An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach

We present a numerical method to accurately simulate particle size distributions within the formalism of rate equation cluster dynamics. This method is based on a discretization of the associated Fokker-Planck equation. We show that particular care has to be taken to discretize the advection part of the Fokker-Planck equation, in order to avoid distortions of the distribution due to numerical diffusion. For this purpose we use the Kurganov-Noelle-Petrova scheme coupled with the monotonicity-preserving reconstruction MP5, which leads to very accurate results. The interest of the method is highlighted on the case of loop coarsening in aluminum. We show that the choice of the models to describe the energetics of loops does not significantly change the normalized loop distribution, while the choice of the models for the absorption coefficients seems to have a significant impact on it

Existence of global Chebyshev nets on surfaces of absolute Gaussian curvature less than 2π

International audienceWe prove the existence of a global smooth Chebyshev net on complete, simply connected surfaces when the total absolute curvature is bounded by 2π. Following Samelson and Dayawansa, we look at Chebyshev nets given by a dual curve, splitting the surface into two connected half-surfaces, and a distribution of angles along it. An analogue to the Hazzidakis formula is used to control the angles of the net on each half-surface with the integral of the Gaussian curvature of this half-surface and the Cauchy boundary conditions. We can then prove the main result using a theorem about splitting the Gaussian curvature with a geodesic, obtained by Bonk and Lang

A consistent discrete element method for quasi-static and dynamic elasto-plasticity

We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's ratio). We consider quasi-static and dynamic elasto-plasticity, and in the latter situation, a pseudo-energy conserving time-integration method is employed. The computational cost of the time-stepping method is moderate since it is explicit and used with a naturally diagonal mass matrix. Numerical examples are presented to illustrate the robustness and versatility of the method for quasi-static and dynamic elasto-plastic evolutions

Tree-Based Morse Regions: A Topological Approach to Local Feature Detection

International audience—This paper introduces a topological approach to local invariant feature detection motivated by Morse theory. We use the critical points of the graph of the intensity image, revealing directly the topology information as initial " interest " points. Critical points are selected from what we call a tree-based shape-space. Specifically, they are selected from both the connected components of the upper level sets of the image (the Max-tree) and those of the lower level sets (the Min-tree). They correspond to specific nodes on those two trees: (1) to the leaves (extrema) and (2) to the nodes having bifurcation (saddle points). We then associate to each critical point the largest region that contains it and is topologically equivalent in its tree. We call such largest regions the Tree-Based Morse Regions (TBMR). TBMR can be seen as a variant of MSER, which are contrasted regions. Contrarily to MSER, TBMR relies only on topological information and thus fully inherit the invariance properties of the space of shapes (e.g., invariance to affine contrast changes and covariance to continuous transformations). In particular, TBMR extracts the regions independently of the contrast, which makes it truly contrast invariant. Furthermore, it is quasi parameter-free. TBMR extraction is fast, having the same complexity as MSER. Experimentally, TBMR achieves a repeatability on par with state-of-the-art methods, but obtains a significantly higher number of features. Both the accuracy and the robustness of TBMR are demonstrated by applications to image registration and 3D reconstruction

Fokker-Planck approach of Ostwald ripening: simulation of a modified Lifschitz-Slyozov-Wagner system with a diffusive correction

International audienceWe propose a well-balanced scheme for the modified Lifshitz-Slyozov equation, that incorporates a size-diffusion term. The method uses the Fokker-Planck structure of the equation. In turn, large time simulations can be performed with a reduced computational cost, since the time step constraints are relaxed. The simulations bring out the critical mass threshold and the relaxation to equilibrium, which can be expected from the formal analogies with the Becker-Döring system

3d conservative coupling method between a compressible fluid flow and a deformable structure

In this work, we present a conservative method for three-dimensional inviscid fluid-structure interaction problems. On the fluid side, we consider an inviscid Euler fluid in conservative form. The Finite Volume method uses the OSMP high-order flux with a Strang operator directional splitting [1]. On the solid side, we consider an elastic deformable solid. In order to examine the issue of energy conservation, the behavior law is here assumed to be linear elasticity. In order to ultimately deal with rupture, we use a Discrete Element method for the discretization of the solid [2]. An immersed boundary technique is employed through the modification of the Finite Volume fluxes in the vicinity of the solid. Since both fluid and solid methods are explicit, the coupling scheme is designed to be globally explicit too. The computational cost of the fluid and solid methods lies mainly in the evaluation of fluxes on the fluid side and of forces and torques on the solid side. The coupling algorithm evaluates these only once every time step, ensuring the computational efficiency of the coupling. Our approach is an extension to the three-dimensional deformable case of the conservative method developed in [3]. We focus herein numerical results assessing the robustness of the method in the case of a undeformable solid with large displacements subjected to a compressible fluid flow

Un algorithme de couplage conservatif pour l'interaction fluide-structure dans le cas compressible

On présente une méthode de couplage entre un solide rigide et un écoulement compressible, pouvant comporter des ondes de choc. On considère une approche de type « frontières immergées » qui permet de traiter le fluide en maillage cartésien quelque soit la géométrie du solide. Le solide est traité en utilisant une méthode d'Eléments Discrets capable de modéliser également des solides déformables, voire la rupture. On démontre plusieurs résultats nouveaux de conservation de la masse, de la quantité de mouvement et de l'énergie du système solide-fluide

Analyse d'une méthode éléments finis discrets et couplage avec une méthode d'écoulements fluides compressibles

This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an undeformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi-implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our methodDans cette thèse, nous avons étudié la simulation numérique des phénomènes d'interaction fluide-structure entre un fluide compressible et une structure déformable. En particulier, nous nous sommes intéressés au couplage par une approche partitionnée entre une méthode de Volumes Finis pour résoudre les équations de la mécanique des fluides compressibles et une méthode d'Eléments discrets pour le solide, capable de prendre en compte la fissuration. La revue des méthodes existantes de domaines fictifs ainsi que des algorithmes partitionnés couramment utilisés pour le couplage conduit à choisir une méthode de frontières immergées conservative et un schéma de couplage explicite. Il est établi que la méthode d'Eléments Discrets utilisée permet de retrouver le comportement macroscopique du matériau et que le schéma symplectique employé assure la préservation de l'énergie du solide. Puis nous avons développé un algorithme de couplage explicite entre un fluide compressible non-visqueux et un solide indéformable. Nous avons montré des propriétés de conservation exacte de masse, de quantité de mouvement et d'énergie du système ainsi que de consistance du schéma de couplage. Cet algorithme a été étendu au couplage avec un solide déformable, sous la forme d'un schéma semi-implicite. Cette méthode a été appliquée à l'étude de problèmes d'écoulements non-visqueux autour de structures mobiles : les comparaisons avec des résultats numériques et expérimentaux existants démontrent la très bonne précision de notre méthod

Analyse d'une méthode de couplage entre un fluide compressible et une structure déformable

This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible uid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an undeformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi-implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures : comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method.Dans cette thèse, nous avons étudié la simulation numérique des phénomènes d'interaction fluide-structure entre un fluide compressible et une structure déformable. En particulier, nous nous sommes intéressés au couplage par une approche partitionnée entre une méthode de Volumes Finis pour résoudre les équations de la mécanique des fl uides compressibles et une méthode d'Éléments discrets pour le solide, capable de prendre en compte la fissuration. La revue des méthodes existantes de domaines fictifs ainsi que des algorithmes partitionnés couramment utilisés pour le couplage conduit à choisir une méthode de frontières immergées conservative et un schéma de couplage explicite. Il est établi que la méthode d'Éléments Discrets utilisée permet de retrouver le comportement macroscopique du matériau et que le schéma symplectique employé assure la préservation de l'énergie du solide. Puis nous avons développé un algorithme de couplage explicite entre un fluide compressible non-visqueux et un solide indéformable. Nous avons montré des propriétés de conservation exacte de masse, de quantité de mouvement et d'énergie du système ainsi que de consistance du schéma de couplage. Cet algorithme a été étendu au couplage avec un solide déformable, sous la forme d'un schéma semi-implicite. Cette méthode a été appliquée à l'étude de problèmes d'écoulements non-visqueux autour de structures mobiles : les comparaisons avec des résultats numériques et expérimentaux existants démontrent la très bonne précision de notre méthode