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7 results on '"Pascal Omnes"'

1. Benchmark Proposal for the FVCA8 Conference: Finite Volume Methods for the Stokes and Navier–Stokes Equations

Author

Franck Boyer, Pascal Omnes, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord

Subjects
general meshes, MSC (2010): 65M08, 65N08, 76D05, 76D07, Finite volume method, Computer science, Benchmark, Finite volume methods, Physics::Fluid Dynamics, incompressible fluids, Pressure-correction method, Incompressible flow, Robustness (computer science), Hagen–Poiseuille flow from the Navier–Stokes equations, Compressibility, Applied mathematics, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Statistical physics, Navier-Stokes equations, Navier–Stokes equations, Reynolds-averaged Navier–Stokes equations, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

FVCA 2017 : International Conference on Finite Volumes for Complex Applications; This benchmark proposes test-cases to assess innovative finite volume type methods developped to solve the equations of incompressible fluid mechanics. Emphasis is set on the ability to handle very general meshes, on accuracy, robustness and computational complexity. Two-dimensional as well as three-dimensional tests with known analytical solutions are proposed for the steady Stokes and both steady and unsteady Navier-Stokes equations, as well as classical lid-driven cavity tests.

Published
2017
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3. Space–Time Domain Decomposition with Finite Volumes for Porous Media Applications

Author

Pascal Omnes, Paul-Marie Berthe, and Caroline Japhet

Subjects
Well-posed problem, Finite volume method, Discretization, Iterative method, Discontinuous Galerkin method, Computer science, Applied mathematics, Duality (optimization), Domain decomposition methods, Porous medium
Abstract

We present an extension of the Optimized Schwarz Waveform Relaxation method with Robin transmission conditions to finite volume schemes of DDFV type (Discrete Duality Finite Volumes) for solving heterogeneous time-dependent advection-diffusion problems. We propose a new strategy which is well adapted to domain decomposition for coupling upwind discretization of the convection with diffusion in the context of a finite volume method. The method is proven to be well posed and we prove the convergence of the iterative algorithm. Then we present numerical results to illustrate the method.

Published
2014
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4. Non-isothermal Compositional Two-Phase Darcy Flow: Formulation and Outflow Boundary Condition

Author

Farid Smaï, Laurence Beaude, Roland Masson, Simon Lopez, Konstantin Brenner, COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Clément Cancès, Pascal Omnes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (LJAD), and ANR-16-CE06-0009,CHARMS,Modèles de Réservoirs Quantitatifs pour les Systèmes Hydrothermaux Complexes(2016)

Subjects
Convection, Darcy's law, Materials science, Boundary conditions for the interaction ground-atmosphere, business.industry, Geothermal energy, 010103 numerical & computational mathematics, Geophysics, Mechanics, 010502 geochemistry & geophysics, 01 natural sciences, 7. Clean energy, Isothermal process, Physics::Fluid Dynamics, Permeability (earth sciences), Finite volume scheme, Non-isothermal compositional two-phase Darcy flow model, Outflow, Boundary value problem, 0101 mathematics, Porous medium, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], 0105 earth and related environmental sciences
Abstract

International audience; This article deals with the modelling and formulation of compositional gasliquid Darcy flow. Our model includes an advanced boundary condition at the interface between the porous medium and the atmosphere accounting for convective mass and energy transfer, liquid evaporation, and liquid outflow. The formulation is based on a fixed set of unknowns whatever the set of present phases. The thermodynamical equilibrium is expressed as complementary constraints. The model and its formulation are applied to the simulation of the Bouillante high energy geothermal field in Guadeloupe characterized by a high temperature closed to the surface.

Published
2017
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5. A Weighted Splitting Approach for Low-Mach Number Flows

Author

David Iampietro, Pascal Galon, Jean-Marc Hérard, Frédéric Daude, EDF (EDF), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Clément Cancès - Pascal Omnes, and Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)

Subjects
Physics, Convection, Shock wave, 010103 numerical & computational mathematics, State (functional analysis), Mechanics, 7. Clean energy, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, Operator splitting, symbols.namesake, Mach number, Flow (mathematics), symbols, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics
Abstract

International audience; In steady-state regimes, water circulating in the nuclear power plants pipes behaves as a low Mach number flow. However, when steep phenomena occur, strong shock waves are produced. Herein, a fractional step approach allowing to decouple the convective from the acoustic effects is proposed. The originality is that the splitting between these two parts of the physics evolves dynamically in time according to the Mach number. The first one-dimensional explicit and implicit numerical results on a wide panel of Mach numbers show that this approach is as accurate and CPU-consuming as a state of the art Lagrange-Projection-type method.

Published
2017
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6. Uniform-in-Time Convergence of Numerical Schemes for a Two-Phase Discrete Fracture Model

Author

Julian Hennicker, Jérôme Droniou, Roland Masson, School of Mathematical Sciences [Clayton], Monash University [Clayton], TOTAL CSTJF, F-64018 Pau, France, COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Pascal Omnes, Centre scientifique et Technique Jean Feger (CSTJF), TOTAL FINA ELF, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), and Laboratoire Jean Alexandre Dieudonné (LJAD)

Subjects
Discrete fracture model, Capillary pressure, Hydrogeology, Darcy's law, Weak solution, 010103 numerical & computational mathematics, Mechanics, Two-phase Darcy flow, 01 natural sciences, Uniform-in-time convergence, Gradient discretization method, Physics::Geophysics, 010101 applied mathematics, Matrix (mathematics), Flow (mathematics), Fracture (geology), 0101 mathematics, Porous medium, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Geology
Abstract

International audience; Flow and transport in fracturedporous media are of paramount importance for many applications such as petroleum exploration and production, geological storage of carbon dioxide, hydrogeology, or geothermal energy. We consider here the two-phase discrete fracture model introduced in [3] which represents explicitly the fractures as codimension one surfaces immersed in the surrounding matrix domain. Then, the two-phase Darcy flow in the matrix is coupled with the two-phase Darcy flow in the fractures using transmission conditions accounting for fractures acting either as drains or barriers. The model takes into account complex networks of fractures, discontinuous capillary pressure curves at the matrix fracture interfaces and can be easily extended to account for gravity including in the width of the fractures. It also includes a layer of damaged rock at the matrix fracture interface with its own mobility and capillary pressure functions. In this work, the convergence analysis carried out in [3] in the framework of gradient discretizations [2] is extended to obtain the uniform-in-time convergence of the discrete solutions to a weak solution of the model.

Published
2017
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7. A Nonlinear Domain Decomposition Method to Couple Compositional Gas Liquid Darcy and Free Gas Flows

Author

Roland Masson, Nabil Birgle, Laurent Trenty, Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Agence Nationale pour la Gestion des Déchets Radioactifs (ANDRA), Clément Cancès, Pascal Omnes, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)

Subjects
Compositional gas liquid darcy flow, Darcy's law, Chemistry, 0207 environmental engineering, Thermodynamics, Domain decomposition methods, Coupling algorithm, 02 engineering and technology, Mechanics, 01 natural sciences, Nonlinear domain decomposition method, Robin boundary condition, 010305 fluids & plasmas, Physics::Fluid Dynamics, Permeability (earth sciences), Nonlinear system, Free gas flow, 0103 physical sciences, 020701 environmental engineering, Reynolds-averaged Navier–Stokes equations, Porous medium, Convection–diffusion equation, Drying model, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; A domain decomposition algorithm is proposed to couple at the interface a gas liquid compositional Darcy flow and a compositional free gas flow. At each time step, our algorithm solves iteratively the nonlinear system coupling the compositional Darcy flow in the porous medium, the RANS gas flow in the free flow domain, and the convection diffusion of the species in the free flow domain. In order to speed up the convergence of the algorithm, the transmission conditions at the interface are replaced by Robin boundary conditions. Each Robin coefficient is obtained from a diagonal approximation of the Dirichlet to Neumann operator related to a scalar simplified model in the neighbouring subdomain. The efficiency of our domain decomposition algorithm is assessed in the case of the modelling of the mass exchanges at the interface between the geological formation and the ventilation galleries of geological radioactive waste disposal.

Published
2017
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