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1. Some analytical solutions for validation of free surface flow computational codes

Author

Bernard Di Martino, Fabien Souillé, Jacques Sainte-Marie, Marie-Odile Bristeau, Anne Mangeney, Numerical Analysis, Geophysics and Ecology (ANGE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Physique du Globe de Paris (IPGP (UMR_7154)), Institut national des sciences de l'Univers (INSU - CNRS)-Université de La Réunion (UR)-Institut de Physique du Globe de Paris (IPG Paris)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), The work presented in this paper was supported in part by the ANR Mimosa (ANR-14-CE01-0012) and ERC contract ERC-CG-2013-PE10-617472 SLIDEQUAKES. The authors also acknowledge the Inria Project Lab 'Algae in Silico' for its financial support., ANR-14-CE01-0012,MIMOSA,Analyse, modélisation et utilisation du bruit sismique large bande: des microséismes aux oscillations libres de la terre(2014), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut de Physique du Globe de Paris (IPGP), Institut national des sciences de l'Univers (INSU - CNRS)-IPG PARIS-Université de La Réunion (UR)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de La Réunion (UR)-Université Paris Diderot - Paris 7 (UPD7)-IPG PARIS-Institut national des sciences de l'Univers (INSU - CNRS)

Subjects
010103 numerical & computational mathematics, Analytical solutions, 01 natural sciences, law.invention, Physics::Fluid Dynamics, Free surface Euler equations, symbols.namesake, law, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, [MATH]Mathematics [math], Mathematics, Computer simulation, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Mechanical Engineering, Mechanics, Euler system, Condensed Matter Physics, River dynamics, Euler equations, 010101 applied mathematics, Flow (mathematics), Mechanics of Materials, Free surface, symbols, Compressibility, Hydrostatic equilibrium
Abstract

We present several time dependent analytical solutions for the incompressible Euler system with free surface. These analytical solutions give quantitative descriptions of some physical phenomena and can be used as reference solutions when validating numerical simulation codes. They concern fluid flows governed by Euler equations with or withouthydrostatic hypothesis including wet/dry interface, variable density, wide variety of boundary conditions and possibly non-uniform bottom topographies. Some of these analytical solutions concern shallow water type models or free surface Navier-Stokes model i.e. with a viscous fluid.

Published
2021

2. Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation

Author

Aurélien Alfonsi, Rafaël Coyaud, Virginie Ehrlacher, Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), Mathematical Risk Handling (MATHRISK), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), MATHematics for MatERIALS (MATHERIALS), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC), The Labex Bézout is acknowledged for funding the PhD thesis of Rafaël Coyaud. Aurélien Alfonsi benefited from the support of the 'Chaire Risques Financiers', Fondation du Risque. We are very grateful to Gero Friesecke, Daniela Vögler, Tony Lelièvre, Gabriel Stoltz and Pierre Monmarché for stimulating discussions, as well as Mathieu Lewin for precious comments on the paper. This publication is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme – Grant Agreement n◦ 810367., European Project: 810367,EMC2(2019), and École des Ponts ParisTech (ENPC)-École des Ponts ParisTech (ENPC)-Inria de Paris

Subjects
Applied Mathematics, Modeling and Simulation, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), [MATH]Mathematics [math]
Abstract

The Strictly Correlated Electrons (SCE) limit of the Levy–Lieb functional in Density Functional Theory (DFT) gives rise to a symmetric multi-marginal optimal transport problem with Coulomb cost, where the number of marginal laws is equal to the number of electrons in the system, which can be very large in relevant applications. In this work, we design a numerical method, built upon constrained overdamped Langevin processes to solve Moment Constrained Optimal Transport (MCOT) relaxations (introduced in [A. Alfonsi, R. Coyaud, V. Ehrlacher and D. Lombardi, Approximation of optimal transport problems with marginal moments constraints, Math. Comp. 90 (2021) 689–737; C. Villani, Optimal Transport: Old and New (Springer Science & Business Media, 2008)]) of symmetric multi-marginal optimal transport problems with Coulomb cost. Some minimizers of such relaxations can be written as discrete measures charging a low number of points belonging to a space whose dimension, in the symmetrical case, scales linearly with the number of marginal laws. We leverage the sparsity of those minimizers in the design of the numerical method and prove that there is no strict local minimizer to the resulting problem. We illustrate the performance of the proposed method by numerical examples which solves MCOT relaxations of 3D systems with up to 100 electrons.

Published
2021

3. A well balanced finite volume scheme for general relativity

Author

Gaburro, Elena, Castro, Manuel, Dumbser, Michael, Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Universidad de Málaga [Málaga] = University of Málaga [Málaga], University of Trento [Trento], E. G gratefully acknowledges the support received from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Individual Fellowship SuPerMan, grant agreement No. 101025563. E. G. has been also supported by a national mobility grant for young researchers in Italy funded by GNCS-INdAM, and she received funding from the University of Trento via the Strategic Initiative Starting Grant Giovani Ricercatori 2019. Moreover, the research presented in this paper has been partially funded by the European Union’s Horizon 2020 Research and Innovation Programme under the project ExaHyPE, grant No. 671698 (call FETHPC-1-2014).M. D. also acknowledges the financial support received from the Italian Ministry of Education, University and Research (MIUR) in the frame of the Departments of Excellence Initiative 2018–2022 attributed to DICAM of the University of Trento (grant 605 L. 232/2016) and in the frame of the PRIN 2017 project Innovative numerical methods for evolutionary partial differential equations and applications. Furthermore, M. D. has also received funding from the University of Trento via the Strategic Initiative Modeling and Simulation. The research of M.J. Castro was partially supported by the Spanish Government (SG), the European Regional Development Fund (ERDF), the Regional Government of Andalusia (RGA), and the University of Malaga(UMA) through the projects of references RTI2018-096064-B-C21 (SG-ERDF), UMA18-Federja-161 (RGA-ERDF-613 UMA), and P18-RT-3163 (RGA-ERDF)., and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
010308 nuclear & particles physics, Applied Mathematics, FOS: Physical sciences, Well balanced schemes 23 (WB), General Relativity and Quantum Cosmology (gr-qc), Numerical Analysis (math.NA), 01 natural sciences, General Relativity and Quantum Cosmology, General relativistic magnetohydrodynamics (GRMHD), TOV neutron star, AMS subject classifications. 35L40, 65M08, 83C05, 83C10, 85-08, 85-10, 85A30, Computational Mathematics, 0103 physical sciences, FOS: Mathematics, Michel accretion disk, Mathematics - Numerical Analysis, [MATH]Mathematics [math], 010306 general physics, Frst order conformal and covariant 24 reformulation of the Einstein field equations (FO-CCZ4), Fnite volume schemes (FV), First order hyperbolic systems
Abstract

International audience; In this work we present a novel second order accurate well balanced (WB) finite volume (FV) scheme for the solution of the general relativistic magnetohydrodynamics (GRMHD) equations and the first order CCZ4 formulation (FO-CCZ4) of the Einstein field equations of general relativity, as well as the fully coupled FO-CCZ4 + GRMHD system. These systems of first order hyperbolic PDEs allow to study the dynamics of the matter and the dynamics of the space-time according to the theory of general relativity. The new well balanced finite volume scheme presented here exploits the knowledge of an equilibrium solution of interest when integrating the conservative fluxes, the nonconservative products and the algebraic source terms, and also when performing the piecewise linear data reconstruction. This results in a rather simple modification of the underlying second order FV scheme, which, however, being able to cancel numerical errors committed with respect to the equilibrium component of the numerical solution, substantially improves the accuracy and long-time stability of the numerical scheme when simulating small perturbations of stationary equilibria. In particular, the need for well balanced techniques appears to be more and more crucial as the applications increase their complexity. We close the paper with a series of numerical tests of increasing difficulty, where we study the evolution of small perturbations of accretion problems and stable TOV neutron stars. Our results show that the well balancing significantly improves the long-time stability of the finite volume scheme compared to a standard one.

Published
2021
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4. Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles

Author

Emmanuel Maitre, Mourad E. H. Ismail, Arnaud Sengers, Thibaut Metivet, ModELisation de l'apparence des phénomènes Non-linéaires (ELAN), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), DYnamique des Fluides COmplexes et Morphogénèse [Grenoble] (DYFCOM-LIPhy ), Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] (LIPhy ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Most of the computations presented in this paper were performed using the Froggy platform of the GRICAD infrastructure (https://gricad.univ-grenoble-alpes.fr), which is supported by the Rhône-Alpes region (GRANT CPER07_13 CIRA) and the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche, and the Atlas cluster from the Research Institute in Advanced Mathematics (IRMA - UMR7501)., ANR-10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), DYnamique des Fluides COmplexes et Morphogénèse [Grenoble] [2020-….] (DYFCOM-LIPhy [2020-….]), Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] [2020-….] (LIPhy [2020-….]), and Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)

Subjects
Volume and area preserving, Vol- ume and area preserving, Diffusion generated motion, Physics and Astronomy (miscellaneous), Computer science, Interface (Java), and phrases: Diffusion generated motion, Signed distance function, Clifford torus, 010103 numerical & computational mathematics, Willmore flow, 01 natural sciences, Level set, Dimension (vector space), FOS: Mathematics, Applied mathematics, Mathematics - Numerical Analysis, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, Diffusion (business), [MATH]Mathematics [math], High-order geometrical flow, Numerical Analysis, Level set (data structures), Applied Mathematics, Numerical Analysis (math.NA), Thresholding, Computer Science Applications, 010101 applied mathematics, Computational Mathematics, Flow (mathematics), Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore flow in both two and three dimensions. These algorithms rely on alternating diffusions of the signed distance function to the interface and a redistanciation step, and with careful choice of the applied diffusions, end up moving the zero level-set of the distance function by some geometrical quantity without resorting to any explicit transport equation. The constraints are enforced between the diffusion and redistanciation steps via a simple rescaling method. The energy globally decreases at the end of each global step. The algorithms feature the computational efficiency of thresholding methods without requiring any adaptive remeshing thanks to the use of a signed distance function to describe the interface. This opens their application to dynamic fluid-structure simulations for large and realistic cases. The methodology is validated by computing the equilibrium shapes of two- and three-dimensional vesicles, as well as the Clifford torus.

Published
2020

5. A Spectral Approach to Uncertainty Quantification in Water Distribution Networks

Author

Olivier Piller, Iraj Mortazavi, M. Braun, Angelo Iollo, Environnement, territoires et infrastructures (UR ETBX), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modeling Enablers for Multi-PHysics and InteractionS (MEMPHIS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'enseignement Cnam Paris (CNAM Paris), Conservatoire National des Arts et Métiers [CNAM] (CNAM), The work presented in the paper is part of the French-German collaborative research project ResiWater that is funded by the French National Research Agency (ANR, project: ANR-14-PICS-0003) and the German Federal Ministry of Education and Research (BMBF, project: BMBF-13N13690), ANR-14-PICS-0003,ResiWater,Outils, modèles et réseaux sécurisés et innovants de capteurs pour une résilience augmentée des infrastructures liées à l'eau(2014), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)

Subjects
Spectral approach, 010504 meteorology & atmospheric sciences, Distribution networks, Hydraulics, Computer science, Geography, Planning and Development, 0207 environmental engineering, 02 engineering and technology, Management, Monitoring, Policy and Law, 01 natural sciences, law.invention, modelling, [SPI]Engineering Sciences [physics], INCERTITUDE, Computer Science::Systems and Control, law, Mathematics::Metric Geometry, Statistical physics, RESEAU DE DISTRIBUTION D'EAU, Uncertainty quantification, [MATH]Mathematics [math], 020701 environmental engineering, water distribution system, 0105 earth and related environmental sciences, Water Science and Technology, Civil and Structural Engineering, statistical uncertainty, Réseau de distribution d'eau, MODELISATION, 6. Clean water, Modélisation, SIMULATION, [SDE]Environmental Sciences
Abstract

[Departement_IRSTEA]Eaux [TR1_IRSTEA]GEUSI [ADD1_IRSTEA]Gestion intégrée de la ressource et des infrastructures; International audience; To date, the hydraulics of water distribution networks are calculated using deterministic models. Because many of the parameters in these models are not known exactly, it is important to evaluate the effects of their uncertainties on the results through uncertainty analysis. For the propagation of uncertain parameters, this article for the first time applies the polynomial chaos expansion to a hydraulic model and compares the results with those from classical approaches like the first-order second-moment method and Monte Carlo simulations. Results presented in this article show that the accuracy of the polynomial chaos expansion is on the same level as the Monte Carlo simulation. Further, it is concluded that due to its computational efficiency, polynomial chaos expansion is superior to the Monte Carlo simulation.

Published
2020

6. Quantification d'incertitude par propagation spectrale pour le temps de séjour de l'eau dans les réseau

Author

Olivier Piller, Iraj Mortazavi, Angelo Iollo, M. Braun, Jochen Deuerlein, Environnement, territoires et infrastructures (UR ETBX), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), University of Adelaide, Conservatoire National des Arts et Métiers [CNAM] (CNAM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modeling Enablers for Multi-PHysics and InteractionS (MEMPHIS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), The work presented in the paper is part of the French–German collaborative research project ResiWater that is funded by the French National Research Agency (ANR, project: ANR-14-PICS-0003) and the German Federal Ministry of Education and Research (BMBF, project:BMBF-13N13690)., ANR-14-PICS-0003,ResiWater,Outils, modèles et réseaux sécurisés et innovants de capteurs pour une résilience augmentée des infrastructures liées à l'eau(2014), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest

Subjects
Atmospheric Science, Waterdistribution systems, Computer science, 0208 environmental biotechnology, Water supply, 02 engineering and technology, 010501 environmental sciences, 01 natural sciences, Multimodal distribution, [SPI]Engineering Sciences [physics], Réseau réel, Uncertainty quantification, [MATH]Mathematics [math], 0105 earth and related environmental sciences, Civil and Structural Engineering, Water Science and Technology, business.industry, Water age, Environmental engineering, Geotechnical Engineering and Engineering Geology, 6. Clean water, 020801 environmental engineering, Distribution multimodale, Quantification d'incertitude, Real network, business
Abstract

[Departement_IRSTEA]Eaux [TR1_IRSTEA]GEUSI [ADD1_IRSTEA]Gestion intégrée de la ressource et des infrastructures; International audience; Water distribution networks are critical infrastructures that should ensure the reliable supply of high quality potable water to its users. Numerical models of these networks are generally governed by many parameters for which the exact value is not known. This may be due to a lack of precise knowledge like for consumer demand or due to a lack of accessibility as for the pipe roughness. For network managers, the effect of these uncertainties on the network state is important information that supports them in the decision-making process. This effect is generally evaluated by propagating the uncertainties using the mathematical model. In the past, perturbation, fuzzy and stochastic collocation methods have been used for uncertainty propagation. However, these methods are limited either in the accuracy of the results or the computational effort of the necessary calculations. This paper uses an alternative spectral approach that uses the polynomial chaos expansion and has the potential to give results of comparable accuracy to the Monte Carlo sampling through the definition of a stochastic model. This approach is applied to the hydraulic model of two real networks in order to evaluate the influence of uncertain demands on the water age.

Published
2020

7. A Spectral Approach to Uncertainty Quantification in Water Distribution Networks

Author

Braun, M., Piller, O., Iollo, A., Mortazavi, I., Environnement, territoires et infrastructures (UR ETBX), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modeling Enablers for Multi-PHysics and InteractionS (MEMPHIS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'enseignement Cnam Paris (CNAM Paris), Conservatoire National des Arts et Métiers [CNAM] (CNAM), The work presented in the paper is part of the French-German collaborative research project ResiWater that is funded by the French National Research Agency (ANR, project: ANR-14-PICS-0003) and the German Federal Ministry of Education and Research (BMBF, project: BMBF-13N13690), and ANR-14-PICS-0003,ResiWater,Outils, modèles et réseaux sécurisés et innovants de capteurs pour une résilience augmentée des infrastructures liées à l'eau(2014)

Subjects
[SPI]Engineering Sciences [physics], Water distribution system, Modélisation, Statistical uncertainty, [SDE]Environmental Sciences, Incertitude, RESEAU DE DISTRIBUTION D'EAU, Réseau de distribution d'eau, [MATH]Mathematics [math], MODELISATION, Simulation, Modelling
Abstract

International audience; To date, the hydraulics of water distribution networks are calculated using deterministic models. Because many of the parameters in these models are not known exactly, it is important to evaluate the effects of their uncertainties on the results through uncertainty analysis. For the propagation of uncertain parameters, this article for the first time applies the polynomial chaos expansion to a hydraulic model and compares the results with those from classical approaches like the first-order second-moment method and Monte Carlo simulations. Results presented in this article show that the accuracy of the polynomial chaos expansion is on the same level as the Monte Carlo simulation. Further, it is concluded that due to its computational efficiency, polynomial chaos expansion is superior to the Monte Carlo simulation.

Published
2020

8. EULERIAN MOMENT METHODS FOR AUTOMOTIVE SPRAYS

Author

O. Emre, Frédérique Laurent, A. Velghe, Quang Huy Tran, Marc Massot, Rodney O. Fox, Damien Kah, Stéphane Jay, S. de Chaisemartin, Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C), Université Paris Saclay (COmUE)-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec, IFP Energies nouvelles (IFPEN), Ecole Centrale Paris, Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487), Ecole Centrale Paris-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and The main contribution of this review paper relies on the Ph.D. works conducted byD. Kah (2007–2010) and O. Emre (2010–2014). These doctorates are the result of afruitful collaboration between IFPEN and EM2C Laboratory at Ecole Centrale Paris andwere co-advised by S. Jay and S. de Chaisemartin at IFPEN and F. Laurent-Nègre andM. Massot at Ecole Centrale Paris in collaboration with Rodney O. Fox. The researchof R.O.F. leading to some of the results reported in the present work on quadrature-basedmoment methods and turbulence modeling has received funding from the EuropeanUnion Seventh Framework Program (FP7/2007-2013) under grant agreementNo. 246556.

Subjects
business.industry, Turbulence, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, General Chemical Engineering, Multiphase flow, Mechanical engineering, Eulerian path, Computational fluid dynamics, Solver, System of linear equations, Moment (mathematics), [SPI]Engineering Sciences [physics], symbols.namesake, Flow (mathematics), symbols, Statistical physics, [MATH]Mathematics [math], business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; To assist industrial engine design, 3D simulations are increasingly used as they allow evaluation of a wide range of engine configurations and operating conditions and bring a comprehension of the underlying physics comple-mentary to experiments. While the gaseous flow description has reached a certain level of maturity, the multiphase flow description involving the liquid jet fuel injected into the chamber still faces some major challenges. There is a pressing need for a spray model that is time efficient and accurately describes the fuel-particle cloud dynamics downstream of the injector, which is an essential prerequisite for predictive combustion simulations. Due to the highly unsteady nature of the flow following the high-pressure injection process and the complexity of the flow regimes from separated/dense compressible phases to fully developed turbulent spray with evaporating droplets, Eulerian-Eulerian descriptions of two-phase flows are seen as very promising approaches towards realistic and predictive simulations of the mixing process. However they require some effort in terms of physical modeling and numerical analysis related to the more complex mathematical structure of the system of equations and to the unclosed terms appearing in space/time-average equations. Among the various challenges faced, one critical as-pect is to capture spray polydispersity in this framework. A review of recent developments that have permitted key advances in the spray modeling community is proposed in this paper. It is divided into four parts. First, an introduction to automotive spray modeling is provided. Then the formalisms for the description of the disperse region of an engine spray are presented with particular emphasis on the pros and cons of classical Lagrangian par-ticle methods versus Eulerian approaches. The third part presents the motivation for and the recent developments of Eulerian high-order moment methods for size polydispersion. Finally, the extension to fully two-way coupled interactions with the gas phase and the implementation of such methods for variable-geometry applications in CFD codes is described in the fourth part. Using realistic direct injection conditions computed with the IFP-C3D solver, the application and efficiency of Eulerian approaches is illustrated.

Published
2015

9. A benchmark of kriging-based infill criteria for noisy optimization

Author

Tobias Wagner, David Ginsbourger, Victor Picheny, Unité de Mathématiques et Informatique Appliquées de Toulouse (MIAT INRA), Institut National de la Recherche Agronomique (INRA), Technische Universität Dortmund [Dortmund] (TU), University of Bern, Deutsche Forschungsgemeinschaft (DFG) [SFB/TR TRR 30] Funding Text : The contributions of Tobias Wagner to this paper are based on investigations of the project D5 of the Collaborative Research Center SFB/TR TRR 30, which is kindly supported by the Deutsche Forschungsgemeinschaft (DFG)., and Picheny, Victor

Subjects
Mathematical optimization, Control and Optimization, Covariance function, 0211 other engineering and technologies, 02 engineering and technology, Metamodeling, symbols.namesake, 510 Mathematics, DESIGN, Kriging, Homoscedasticity, 0202 electrical engineering, electronic engineering, information engineering, [INFO]Computer Science [cs], [MATH]Mathematics [math], Gaussian process, GLOBAL OPTIMIZATION, Mathematics, EGO, 021103 operations research, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Covariance, Computer Graphics and Computer-Aided Design, Computer Science Applications, COMPUTER EXPERIMENTS, Control and Systems Engineering, Gaussian noise, SIMULATION, symbols, 020201 artificial intelligence & image processing, Engineering design process, Noise, Software
Abstract

International audience; Responses of many real-world problems can only be evaluated perturbed by noise. In order to make an efficient optimization of these problems possible, intelligent optimization strategies successfully coping with noisy evaluations are required. In this article, a comprehensive review of existing kriging-based methods for the optimization of noisy functions is provided. In summary, ten methods for choosing the sequential samples are described using a unified formalism. They are compared on analytical benchmark problems, whereby the usual assumption of homoscedastic Gaussian noise made in the underlying models is meet. Different problem configurations (noise level, maximum number of observations, initial number of observations) and setups (covariance functions, budget, initial sample size) are considered. It is found that the choices of the initial sample size and the covariance function are not critical. The choice of the method, however, can result in significant differences in the performance. In particular, the three most intuitive criteria are found as poor alternatives. Although no criterion is found consistently more efficient than the others, two specialized methods appear more robust on average.

Published
2013

10. A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones

Author

Karsten Schölzel, Miguel Couceiro, Lucien Haddad, Tamás Waldhauser, Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision (LAMSADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Knowledge representation, reasonning (ORPAILLEUR), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Natural Language Processing & Knowledge Discovery (LORIA - NLPKD), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Royal Military College of Canada (RMCC), Royal Military College of Canada, Mathematics Research Unit, University of Luxembourg [Luxembourg], Bolyai Institute [Szeged], University of Szeged [Szeged], Université du Luxembourg (Uni.lu), and The authors thank the anonymous referees for their valuable comments on the previous version of this paper. L. Haddad is supported by Academic Research Program of RMC. K. Sch¨olzel is supported by the internal research project MRDO2 of the University of Luxembourg. T. Waldhauser acknowledges that the present project is supported by the Hungarian National Foundation for Scientific Research under grants no. K83219 and K104251. The present project is supported by the European Union and co-funded by the European Social Fund under the project 'Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences' of project number 'TAMOP-4.2.2.A-11/1/KONV-2012-0073'.

Subjects
Discrete mathematics, 021103 operations research, Parity function, Two-element Boolean algebra, 010102 general mathematics, 0211 other engineering and technologies, 02 engineering and technology, Boolean algebras canonically defined, Complete Boolean algebra, 01 natural sciences, Combinatorics, Boolean domain, Maximum satisfiability problem, Free Boolean algebra, Boolean expression, [INFO]Computer Science [cs], 0101 mathematics, [MATH]Mathematics [math], Mathematics
Abstract

International audience; The following natural problem, first considered by D. Lau, has been tackled by several authors recently: Let C be a total clone on 2 := {0, 1}. Describe the interval I(C) of all partial clones on 2 whose total component is C. We establish some results in this direction and combine them with previous ones to show the following dichotomy result: For every total clone C on 2, the set I(C) is either finite or of continuum cardinality. 1. Preliminaries Let k ≥ 2 be an integer and let k be a k-element set. Without loss of generality we assume that k := {0,. .. , k − 1}. For a positive integer n, an n-ary partial function on k is a map f : dom (f) → k where dom (f) is a subset of k n , called the domain of f. Let Par (n) (k) denote the set of all n-ary partial functions on k and let Par(k) := n≥1