2022-05055 - Post-Doctoral Research Visit F/M Energy conservation and transformation in bore propagation: from model to numerics to applications and field observations
Le descriptif de l’offre ci-dessous est en Anglais

Type de contrat : CDD

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

A propos du centre ou de la direction fonctionnelle

The Inria Bordeaux Sud-Ouest centre is one of Inria's nine centres and has around twenty research teams. The Inria centre is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative SMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute...

Mission confiée

We want to study the dynamics and impact of bore propagation in natural and man made channels. This includes undular bores, as well as breaking ones, both tidal and tsunami bores.

The ultimate objective of the project is to characterize the impact on bore dynamics of dispersion, nonlinearity, dissipation as well as the role of the bathymetry and in particular cross- sectional variations, following the initial work of Filippini et al., JFM 2019. The study will focus on the robust simulation of bore propagation by means of depth averaged models, possibly embedding at least weak dispersive effects. Physical dissipation may be modelled by friction, as well as explicit viscous regularizations.

The work of El and collaborators has shown a richness in regimes obtainable with dispersive/ diffusive regularisations of the Burger's equations: from (more or less sharp) smooth transitions, to classical shocks, to dispersive shocks eventually leading to solitary wave fission, to undular bores with a finite wavelength determined by the interaction nonlinearity/dispersion/dissipation. When simulating these dynamics on large scale domains as e.g. estuaries, to characterize the impact of parameters as nonlinearity (Tidal range) or geometry (bathymetric variations) the impact of numerics becomes relevant. For depth averaged dispersive models one of the most
challenging aspects is making sure that numerical dispersion and dissipation do not alter the small scale dynamics of bores. In this respect there are several challenges involving

  •  verifying the impact of numerical dissipation/dispersion on undular bore dynamics
  • devising genuinely energy conservative schemes for non-dissipative dispersive models based on correction and/or relaxation techniques
  • introduced dissipative corrections of the model viscous effects, and provide systematic calibration allowing to reproduce the behaviour observed in laboratory experiments, direct simulations based on Navier-Stokes simulations, and observations in natural environnements
  • Exploit the resulting models for a full parametric characterisation of bore propagation in channels with various geometrical sections, possibly investigating the occurrence of amplitude related transitions using modulation theory (El et al, Tkachenko et al)

The project mixes several advanced notions related to PDE modelling, and in particular modelling nonlinear dispersive free surface waves, numerical analysis, and in particular the design of conservative discretizations for dispersive PDEs, and wave physics. The availability of standard experimental sets will also allow to confirm all the fundamental developments on real flows. The subject will allow to bring together different skills in CARDAMOM on high order schemes and dispersive wave models (E. Gaburro, M. Kazolea, M. Parisot, and M. Ricchiuto), and will benefit from ongoing interactions with the geophysics department EPOC in Bordeaux (P. Bonneton).


  • R. Abgrall, P. Öffner, H. Ranocha. Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes. arXiv:1908.04556
  • R. Chassagne, A.G. Filippini, M. Ricchiuto and P. Bonneton, Dispersive and dispersive-like bores
    in channels with sloping banks, Journal of Fluid Mechanics 870, pp. 595-616, 2019
  • G.A. El, M.A. Hoefer, Dispersive shock waves and modulation theory, Physica D: Nonlinear
    Phenomena 333, 2016
  • A.G. Filippini, L. Arpaia, P. Bonneton, and M. Ricchiuto, Modelling analysis of tidal bore formation
    in convergent estuaries, Eur.J.Mech. B/Fluids 73, 2019
  • A. Filippini, M. Kazolea and M. Ricchiuto. A flexible genuinely nonlinear approach for wave
    propagation, breaking and runup. J.Comput.Phys., 310:381–417, 2016
  • E. Gaburro, P. Offner, M. Ricchiuto, and D. Torlo, High order entropy preserving ADER-DG
    schemes, submitted to Applied Mathematics and Computation
  • M. Parisot , Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free
    surface flow, International Journal for Numerical Methods in Fluids 91, 2019
  • H. Ranocha, D. Mitsotakis, D. I. Ketcheson. A Broad Class of Conservative Numerical Methods for
    Dispersive Wave Equations. Communications in Computational Physics, 2021.
  • H. Ranocha, M. Sayyari, L. Dalcin, M. Parsani, D. I. Ketcheson. Relaxation Runge-Kutta Methods:
    Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes
    Equations. SIAM SISC, 42.2: A612-A638, 2020
  • S Tkachenko, S Gavrilyuk, KM Shyue, Hyperbolicity of the modulation equations for the Serre–
    Green–Naghdi model Water Waves 2 (2), 299-326, 2020
  • S Tkachenko, S Gavrilyuk, J. Massoni, Extended Lagrangian Approach for the Numerical Study of
    Multidimensional Dispersive Waves: Applications to the Serre-Green-Naghdi Equations,
    SSRN Electronic Journal, DOI: 10.2139/ssrn.4080776
  • A. Treske, Undular bores (favre-waves) in open channels – experimental studies. J. Hydraul. Res.
    32 (3), 355–370, 1994



Principales activités


  • preliminary benchmarking of solution approaches for dispersive waves based on the
    formulations by Filippini and al (elliptic/hyperbolic splitting), Parisot (projection method), Tkachenko et al (hyperbolic extended Lagrangian)
  • Energy analysis, Legendre transform, and study of dissipative regularisations leading to explicit net energy conservation at the PDE level for the three formulations
  •  Design of discrete regularisation mimicking the continuous dissipative one.
  •  Explicit relaxation, and study of IMEX relaxation in time (cf Ranocha et al) to obtain fully discrete conservation
  • applications to tidal bores and parametrisation of physical dissipation (rectangular channels)
  • application to the study of bores in trapezoidal channels with varying geometries (cf Chassagne et al)


Technical skills and level required :  high proficiency in applied math, PDE modelling and numerical analysis, and preferably in the
modelling of dispersive waves, and in the discretization of the resulting PDEs

Languages : French,English

Programming skills: Fortran, C, C++


  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of partial teleworking and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training


this will be a fixed-term contract

The gross monthly salary will be 2653 euros (before social charges on salary and monthly withholding taxes for income)