Fabien Marche - Research

Research interests: modelization, numerical analysis, scientific computing

Models. Conservation laws, non-linear hyperbolic systems of PDEs, dispersive waves equations and solitary waves, Cahn-Hilliard equations, relaxation models, multiscale problems, models coupling…

Numerics. Finite Volume methods, Finite-Elements and discontinuous-Galerkin methods, Hybridized Discontinuous Galerkin (HDG) and Hybrid High-Order methods (HHO), well-balanced schemes, relaxation schemes, asymptotic-preserving schemes …

Scientific computing. Object oriented and generic programming for scientific computing, parallel and heterogeneous programming, graphics processing unit (GPU) programming, ... …

Applications. Shallow water flows, wave-current interactions, dispersive waves, coastal engineering, nearshore processes, geophysical flows, sediment transport, flooding and inundations, phase separations, ... …

Current Research Projects / Fundings


CNRS-INSU LEFE MANU: UHAINA: un modèle communautaire pour la simulation des vagues extrêmes (appel à projet LEFE-MANU - 2017-2018)

ANR NABUCO: NumericAl BoUndaries and COupling

There is a large variety of physical phenomena in which dispersion plays a predominant role with respect to diffusion. In the past decades, significant effort has been made to improve our understanding of evolution equations of dispersive type. Among other directions, let us mention, from the analytical point of view, the numerous works on local/global in time solvability of Cauchy problems, large time existence for small data or blow-up phenomena. From the numerical point of view, many efficient discretization techniques have been developed, like for instance hybrid Finite- Volume/Finite-Element or non-conforming discontinuous Finite-Element formulations to study the propagation of weakly dispersive and highly non-linear surface water waves. Yet, many of these works still deal with idealized situations where either spatial domains do not incorporate any bound- ary, or the impact of the numerical boundary conditions is made negligible on the overall solution. In a nutshell: the present proposal aims at studying the influence of boundary conditions on dispersive phenomena, with a specific emphasis on discretized models and/or water waves.

Past research projects

ANR HHOMM: Hybrid High-Order Methods on polyhedral Meshes

In the HHOMM project, we focus on the Hybrid High-Order (HHO) schemes. Prominent features of HHO schemes include: (i) the capability of handling general polyhedral meshes; (ii) dimension-independent construction; (iii) arbitrary approximation order; (iv) reproduction of desirable continuum properties at the discrete level; (v) reduced computational cost. Such features have generated significant interest, as testified by large-scale scientific initiatives (including the IHP quarter NMPDEs coordinated by the applicant) and industrial collaborations (with partners including Saint- Gobain, BRGM and EDF). The goal of the HHOMM project is to help the HHO technology ripen and promote its use in engineering applications. This will be achieved through: 1. theoretical developments; 2. ap- plications to complex problems; 3. development of computational methods and tools.

MERIC / CIGIDEN: Marine Energy Research and Innovation Center

Workpackage "Resource assessment and site caracterization" (with R.Cienfuegos and P.Bonneton).

ANR ACHYLLES: Asymptotic Capturing for HYperbolic conservation Laws with LargE Source terms

The ACHYLLES project focuses on Long-Time Asymptotic-Preserving (LTAP) numerical schemes for hyperbolic systems of conservation laws supplemented by potentially stiff source terms. It ambitions to perform a breakthrough in the understanding and efficiency of LTAP schemes by: 1. analyzing the behavior of the degeneracy of the solutions of the considered systems towards the asymptotic limit, 2. proposing relevant benchmarks, 3. improving existing LTAP schemes, 4. extending their range to take into account atypical situations. An open-source computational platform will also be designed. Based on the numerical techniques developed in this project, it aims at being easily adaptable to any application involving systems of the same class.

ANR BoND: Boundaries, numerics and Dispersion

This project is focussed on evolution problems in which dispersion is predominant compared to dissipative or diffusive mechanisms. It is motivated by physical applications in which the total energy is - to some extent - conserved, and also by numerical issues regarding the approximation, with the least possible amount of numerical viscosity, of hyperbolic systems of conservation laws. The model, dispersive equations that are being considered include the Korteweg-de Vries, Nonlinear Schrödinger, Kadomtsev– Petviashvili, Kawahara, and the Davey–Stewartson equations, but also the more complicated systems of Euler–Korteweg (for capillary fluids), and of Green–Naghdi (for water waves). All these equations and systems are taken in their most general form, which means that their nonlinearities are not predefined, and that integrability arguments should not have a preponderant importance in the proposed work.


CNRS-INSU LEFE-MANU SoLi: Singularités en Océanographie LIttorale (2013-2015)

Project Phi-0 with Saint-Gobain SVI: Résolution numérique d’écoulements dominés par la capillarité à l’aide de méthodes de discrétisation hybrides d’ordre élevé (2015-2016)

JOHANNA: vers une prédiction des coûts des dommages liés aux submersions marines et aux vagues lors des tempêtes (with the BRGM, UBO and the Fundation MAIF)
Simulation de la montée des eaux à Gâvres effectuée avec le logiciel SURF-WB

ANR MATHOCEAN: Analyse mathématique en océanographie et applications

Ce projet de recherche a pour objectif une meilleure compréhension de certains phénomènes observés en océanographie. La complexité et la variété de ces phénomènes (par exemple: déferlement des vagues, turbulence faible, optimisation de structures côtières, etc.) requiert des outils novateurs dans des domaines de recherche souvent disjoints et qui vont de la modélisation physique à l'analyse mathématique abstraite, en passant par les simulations numériques et les applications environnementales. Nous obtiendrons de nouveaux modèles physiques et développerons des outils mathématiques efficaces pour décrire ces phénomènes. Ces résultats seront validés dans des configurations industrielles et des expériences in situ. L'équipe à l'origine de ce projet s'est consitituée en vue de couvrir un large spectre scientifique, et avec l'intention partagée de travailler pour une meilleure articulation, au niveau national et international, des efforts de recherche dans les domaines qui touchent à l'océanographie (à travers des sites webs, des workshops interdisciplinaires, etc.). Elle rassemble des océanographes (Universités de Bordeaux et Montpellier), des mathématiciens spécialisés dans l'analyse d'équations provenant de la mécanique des fluides (Universités de Bordeaux, Chambéry et Montpellier, et ENS Paris), ainsi que des experts dans la simulation numérique de phénomènes océaniques (Universités de Bordeaux, Chambéry et Montpellier). Les outils mathématiques et numériques développés durant ce projet devraient avoir une portée qui dépasse de loin le domaine de l'océanographie. En particulier, une attention spéciale sera prêtée à deux problèmes mathématiques: l'analyse de problèmes au bord (et du couplage) de systèmes complexes d'EDP, et une approche rigoureuse de la turbulence faible. Dans le même esprit, des algorithmes numériques d'un intérêt général seront développés (algorithmes d'optimisation, nouveaux schémas de type well-balanced ou basés sur la méthode des résidus).

ANR MISEEVA: Marine Inundation hazard exposure modelling and Social, Economic and Environmental Vulnerability Assessment in regard to global changes. (ANR VMC 2007)

Le projet ANR Miseeva visait à définir la vulnérabilité du littoral à l’aléa de submersion marine dans le contexte du changement climatique, en intégrant toutes les composantes de l’aléa et en évaluant l’ensemble des enjeux. Réunissant océanographes, géologues, géographes, sociologues et économistes, la démarche a été conduite sur le littoral du Languedoc-Roussillon. Fondée sur plusieurs scénarios en termes d’événements météo-marins et d’élévation du niveau de la mer induite par le changement climatique aux échéances 2030 et 2100 (bases : GIEC 2007), elle a pris pour hypothèse la poursuite des tendances démographiques et économiques actuelles.
Voir aussi cet Acte de Conférences.

PRECODD Europe AMPERA ERA-NET: OILDEBEACH: Buried oil in the intertidal beach zone: coupling between morphodynamics, natural degradation, forcing mechanisms and biological activity - 2009-2011.

ECOS-CONYCIT: Morphodynamique numérique des plages sableuses et rip currents (with the Hydraulic and Environmental Engineering Department, Pontificia Universidad Catolica de Chile and the LEGI, Grenoble) - 2007-2009.

Publications

Submitted papers

  1. A.Haidar, F.Marche, F. Vilar [HAL]
    A robust DG-ALE formulation for nonlinear shallow water interactions with a partially immersed object.

Book chapters and reviewed "in proceedings" papers

  1. Filippini A.G., de Brye S., Perrier V., Marche F., Ricchiuto M., Lannes, D., Bonneton, P. [HAL]
    UHAINA: A parallel high performance unstructured near-shore wave model.
    XVie Journées Nationales Génie Côtier-Géne Civil , pages 47-56, Paralia, 2018.
  2. F.Chave, D.A.Di Pietro, F.Marche [arxiv]
    A Hybrid High-Order method for the convective Cahn-Hilliard problem in mixed form.
    Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, pages 517-525, Springer, 2018.

Published papers in international journals

  1. F. Marche, M. Zefzouf [HAL]
    A new Symmetric Internal Penalty Discontinuous Galerkin formulation for the Serre-Green-Naghdi equations.
    Numerical Methods for Partial Differential Equations, volume xxx, pages xxx, 2022.
  2. A.Haidar, F.Marche, F. Vilar [HAL]
    A posteriori Finite-Volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equations.
    J. Comput. Phys. , volume 452, pages 110902, 2022.
  3. F.Marche [HAL]
    A combined Hybridized Discontinuous Galerkin (HDG) and Discontinuous Galerkin (DG) discrete formulation for Green-Naghdi equations on unstructured meshes.
    J. Comput. Phys. , volume 418, pages 109637, 2020.
  4. D.A.Di Pietro, F.Marche [HAL]
    Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows .
    J. Comput. Phys. , volume 355, pages 285-309, 2018.
  5. A.Duran, F.Marche [HAL]
    Discontinuous Galerkin discretization of Green-Naghdi equations on unstructured simplicial meshes.
    Applied Mathematical Modelling , volume 45, pages 840-864, 2017.
  6. F.Chave, D.A.Di Pietro, F.Marche, F.Pigeonneau [HAL]
    A Hybrid High-Order method for the Cahn–Hilliard problem in mixed form.
    SIAM J. Numer. Anal. , volume 54(3), pages 1873-1898, 2016.
  7. D.Lannes, F.Marche [HAL]
    Nonlinear wave-current interactions in shallow water.
    Studies in Applied Math., volume 136(4), pages 382–423, 2016.
    Special distinction: Highlights of the year 2016 (four papers out of all those published by this journal in 2016 were selected as “Highlights of the Year” for their novelty, quality and importance)
  8. A.Duran, C.Berthon, F.Marche, R.Turpault [journal]
    Asymptotic Preserving Scheme for the Shallow Water equations with source terms on unstructured meshes.
    J. Comput. Phys., volume 287, pages 184–206, 2015.
  9. D.Lannes, F.Marche [journal]
    A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations.
    J. Comput. Phys., volume 282, pages 238–268, 2015.
  10. A.Duran, F.Marche [journal]
    Discontinuous-Galerkin discretization of a new class of Green-Naghdi equations.
    Comm. Comput. Phys., volume 17(3), pages 721-760, 2015.
  11. S.Le Roy, R.Pedreros, C.André, F.Paris, S.Lecacheux, F.Marche,C.Vinchon [journal]
    Coastal flooding of urban areas by overtopping: dynamic modelling application to the Johanna storm (2008) in Gâvres (France).
    Natural Hazards and Earth System Sciences, volume 15, pages 2497-2510, 2015.
  12. A.Duran, F.Marche [journal]
    Recent advances on the discontinuous Galerkin method for shallow water equations with topography source terms.
    Computers & Fluids, volume 101, pages 88–104, 2014.
  13. M.Guerra, R.Cienfuegos, C.Escauriaza, F.Marche, J.Galaz [journal]
    Modeling Rapid Flood Propagation Over Natural Terrains Using a Well-Balanced Scheme.
    J. Hydraul. Eng., volume 140(7), 2014.
  14. A.Duran, Q.Liang, F.Marche [journal]
    On the well-balanced numerical discretization of shallow water equations on unstructured meshes.
    J. Comput. Phys., volume 235, pages 565--586, 2013.
  15. M.Tissier, P.Bonneton, F.Marche, F.Chazel, D.Lannes [journal]
    A new approach to handle wave breaking in fully non-linear Boussinesq models.
    Coastal Engineering, volume 67, pages 54--66, 2012.
  16. P.Bonneton, E. Barthelemy, F.Chazel, R.Cienfuegos, D.Lannes, F.Marche, M.Tissier [journal]
    Recent advances in Serre-Green-Naghdi modelling for wave transformation, breaking and runup processes.
    Eur. J. Mech. B Fluids, volume 30(6), pages 589–597, 2011.
  17. M.Tissier, P.Bonneton, F.Marche, F.Chazel, D.Lannes [journal]
    Nearshore Dynamics of Tsunami-like Undular Bores using a Fully Nonlinear Boussinesq Model.
    J. Coastal. Res., SI 64, pages 603-607, 2011.
  18. C.Berthon, F.Marche, R.Turpault [journal]
    An efficient scheme on wet/dry transitions for shallow water equations with friction.
    Computers & Fluids, volume 48(1), pages 192 - 201, 2011.
  19. P.Bonneton, F. Chazel, D.Lannes, F.Marche, M.Tissier [journal]
    A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model.
    J. Comput. Phys., volume 230(4), pages 1479 - 1498, 2011.
  20. F. Chazel, D.Lannes, F.Marche. [journal]
    Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model.
    J. Sci. Comput., volume 48(3), pages 105-116, 2011.
  21. A. Bouharguane, P.Azerad, F.Bouchette, F.Marche, B.Mohammadi. [journal]
    Low complexity shape optimization & a posteriori high fidelity validation.
    Discrete Contin. Dyn. Syst. Ser. B., volume 13(4), pages 759-772, 2010.
  22. O.Delestre, F.Marche. [journal]
    A numerical scheme for a viscous shallow water model with friction.
    J. Sci. Comput., volume 48(1), pages 41--51, 2011.
  23. P.Bonneton, N.Bruneau, B.Castelle, F.Marche [journal]
    Large-Scale vorticity generation due to dissipating waves in the surf zone.
    Discrete Contin. Dyn. Syst. Ser. B., volume 13(4), pages 729-738, 2010.
  24. Q.Liang, F.Marche [journal]
    Numerical resolution of well-balanced shallow water equations with complex source terms.
    Adv. Water Res., volume 32(6), pages 873-884, 2009.
  25. P.Fabrie, F.Marche [journal]
    Another Proof of Stability for Global Weak Solutions of 2D Degenerated Shallow Water Models.
    J. Math. Fluid Mech., volume 11(4), pages 536-551, 2009.
  26. C.Berthon, F.Marche [journal]
    A positive preserving high order VFRoe scheme for shallow water equations: a class of relaxation schemes.
    SIAM J. Sci. Comput., volume 30(5), pages 2587-2612, 2008.
  27. F.Marche [journal]
    Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects.
    Eur. J. Mech. B Fluids, volume 26(1), pages 49-63, 2007.
  28. F. Marche, P. Bonneton, P. Fabrie, N. Seguin [journal]
    Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes.
    International Journal for Numerical Methods in Fluids, volume 53(5), pages 867-894, 2007.

Habilitation à diriger des recherches

H.D.R. defended on December, 2014, Université de Montpellier
Contributions to the numerical approximation of shallow water asymptotics

PhD Thesis

Ph.D. thesis advised by Pierre Fabrie and Philippe Bonneton defended on December, 2005, Université de Bordeaux
Theoretical and Numerical Study of Shallow Water Models. Applications to Nearshore Hydrodynamics

Workshop: NumWave (december 11-13, 2017) at IMAG

(Numerical Advances on Wave Propagation in Shallow Waters): it's here

Ph.D. supervising

LJLL UPMC     CNRS