A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data

We generalize the wavelet transform modulus maxima (WTMM) method to multifractal analysis of 3D random fields. This method is calibrated on synthetic 3D monofractal fractional Brownian fields and on 3D multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration. Then we apply the 3D WTMM method to the dissipation field issue from 3D isotropic turbulence simulations. We comment on the need to revisiting previous box-counting analysis which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master non-conservative singular cascade measures.Comment: 5 pages, 3figures, submitted to Phys. Rev. Let

A large time-step and well-balanced Lagrange-Projection type scheme for the shallow-water equations

This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of compressibleflows, with or without stiff source terms. These methods enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, and maintain accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms in SWE and more specifically to the well-known well-balanced property. We prove that the proposed numerical strategy enjoys important non linear stability properties and we illustrate its behaviour past several relevant test cases

Automated Detection of Coronal Loops using a Wavelet Transform Modulus Maxima Method

We propose and test a wavelet transform modulus maxima method for the au- tomated detection and extraction of coronal loops in extreme ultraviolet images of the solar corona. This method decomposes an image into a number of size scales and tracks enhanced power along each ridge corresponding to a coronal loop at each scale. We compare the results across scales and suggest the optimum set of parameters to maximise completeness while minimising detection of noise. For a test coronal image, we compare the global statistics (e.g., number of loops at each length) to previous automated coronal-loop detection algorithms

Analyse multifractale 2D et 3D à l'aide de la transformation en ondelettes : application en mammographie et en turbulence développée

Président du jury : Mohamed Najim rapporteurs : Patrick Flandrin et Michael Unser examinateurs : Yves Gagne, Jean-Luc Starck invité : Alex Grossmann directeur de thèse : Alain ArnéodoSince the end 80's, wavelet transform has been recognized as a privileged tool to study fractal objects, providing a unified multifractal formalism for both functions and measures. In the first part, we use the 2D WTMM (Wavelet Transform Modulus Maxima) methodology to study mammography. We illustrate the usefulness of the methodology in the study of texture segmentation of rough surfaces and in the geometric characterization of clusters of microcalcifications, which are early signs of breast cancer. In a second methodologic part, we generalize the WTMM method to provide a multifractal description of both 3D scalar and vectorial data fields, introducing the tensorial wavelet transform. We show that a recursive filter technique allows to save between 25 \% and 60 \% of computing time, as compared with FFT based filtering techniques. Then we apply the 3D WTMM method to Direct Numerical Simulations (DNS) of the Navier-Stokes equations in turbulent regime with moderate Reynolds numbers. By mesuring a significantly non-zero cancellation exponent, we bring evidence that multifractal properties of both 3D dissipation and enstrophy fields are well accounted for non-conservative multiplicative cascading processes. Moreover, we observe that the cancellation exponent decreases as the Reynolds number increases. Finally, we present the first results of a fully vectorial multifractal analysis of both velocity and vorticity fields on the same numerical simulations showing that the value of the intermittence parameter $C_2$, as measured by the tensorial 3D WTMM method, is significantly larger than the one obtained by studying 1D longitudinal velocity increments.Depuis une dizaine d'années, la transformée en ondelettes a été reconnue comme un outil privilégié d'analyse des objets fractals, en permettant de définir un formalisme multifractal généralisé des mesures aux fonctions. Dans une première partie, nous utilisons la méthode MMTO (Maxima du Module de la Transformée en Ondelettes) 2D, outil d'analyse multifractale en traitement d'images pour étudier des mammographies. On démontre les potentialités de la méthode pour le problème de la segmentation de texture rugueuse et la caractérisation géométrique d'amas de microcalcifications, signes précoces d'apparition du cancer du sein. Dans une deuxième partie méthodologique, nous généralisons la méthode MMTO pour l'analyse multifractale de données 3D scalaires et vectorielles, en détaillant la mise en oeuvre numérique et un introduisant la transformée en ondelettes tensorielle. On démontre en particulier que l'utilisation d'une technique de filtres récursifs permet un gain de 25 a 60 \% en temps de calcul suivant l'ondelette analysatrice choisie par rapport à un filtrage par FFT. La méthode MMTO 3D est appliquée sur des simulations numériques directes (SND) des équations de Navier-Stokes en régime turbulent. On montre que les champs 3D de dissipation et d'enstrophie pour des nombres de Reynolds modérés sont bien modélisés par des processus multiplicatifs de cascades non-conservatifs comme en témoigne la mesure de l'exposant d'extinction $\kappa$ qui diffère significativement de zéro. On observe en outre que celui-ci diminue lorsqu'on augmente le nombre de Reynolds. Enfin, on présente les premiers résultats d'une analyse multifractale pleinement vectorielle des champs de vitesse et de vorticité des mêmes simulations numériques en montrant que la valeur du paramètre d'intermittence $C_2$, mesuré par la méthode MMTO 3D tensorielle, est significativement plus grande que celle obtenue en étudiant les incréments de vitesse longitudinaux 1D

Analyse multifractale 2D et 3D à l'aide de la transformation en ondelettes (application en mammographie et en turbulence développée)

Depuis une dizaine d'années, la transformée en ondelettes a été reconnue comme un outil privilégié d'analyse des objets fractals, en permettant de définir un formalisme multifractal généralisé des mesures aux fonctions. Dans une première partie, nous utilisons la méthode MMTO (Maxima du Module de la Transformée en Ondelettes) 2D, outil d'analyse multifractale en traitement d'images pour étudier des mammographies. On démontre les potentialités de la méthode pour le problème de la segmentation de texture rugueuse et la caractérisation géométrique d'amas de microcalcifications, signes précoces d'apparition du cancer du sein. Dans une deuxième partie méthodologique, nous généralisons la méthode MMTO pour l'analyse multifractale de données 3D scalaires et vectorielles, en détaillant la mise en oeuvre numérique et un introduisant la transformée en ondelettes tensorielle. On démontre en particulier que l'utilisation d'une technique de filtres récursifs permet un gain de 25 à 60 % en temps de calcul suivant l'ondelette analysatrice choisiepar rapport à un filtrage par FFT. La méthode MMTO 3D est appliquée sur des simulations numériques directes SND) des équations de Navier-Stokes en régime turbulent. On montre que les champs 3D de dissipation et d'enstrophie pour des nombres de Reynolds modérés sont bien modélisés par des processus multiplicatifs de cascades non-conservatifs comme en témoigne la mesure de l'exposant d'extinction kappa qui diffère significativement de zéro. On observe en outre que celui-ci diminue lorsqu'on augmente le nombre de Reynolds. Enfin, on présente les premiers résultats d'une analyse multifractale pleinement vectorielle des champs de vitesse et de vorticité des m^emes simulations numériques en montrant que la valeur du paramètre d'intermittence C_2, mesuré par la méthode MMTO 3D tensorielle, est significativement plus grand que celle obtenue en étudiant les incréments de vitesse longitudinaux 1D.Since the end 80's, wavelet transform has been recognized as a privileged tool to study fractal objects, providing a unified multifractal formalism for both functions and measures. In the first part, we use the 2D WTMM (Wavelet Transform Modulus Maxima) methodology to study mammography. We illustrate the usefulness of the methodology in the study of texture segmentation of rough surfaces and in the geometric characterization of clusters of microcalcifications, which are early signs of breast cancer. In a second methodologic part, we generalize the WTMM method to provide a multifractal description of both 3D scalar and vectorial data fields, introducing the tensorial wavelet transform. We show that a recursive filter technique allows to save between 25 % and 60 % of computing time, as compared with FFT based filtering techniques. Then we apply the 3D WTMM method to Direct Numerical Simulations (DNS)of the Navier-Stokes equations in turbulent regime with moderate Reynolds numbers. By mesuring a significantly non-zero cancellation exponent, we bring evidence that multifractal properties of both 3D dissipation and enstrophy fields are well accounted for non-conservative multiplicative cascading processes. Moreover, we observe that the cancellation exponent decreases as the Reynolds number increases. Finally, we present the first results of a fully vectorial multifractal analysis of both velocity and vorticity fields on the same numerical simulations showing that the value of the intermittence parameter C_2, as measured by the tensorial 3D WTMM method, is significantly larger than the one obtained by studying 1D longitudinal velocity increments.BORDEAUX1-BU Sciences-Talence (335222101) / SudocSudocFranceF

A multifractal formalism for vector-valued random fields based on wavelet analysis: application to turbulent velocity and vorticity 3D numerical data.

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Performance portability of lattice Boltzmann methods for two-phase flows with phase change

International audienceNumerical codes using the lattice Boltzmann methods (LBM) for simulating one- or two-phase flows are widely compiledand run on graphical process units. However, those computational units necessitate to re-write the program by using a low-levellanguage which is suited to those architectures (e.g. CUDA for GPU NVIDIA ® or OpenCL). In this paper we focus our efforton the performance portability of LBM i.e. the possibility of writing LB algorithms with a high-level of abstraction whileremaining efficient on a wide range of architectures such as multicores x86, GPU NVIDIA ® , ARM, and so on. For such apurpose, implementation of LBM is carried out by developing a unique code, LBM_saclay written in the C++ language, coupledwith the Kokkos library for performance portability in the context of High Performance Computing. In this paper, the LBM isused to simulate a phase-field model for two-phase flow problems with phase change. The mathematical model is composedof the incompressible Navier–Stokes equations coupled with the conservative Allen–Cahn model. Initially developed in theliterature for immiscible binary fluids, the model is extended here to simulate phase change occurring at the interface betweenliquid and gas. For that purpose, a heat equation is added with a source term involving the time derivative of the phase field.In the phase-field equation a source term is added to approximate the mass production rate at the interface. Several validationsare carried out to check step-by-step the implementation of the full model. Finally, computational times are compared on CPUand GPU platforms for the physical problem of film boiling

Wavelet-based multifractal analysis.

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