées. Dans un second temps, la grille Cubed-Sphere est introduite et analysée. La structure de ce maillage est analogue à celle d’un cube. L'interprétation de la Cubed-Sphere à l’aide de grands cercles permet de construire des opérateurs sphériques discrets gradient, divergence et vorticité d'ordre au moins égal à 3 (en pratique d'ordre 4). La troisième partie de la thèse est dédiée à différents tests pour le système d’équations Shallow Water ainsi que pour l’équation d’advection. Les résultats démontrent une précision proche de celle obtenue par les algorithmes conservatifs d'ordre 4 les plus récentsThe problem to obtain accurate simulations of the atmospheric and oceanic equations has become essential in recent years for a proper understanding of the climate change. The full mathematical model to simulate is rather complex. It consists of the coupling of several equations involving fluid dynamics and thermodynamics. In the 19th century, Adhémar Barré de Saint-Venant first formulated the equations describing the dynamic of a fluid subject to gravity and bottom topography. This system is Shallow Water equations. The goal of this thesis is to develop and analyze a numerical scheme to solve the shallow water equation on a rotating sphere. First, a mathematical analsysis of finite difference operators that will be used on the sphere is presented. These schemes are then used to solve various equations in a spehreical setting, in particular the advection equation, the wave equation and the Burgers equation. Stability, accuracy and conservation properties are studied. In a second part, I consider in detail the Cubed-Sphere grid. This particular spherical grid has the mesh topology of a cube. Another interpretation makes use of great circles, this allows to obtain spherical discret operators gradient, divergence and curl of a preved third order. These operators are numercially of 4th order. Numerial results are show in particular for the SW equations an acurracy similar to the one of conservative schemes of 4th order published recentl

Spherical Shallow Water Waves Waves Simulation by a Cubed Sphere Finite Difference Solver

International audienceWe consider the test suite for the Shallow Water (SW) equations on the sphere suggested in [27, 28]. This series of tests consists of zonally propagating wave solutions of the linearized Shallow Water (LSW) equations on the full sphere. Two series of solutions are considered. The first series [27] is referred to as "barotropic". It consists of an extension of the Rossby-Haurwitz test case in [33]. The second series [28] referred to as (Matsuno) "baroclinic", consists of a generalisation of the solution to LSW in an equatorial chanel introduced by Matsuno [17]. The Hermitian Compact Cubed Sphere (HCCS) model which is used in this paper is a Shallow Water solver on the sphere that was introduced in [4]. The spatial approximation is a center finite difference scheme based on high order differencing along great circles. The time stepping is performed by the explicit RK4 scheme or by an exponential scheme. For both test cases, barotropic and baroclinic, the results show a very good agreement of the numerical solution with the analytic one, even for long time simulations

Numerical simulation of propagation problems on the sphere with a compact scheme

We consider propagation problems on the sphere and their approximation by a compact finite difference scheme. The scheme used in this study uses the Cubed Sphere, a particular spherical grid with logically Cartesian structure. A central role is played by the standard one dimensional Hermitian derivative [22]. This compact scheme operates along great circles, thus avoiding any one sided compact scheme. [10, 11]. The scheme is centered. A simple high frequency filter is added to reinforce the stability. The final scheme is reminiscent of compact schemes in Computational Aeroacoustics or in turbulence Direct Numerical Simulation. Numerical results on a broad series of numerical test cases in climatology are presented, including linear convection problems, the linearized shallow water equations and the non linear shallow water equations. The results demonstrate the interest of the present approach in a variety of situations arising in numerical climatology

Fast and Stable Schemes for Phase Fields Models

International audienceWe propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to semi-implicit schemes for which the linear part is simplified using sparse pre-conditioners. The new methods allow to significant obtain a gain of CPU time. The numerical illustrations we give concern applications on pattern dynamics and on image processing (inpainting, segmentation) in two and three dimension cases