2024Activity reportProject-TeamCARDAMOM

6.1.1 SLOWS

• Name:
  Shallow-water fLOWS
• Keywords:
  Simulation, Free surface flows, Unstructured meshes
• Scientific Description:
  Three different approaches are available, based on conditionally depth-positivity preserving implicit schemes, or on conditionally depth-positivity preserving genuinely explicit discretizations, or on an unconditionally depth-positivity preserving space-time approach. Newton and frozen Newton loops are used to solve the implicit nonlinear equations. The linear algebraic systems arising in the discretization can be solved either with the MUMPS library or with the MKL Intel library. Implicit and explicit (extrapolated) multistep higher order time integration methods are available, and a mesh adaptation technique based on simple mesh deformation are also included. This year a new higher order reconstruction for the FV scheme has been added.
• Functional Description:
  SLOWS is a C-platform allowing the simulation of free surface shallow water flows with friction. It can be used to simulate near shore hydrodynamics, wave transformations processes, etc.
• URL:
  https://­team.­inria.­fr/­cardamom/­slows-shallow-water-flows/
• Contact:
  Mario Ricchiuto
• Participants:
  Maria Kazolea, Mario Ricchiuto

6.1.2 GeoFun

• Keywords:
  Geophysical flows, Unified models, Finite volume methods
• Scientific Description:
  GeoFun focuses on applications where different models in different regions in space are needed, with interfaces between these regions that depend on the solution. To deal with this complex boundary problem, the code aims at exploiting unified models available everywhere in the computational domain, and at using asymptotic preserving numerical schemes to recover specific regime flows without an a priori detection of the interfaces.
• Functional Description:
  The GeoFun library is developed as a module on top of the kernel provided by AeroSol. Its objective is to simulate geophysical flows, free surface and underground, at large time and space scales. For this reason, unified vertically integrated (shallow water type) models are considered.
• Contact:
  Martin Parisot
• Participants:
  Martin Parisot, Marco Lorini

6.1.3 UHAINA

• Keywords:
  Simulation, Ocean waves, Unstructured meshes, Finite element modelling
• Scientific Description:

  Operational platform for near shore coastal application based on the following main elements:

  - Fully-nonlinear wave propagation.

  - Wave breaking handled by some mechanism allowing to mimic the energy dissipation in breakers.

  - A high order finite element discretization combined with mesh and polynomial order adaptation for optimal efficiency.

  - An efficient parallel object oriented implementation based on a hierarchical view of all the data management aspects cared for by middle-ware libraries developed at Inria within the finite element platform Aerosol.

  - A modular wrapping allowing for application tailored processing of all input/output data (including mesh generation, and high order visualization).

  - Spherical coordinates based on a local projection on a real 3D spherical map (as of 2021)

  - Compilation with GUIX available (as of 2022)

  - Homogenization and standardization of code outputs and hazard quatification (as of 2022)

  - Correction of the management of dry/wet fronts in the presence of structures represented by a single high point (as of 2022)

  - Use of FES for the calculation of the tide directly in UHAINA through an API. New compilation option for activation (as of 2022)

  - Boundary conditions accounting tides from FES and corrected with the effect of the inverse barometer, for the simulation of the tidal propagation and the surge on domains at the regional scale (as of 2022)

  - Hydraulic connections (e.g. sewers) in the simulation of urban flooding (as of 2022)

  - Mass source term, for the injection of the volume of water overtopping structures not accounted in the elevation model during flooding episodes by sea surges (as of 2022)

• Functional Description:
  Waves simulation
• Contact:
  Mario Ricchiuto
• Participants:
  Mario Ricchiuto, Philippe Bonneton, David Lannes, Fabien Marche
• Partners:
  EPOC, IMAG, IMB

6.1.4 AleVoronoi

• Name:
  Direct Arbitrary Lagrangian Eulerian Finite Volume and Discontinous Galerkin schemes on VORONOI moving meshes with topology changes
• Keywords:
  Finite volume methods, Discontinuous Galerkin, High order methods, Centroidal Voronoi tessellation, ALE, Fortran, OpenMP
• Scientific Description:
  We would like to remark that the implementation of AleVoronoi started in April 2018 as a collaboration between E. Gaburro, M. Dumbser (University of Trento, Italy) and W. Boscheri (University of Trento, then University of Ferrara, and now CNRS France). E. Gaburro was the main contributor in particular for what concerns the novelties, however, many parts of the code have been taken from existing codes of the other coauthors. Starting from July 2019, S. Chiocchetti (University of Trento, University of Stuttgart and now University of Cologne) joined the project, becoming a fundamental contributor to it. The work has continued during the years and have been moved to a git account in 2021. The main developers from 2021 up to now have been E. Gaburro and S. Chiocchetti. However, small contributions were introduced also by W. Boscheri and M. Ricchiuto. In addition, M. Dumbser has always participated int the scientific discussion concerning the development line of AleVoronoi.
• Functional Description:

  Explicit, arbitrary high order accurate, one step (ADER), Finite Volume and Discontinuous Galerkin schemes on 2D moving Voronoi meshes for the solution of general first-order hyperbolic PDEs. Main peculiarity: the Voronoi mesh is moved according to the fluid flow using a direct Arbitrary-Lagrangian-Eulerian (ALE) method achieving high quality of the moving mesh for long simulation times. The high quality of the mesh is maintained thanks to a) mesh optimization techniques and b) the additional freedom of allowing topology changes. The high quality of the results is obtained thanks to the high order ADER schemes. The main novelty is the capability of using high-order schemes on moving Voronoi meshes with topology changes.

  The code is written in Fortran + OpenMP.

• Publications:
  hal-03850200, hal-03865596, hal-03850195, hal-02411272
• Contact:
  Elena Gaburro

6.1.5 HOTHYPE

• Name:
  High Order shock Tracking for HYPerbolic Equations
• Keywords:
  Finite volume methods, Discontinuous Galerkin, Partial differential equation, Delaunay triangulation
• Scientific Description:
  We would like to remark that this code born in December 2020, but it was quickly created because many of its part were taken from AleVoronoi and simplified/adapted to the purpose of this code. The code was created and mainly developed by E. Gaburro. However, all the original contributors of AleVoronoi should be acknowledged for their contributions to HOTHYPE: S. Chiocchetti, W. Boscheri, M. Dumbser. During the years, the code was mainly maintained and developed by E Gaburro. Another important contributor has been S. Chiocchetti. Minor parts of this code have been implemented by M. Ciallella under the supervision of M. Ricchiuto.
• Functional Description:
  High order ADER-type Finite Volume and Discontinuous Galerkin schemes on 2D triangular meshes for the solution of hyperbolic partial differential equations.
• Publications:
  hal-03850196, hal-04341999, hal-03865587
• Contact:
  Elena Gaburro

6.1.6 AeroSol

• Keywords:
  High order finite elements, Parallel computing
• Functional Description:
  The AeroSol software is a high order finite element library written in C++. The code has been designed so as to allow for efficient computations, with continuous and discontinuous finite elements methods on hybrid and possibly curvilinear meshes. The work of the team CARDAMOM (previously Bacchus) is focused on continuous finite elements methods, while the team Cagire is focused on discontinuous Galerkin methods. However, everything is done for sharing the largest part of code we can. More precisely, classes concerning IO, finite elements, quadrature, geometry, time iteration, linear solver, models and interface with PaMPA are used by both of the teams. This modularity is achieved by mean of template abstraction for keeping good performances. The distribution of the unknowns is made with the software PaMPA , developed within the team TADAAM (and previously in Bacchus) and the team Castor.
• News of the Year:

  Highlights for the year 2024 concern:

  1. *Functional tests*: reference metrics were added for several tests, allowing to check the convergence order and the execution time (M. Haefele, V. Perrier). 2. Handling of *spherical manifolds* has been merged into the master branch, allowing to support Uhaina on the Lagoon branch from the AeroSol master branch (M. Haefele, V. Perrier). 3. *Tags* have been defined for relevant historical versions of the code. 4. Complete and time-consistent *Guix channels* have been specified to avoid reproducibility issues (L. Cirrottola). 5. Guix packages and channels for legacy compilation of the Uhaina master branch with a legacy AeroSol branch (L. Cirrottola). 6. New test cases for the *curl-/divergence-preserving schemes* (J. Jung, V. Perrier). 7. Several bug fixes (CI, tests). 8. Wiki improvement.

  Contribution statistics: About 300 commits this year, organized in 11 merge requests that were opened and merged into the master branch this year.

• URL:
  https://­team.­inria.­fr/­cardamom/­aerosol/
• Contact:
  Vincent Perrier
• Participants:
  Mario Ricchiuto, Vincent Perrier, Héloïse Beaugendre, Christopher Poette, Marco Lorini, Jonathan Jung, Anthony Bosco, Luca Cirrottola, Romaric Simo Tamou, Ibtissem Lannabi, Matthieu Haefele

6.1.7 DM2

• Name:
  Distributed Mesh and Data Manager
• Keywords:
  HPC, Data parallelism, High order finite elements, Unstructured meshes, Hybrid meshes
• Functional Description:

  DM2 is a C++ library for managing mesh and data on mesh in a MPI parallel environment. It is conceived to provide parallel mesh and data management in high order finite element solvers for continuum mechanics.

  The user should provide a mesh file which is read by the library. Then DM2 is able to:

  - Read the mesh, and read the data provided in the mesh file, possibly in parallel

  - Redistribute the mesh in order to distribute the data on a given set of processors. This redistribution is made through a graph partitioner such as PARMETIS or PT-SCOTCH.

  - Allocate the memory in parallel if a number of unknown by entity type is provided by the user.

  - Centralize the data.

  - Compute the halo required for a numerical method. The halo is adapted for each of the possible discretization.

  - Renumber mesh elements for making a difference between mesh elements that need or need not communication.

  - Aggregate a mesh based on a metric for developing a multigrid method.

• Release Contributions:
  This version introduces overlap regions ("halos") among distributed mesh partitions. These halos are specialized for discontinuous or continuous schemes, but generic with respect to the (geometric) degree of the mesh cells. These halos allow to synchronize numerical data defined on a set of entities of the distributed mesh. Numerical data is again generic with respect to the degree of their polynomial approximation, the number and combinations of scalar/vector fields, and the size of the vector spaces.
• News of the Year:

  Highlights for the 2024 years:

  - Refactoring of *mesh iterators*: dealing with constness, views on specified entity types, generalization of normal (uniform) and non-normal (non-uniform) iterators, handling an entity as a generalized reference. - Refactoring of methods for MPI communication into *generic communication algorithms*. - Refactoring of halo creation methods: no shallow entities, better object-oriented creation. - Passage to the C++14 *standard*. - Development of *generic algorithms for graph permutations*. - Specific *mesh graph composition* for DG or CG schemes. - Towards a consistent handling of 1D meshes: better role distinction between faces and points, remove hard-coded constants, template some methods on the mesh dimension. - Boundary handling: assign boundary faces if not found in the mesh file. - Development of input/output in Vtu format. - Development of input/output in NetCDF. - Full specification of Guix channels for avoiding environment reproducibility issues. - Integration of a two-dimensional finite volume test. - Test references for ParaGMSH objects. - Clean repository paths. - Several bug fixes. - Several small refactorings. - Several small contributions: introducing chronometers, storing the MPI communicator in a variable.

  Contributions statistics: about 1800 commits, organized in 32 merge requests that were opened and merged into the master branch during the last year.

• Contact:
  Vincent Perrier
• Participants:
  Abderrahman Ben Khalifa, Matthieu Haefele, Vincent Perrier, Luca Cirrottola

7.1.1 High order well balanced discretizations

Global flux based schemes.

In the context of preserving stationary states we continued and extended the work initiated in 55 and 14. This work is based on a notion, referred to as global flux or global flux quadrature, in which source terms are replaced by the derivative of some effective flux term to be determined in some way. While in 55 this notion has been applied directly by computing, in one dimensions, primitive of the source term, in 14 we have shown that some more interesting choices are possible. First of all, in the finite element case the method can be written in a fully local fashion. Secondly, by choosing appropriately the quadrature formula defining the source integral, one can enforce full consistency with some ODE integator. This adds freetom to the accuracy obtained at steady state, and allows an extremely fast generation of well prepared initial data. This preperty is retained without the need to apply the ODE integrator explicitly to solve the local Cauchy problem at each time step and in each cell, as in previous work e.g. by 73.

A first extension of these ideas has been performed in the context of WENO finite difference methods. In this case, a nondimensionalapproximation of a primitive of the source can be readily written using high-order multi-step ODE methods on the finite difference grid. Then a standard WENO strategy is employed to reconstruct the global (nodal) flux. By construction, the steady discrete solutions of the proposed schemes are those of the underlying ODE integrator. We tested WENO reconstructions of varying orders (from 3 to 7), combined with multi-step ODE methods of up to order 8. We have verified that the steady-state solution is determined solely by the ODE method. Numerical experiments using scalar balance laws and shallow water equations confirm that the methods achieve optimal convergence for time-dependent solutions and significant error reduction for steady-state solutions. This work has been performed in collaboration with the U. fo Malaga (C. Parés), and presented at the 9th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2024, Jun 2024, in Lisbon, Portugal 18.The full article 31 has been submitted to Computers $\&$ Fluids.

We also extended the same approach to stabilized continuous finite elements. To this end we reformulated several stabilization methods, including SUPG, and continuous interior penalty, in terms of cell value and symmetric face jump integrals of full residuals. In this setting we can naturally include the source, using a formulation similar to the one used in 14. The schemes are specifically designed to guarantee the exact preservation of the lake at rest steady state, on the other hand, some of them make use of general structures to tackle the preservation of general steady states, whose explicit analytical expression is not known. Several basis functions have been considered in the numerical experiments and, in all cases, the numerical results confirm the high order accuracy and the ability of the novel stabilizations to exactly preserve the lake at rest steady state and to capture small perturbations of such equilibrium. Moreover, some of them, based on the notions of space residual and global flux, have shown very good performances and superconvergences in the context of general steady solutions not known in closed-form. Work performed in collaboration with the University of Zurich, and discussed in detail in 15.

We have done initial steps to extend these ideas to the multidimensional case. As a first step we looked at lienar equations. In particular, as an example we focused on the linear acoustics system (in first order hyperbolic form). Already in the homogenous case, steady states are characterized by a solenoidal constraint on the velocity, which is non-trivial to reproduce discretely. Besides this, numerical methods for hyperbolic PDEs require stabilization. For linear acoustics, divergence-free vector fields should remain stationary, but classical Finite Difference methods add incompatible diffusion that dramatically restricts the set of discrete stationary states of the numerical method. Compatible diffusion should vanish on stationary states, e.g. should be a gradient of the divergence. Some Finite Element methods allow to naturally embed this grad-div structure, e.g. the SUPG method or OSS. We prove here that the particular discretization associated to them still fails to be constraint preserving. We then introduce a new framework on Cartesian grids based on surface (volume in 3D) integrated operators inspired by Global Flux quadrature and related to mimetic approaches. We are able to construct constraint-compatible stabilization operators (e.g. of SUPG-type) and show that the resulting methods are vorticity-preserving. We show that the Global Flux approach is even super-convergent on stationary states, we characterize the kernels of the discrete operators and we provide projections onto them. The full paper 29 has been accepted on Numerical Methods for PDEs. The inclusion of artibrary source terms has been also studied with very similar enhancements. This last part of work has been presented to several conferences including the Oberwolfach workshop “Hyperbolic Balance Laws: interplay between scales and randomness”, held in February 2024. A full manuscript is in preparation. Work performed in collaboration with the math department in Bordeaux (W. Barsukow), and U. of Roma-La Sapienza (D. Torlo).

Astrophysics. We develop a new well-balanced discontinuous Galerkin (DG) finite element scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein-Euler equations of general relativity based on a first order hyperbolic reformulation of the Z4 formalism. The first order Z4 system, which is composed of 59 equations, is analysed and proven to be strongly hyperbolic for a general metric. The well-balancing is achieved for arbitrary but a priori known equilibria by subtracting a discrete version of the equilibrium solution from the discretized time-dependent PDE system. Special care has also been taken in the design of the numerical viscosity so that the well-balancing property is achieved. As for the treatment of low density matter, e.g. when simulating massive compact objects like neutron stars surrounded by vacuum, we have introduced a new filter in the conversion from the conserved to the primitive variables, preventing superluminal velocities when the density drops below a certain threshold, and being potentially also very useful for the numerical investigation of highly rarefied relativistic astrophysical flows. Thanks to these improvements, all standard tests of numerical relativity are successfully reproduced, reaching three achievements: (i) we are able to obtain stable long term simulations of stationary black holes, including Kerr black holes with extreme spin, which after an initial perturbation return perfectly back to the equilibrium solution up to machine precision; (ii) a (standard) TOV star under perturbation is evolved in pure vacuum $(\rho =p=0)$ up to $t=1000$ with no need to introduce any artificial atmosphere around the star; and, (iii) we solve the head on collision of two punctures black holes, that was previously considered un-tractable within the Z4 formalism. Due to the above features, we consider that our new algorithm can be particularly beneficial for the numerical study of quasi normal modes of oscillations, both of black holes and of neutron stars 10.

Shallow water equations on manifolds. Last but not least we continued our work on well balanced schemes for shallow water type models had major enhancements. We proposed a novel hyperbolic re-formulation of the shallow water model written in covariant coordinates, i.e. metric independent, and for this system we derived a cheap well balanced method able to maintain at machine precision water at rest equilibria for general metrics and complex-shaped domains. This work has been presented in ICNAAM 2022 - 20th International Conference of Numerical Analysis and Applied Mathematics 23.

7.1.2 Schemes embedding additional discrete conservation constraints

A posteriori sub-cell conservative correction of nonconservative schemes. We proposed a novel quasi-conservative high order discontinuous Galerkin (DG) method able to capture contact discontinuities avoiding any spurious numerical artifacts, thanks to the PDE evolution in primitive variables, while at the same time being strongly conservative on shocks, thanks to a conservative a posteriori subcell finite volume (FV) limiter. In particular, we have verified the improved reliability of our scheme on the multi-fluid Euler system on examples like the interaction of a shock with a helium bubble. The obtained results have been presented at several international conferences, and fully discussed in the CMAME article 12. Currently similar ideas are being explored in collaboration with the U. fo Malaga (C. Parés, E. Pimentel-Garcia), using the discontinuous-reconstruction path conservative method.

Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form In collaboration with H. Ranocha (U. of Mainz), we have constructed numerical approxiamtion of the Serre-Green-Naghdi equations which conserve (to machine accuracy) mass, energy, and, when relevant, momentum. Several forms of the equations have beed studied, both involving a hyperbolic balance law reformulation, and more classical ones requiring the explicit inversion of an elliptic operator. The framework introduced is very general and exploits two main building blocks: the use of so-called summation by parts operators (SBP - which satisfy a fully discrete analog of integration by parts); the use of an appropriate split form, a combination of the conservative and non-conservative form of the PDE terms. The approach can be used with any discretization whcih has the SBP property (finite difference/element/volume). Schemes up to order 6 have been tested on complex problems. The enhancements brought by energy conservation when considerng long time propagation are undeniable. The full manuscript 34 has been submitted to Numerical Methods for PDEs.

7.1.3 Efficient discretizations for free surface flows

IMEX schemes in low Froude regimes We developed and analysed a second order numerical method tailored for shallow water flows in regimes characterized by low Froude numbers. The focus is on modeling oceanic and coastal dynamics across different scales, with particular attention on the variation of the Froude number from 1 near the shoreline to significantly lower values offshore. Classical hyperbolic schemes, such as Riemann solvers, become inefficient in these deep water conditions. To address this challenge, a hybrid numerical approach is proposed where part of the system is treated implicitly, resulting in an ImEx (Implicit-Explicit) scheme. To minimize the computational cost associated with solving linear systems, a fully segregated approach is used. In this method, the water height and hybrid mass fluxes are handled implicitly, while velocities are treated explicitly, thus avoiding large linear system resolutions. While various Runge-Kutta schemes are available for a second-order time integration, we chose here a Crank-Nicolson scheme to reduce the number of linear systems required. Spatial discretization is performed using a second-order MUSCL reconstruction. The novel scheme is demonstrated to be Asymptotic Preserving (AP), ensuring that a consistent discretization of the limit model, known as the “lake equations” is obtained as the Froude number approaches zero. Through a series of one- and two-dimensional test cases, the method is shown to achieve second-order accuracy for different Froude numbers. Additionally, the computational efficiency of the proposed method is compared with that of a fully explicit scheme, demonstrating significant time savings with the ImEx approach, particularly in scenarios governed by low Froude numbers. This work has been presented in HONOM2024 conference 24 and in CEDYA 2024 37. A paper has also been submitted 32

Operational discontinuous Galerkin for coastal flood assessment As a result of a long term collaboration with many partners (BRGM, EPOC, UPPA, CNRS, U. Motpellier) we proposed a free surace model - named UHAINA, Basque for wave - built upon the finite element library AeroSol (mainly developed by the Inria team CAGIRE), and based on some ad hoc developments of the DG discretization : (i) a pragmatic treatment of the solution in partially dry cells which guarantees efficiently well-balancedness, positivity and mass conservation at any polynomial order; (ii) an artificial viscosity method based on the physical dissipation of the system of equations providing nonlinear stability for non-smooth solutions. A set of numerical validations on academic benchmarks is performed to highlight the efficiency of these approaches. Finally, UHAINA is applied on a real operational case of study, demonstrating very satisfactory results. Work published in 11.

Modelling undular bores in channels and estuaries.

We have furhter pursued the work initiated in 52. The last work has shown the existence of two families of undular bores. One is a well known class of waves known as Favre waves (from the well known experiments reported in 64) associated to dispersive processes related to vertical velocity profiles. The second type of waves has a different nature and is generated by kinematics along the transversal direction. These waves are thus fully hydrostatic, despite of their strongly dispersive behaviour. They are refferred to as geometrically dispersiev waves, or dispersive-like waves. One of the issues left open in the last work is the derivation of a genuinely nonlinear one-dimensional model confirming this, and allowing to predict the waves in question. This has been done in 30. In the last work we proposed an fully nonlinear dispersive PDE model, obtained as an asymptotic transvers average approximate of the hyperbolic shallow water equations. The model has many interesting theoretical properties and can be used to simulated the waves observed e.g. in 98 for low Froude numbers.

A second question arising from our previous work is the transition from one type wave to another, observed in the latter experimets. Hoping to obtain a one dimensional model capable to simulate both family of waves, we considered the use of a section averaged dispersive model proposed by Winckler and Liu 102, and derived in a very general setting a priori allowing to incorporate all hydrodynamic effects. This work has been performed in collaboration with EDF, who aims at developing a simulation model for rivers or cooling water channel systems for nuclear plants, using networks of one dimensional solvers. The work done in the PhD of B. Jouy has provided very usefull understasnting of several modelling and numerical issues. In this study, we propose an improved version of section-averaged Boussinesq equations of Winckler-Liu. Removing some modelling hypotheses the model is reformulated in conservative variables, allowing exact mass conservation. Using the approach introduced in 65 we proposed a hybrid finite volume and finite element discretisation which has been verified using new travelling wave analytical solutions we derived. We then investigated the impact of numerical dissiaption of the long time propagation, emphasising the need for great precaution in the application of classical dissipative schemes on coarse meshes to evaluate quantities of engineering interest such as maximum wave amplitudes, even in presence of physical dissipation (e.g. friction). This is in line with the resuts obtained in the study of exactly energy conservative schemes for the Serre-Green-Naghdi equations 34 (cf. above). More surprisingly, theoretical and numerical investigations have shown that the Winckler-Liu model can only predict geometrically dispersive waves. So, depsite currenlty begin the most general Boussinesq approximation available, this model has essentially predictive capabilities similar to those of the model we derived in 30 starting from the shallow water equations. This leaves open the question of proposing a 1D model allowing to predice th transition from dispersive-like to Favre waves, which is currently ongiong work. The results obtained with EDF are published in 13, 25.

CEA-CESTA

Participants: Héloïse Beaugendre.

• Title: Development of models and numerical methods for the degradation of a pyrolysable material
• Type: contrat d'accompagnement for Alexis Cas's PhD.
• Duration: 36 months
• Starting date : 1st October 2023
• Coordinator: Heloise Beaugendre Celine Baranger and Simon Peluchon(CEA)
• Summary: During re-entry into the atmosphere, a spacecraft is subjected to considerable mechanical stress and heat flows. These heat flows, applied to the vehicle's wall, cause the heat shield to heat up significantly. The heat shield is made up of materials that chemically degrade under the effect of heat to limit the temperature rise inside the vehicle. These reactions are known as pyrolysis. Similarly, on the surface, these materials undergo physical degradation known as ablation. Understanding these two phenomena is essential for the design of heat shields. The design of such a shield requires precise numerical simulations of the airflow that is created around the vehicle throughout its trajectory. This airflow must be coupled with ablation and pyrolysis phenomena.

EDF

Participants: Bastien Jouy, Mario Ricchiuto.

• Title: Numerical modelling of Favre waves and undular bores in channels with banks
• Duration: 36 months
• Starting date : 08 November 2021
• Coordinator: Mario Ricchiuto
• Summary: The collaboration with EDF (Eleectricité de France) focuses on the improvement of their in house code TELEMAC-Mascaret, initially for the advection of passive scalars (pollutant transport), and more recently for the simulation of hydrostatic and dispersive (undular) bore dynamics in networks of channels (application to abrupt closing/opening of valves). The past work on advection schemes has been done with J.M. Hervouet (retired) and R. Ata (riadh.ata@edf.fr - currently at FLOW-3D) was an informal collaboration. The ongoing collaboration on bore dynamics is with D. Violeau (damien.violeau@edf.fr) is object of a CIFRE contract. This work aims at increasing the capabilities of EDF’s code to simulate the undulating bores studied in 52.

Airbus

Participants: Nicolas Barral, Clarisse Chabaud, Mario Ricchiuto.

• Title: Curvilinear Mesh Adaptation for Aircraft Design
• Duration: 36 months
• Starting date : 1st October 2024
• Coordinator: Nicolas Barral
• Summary: The aim of this thesis work is to develop a mesh adaptation strategy compatible with the high-order numerical methods in Airbus' code CODA. Of particular interest will be the consideration of complex curved geometric shapes found in aeronautics. The success of this work will be measured by the ability of the chosen strategy to control the numerical error near curved boundaries. To this end, a curvilinear mesh generation tool for the automatic mesh adaptation process by metric specification will be developed in the Flowsimulator environment. A method for correcting the geometric error during spatial integration at wall level will also be developed in the CODA tool. On the basis of these two main technologies, a high-order mesh adaptation process will then be developed, enabling reliable control of the numerical error. The range of applications targeted will be the simulation of highly loaded supercritical wings and hyper-supported configurations in icing conditions.

IFPEN

Participants: Martin Parisot, Sebastien Erdocio.

• Title: Monarc
• Duration: 36 months
• Starting date : 1st November 2024
• Coordinator: Martin Parisot
• Summary: This project is a collaboration with Benoit Chauveau, Leo Argelas and Arnaud Pujol, from IFPEN, to supervised the PdH of Sebastien Erdocio. The objective is to propose a model for the dynamics of unsaturated (Vadose area) and saturated (water table) groundwater. To avoid costly 3D simulations, the strategy is based on a 2D-horizontal Dupuit-Forchheimer model for the dynamics of the water table and several (one by horizontal mesh cell) 1D-vertical infiltration equation. The main issue of the project is the coupling between the water dynamics preserving the physical conservation, i.e. mass and energy conservation. In a second phase, perched water, confined water and exchanges with the surface will be considerated.

9.1.1 Visits of international scientists

9.2.1 Horizon Europe

9.2.2 H2020 projects

ANR GEOFUN

Participants: Manon Carreau, Martin Parisot.

• Title:
  GEOphysical Flows with UNified models
• Type:
  ANR
• Duration:
  48 months
• Starting date :
  1st Jan 2020
• Coordinator:
  Martin Parizot
• Abstract:
  The objective of the GeoFun project is to improve the modeling and simulation of geophysical flows involving at least two different processes. The main application we have in mind is water catchment areas, where a shallow free surface flow stands above a underground flow on porous medium. Our vision of water transport is often naive, because we first think of rivers, lakes, and flooding, but actually, $80\%$ of water in continental areas is underground. Sometimes, the porous substrate is covered with an impermeable rock stratum, which confines the flow as in pipelines, except at certain points where springs and resurgences appear. Our long term goal is to propose a global and unified model of an aquifer. By global, we mean a complete description, including free surface flow (rivers), exchanges with the groundwater in unsaturated area, flows in caves, that might be congested or not, and might contain air pockets. By unified, we mean that we do not aim to decompose the domain and use different models for each part of the aquifer. On the contrary, we plan to propose and study models able to pick the relevant physic by themselves in a multi-physics context. The numerical approximation will be a main concern all along the way. The final contribution of the GeoFun project is the development of a scientific computing library, simulating complex flows in water catchment areas thanks to the numerical strategies analyzed in this project. Since unified models are design to be applied in the whole computational domain with no domain decomposition, the robustness of the numerical strategy at all regime are essential. Our unified numerical schemes will degenerate towards existing schemes in those regions, in order to guarantee a similar feasibility and robustness. Moreover, since the final goal is to test the library on realistic aquifers, the efficiency of the methods is of crucial importance.

ANR LAGOON

Participants: Maria Kazolea, Ralph Lteif, Martin Parisot, Vincent Pilorget, Mario Ricchiuto.

• Title:
  Large scale global storm surge simulations
• Type:
  ANR
• Duration:
  48 months
• Starting date :
  1st Oct 2021
• Coordinator:
  Vincent Perrier (U.Pau et des Pays de l'Adour)
• Abstract:
  The aim of the project is to develop an all-scale shallow water storm-surge model simulating different features of oceanic flows: from large scale linear waves in open ocean to small scale non-linear flows in coastal areas, and using high resolution by combining novel numerical approaches on unstructured grids and high performance computing.

PERPR IRIMA ROM

Participants: Nicolas Barral, Maria Kazolea, Mario Ricchiuto, Dean Yuan.

• Title:
  Seismo-volcanic, tsunami and hydro-climatic risks in overseas France
• Type:
  ANR
• Duration:
  48 months
• Starting date :
  1st Oct 2024
• Inria Contact:
  Mario Ricchiuto
• Coordinator:
  Anne Le Friant (IPGP)
• Abstract:

  The PC Outermer project focuses on the intense and frequent telluric and hydro-meteorological hazards faced by overseas and intertropical populations, such as earthquakes, volcanic eruptions, tsunamis, gravity instabilities, flooding/submersions and coastal erosion in connection with cyclones and climate change. It is essential to take into account the geographical and societal particularities of overseas and intertropical areas (distance from the hexagone, insularity, lack of connection and size of territories, high proportion of the total population of the territory exposed to one or more hazards, diversity of cultural and historical practices, social and political tensions), which require a specific understanding of local capacities for risk prevention and management, as well as adaptation and resilience. Innovative management strategies therefore need to be developed and tested in terms of feasibility/acceptability/inclusivity, taking into account the political and social status of these territories. Knowledge of telluric and hydrometeorological hazards, and of the vulnerabilities of these territories, is essential because of the active observation conditions they offer, and above all in order to meet the challenges of risk and crisis management. However, all our scientific achievements show that there are still limits to our ability to detect changes in the phase of activity as early as possible, to the resilience of our networks, and to our capacity to develop integrated risk management models that can characterize the issues and assess their vulnerability to different hazards. The risks to which overseas populations are exposed need to be reconsidered in order to accurately qualify and model cascading phenomena and forcing processes, and the superposition of hazards and vulnerabilities on the same territories, in order to reduce the consequences of major disasters and help develop relevant risk and resilience policies.

  This project aims to: 1/ identify new observables for the study of natural hazards and their anthropogenic impact on large spatio-temporal scales, 2/ develop holistic and integrated models of complex processes, taking into account the uncertainties associated with climate change projections and the integration of coupled predictive models, 3/ to develop integrated risk management strategies adapted to overseas and intertropical areas, and capable of dealing with the consequences of extreme and cascading events that induce multiple risks (eruptions, instabilities, tsunamis, floods). Inria is participating in WP2 which is devoded in on estimating the damage and socio-economic impact of tsunami hazards, applying our methodologies to Mayotte in the Indian Ocean.

Inria Action Exploratoire: AM${}^2$OR

Participants: Nicolas Barral.

• Title:
  AM${}^2$OR: Adaptive meshes for Model Order Reduction
• Type:
  Inria Action Exploratoire
• Duration:
  48 months
• Starting date :
  1st October 2022
• Coordinator:
  Nicolas Barral
• Partner:
  Tommaso Taddei (Inria MEMPHIS)
• Abstract:
  Mesh adaptation and Model Order Reduction both aim at reducing significantly the computational cost of numerical simulations by taking advantage of the solution's features. Reduced Order Modelling is a method that builds lighter surrogate models of a system's response over a range of parameters, which is particularly useful in the solution of design and optimization inverse problems. Reduced-order models rely on a high-fidelity (e.g., finite element) approximation that should be sufficiently accurate over the whole range of parameters considered: in presence of structures such as shocks and boundary layers, standard mesh refinement techniques would lead to high-fidelity models of intractable size. In this project, we propose a novel adaptive procedure to simultaneously construct a high-fidelity mesh (and associated discretisation) and a reduced-order model for a range of parameters, with particular emphasis on inverse problems in computational fluid dynamics.

RNA PSGAR CORALI

Participants: Maria Kazolea, Martin Parisot, Mario Ricchiuto.

• Title:
  COnnaissances inteRdisciplinaires pour meilleure Adaptation face aux risques LIttoraux
• Duration:
  48 months
• Starting Date:
  December 2024
• Inria Contact:
  Mario Ricchiuto
• Coordinator:
  Prof. Aldo Sottolichio
• Abstract:
  The aim of PSGAR CORALI is to provide the multidisciplinary scientific knowledge needed to better forecast coastal changes and developments, and to better anticipate societal adaptations to the natural risks of erosion and submersion at the land-sea interface. The research proposed will be fundamental and international in scope, with direct application to regional sites in New Aquitaine. To achieve this, the PSGAR will implement a series of research and expert assessments (observation, modeling, analysis and decision support) to accelerate the transition towards a society capable of adapting to and becoming more resilient and sustainable in the face of current and future changes in open and semi-enclosed coastlines. To meet this challenge, heightened by climate change, interdisciplinary research will be encouraged and stimulated. This holistic, integrative approach to knowledge brings together the geosciences, environmental sciences, human and social sciences, and engineering. These disciplines, although involved in these issues, still too often work without direct interaction with society. The PSGAR proposes to integrate them more fully and to encourage the co-construction and transfer of knowledge to public and private coastal stakeholders. The PSGAR CORALI is built around a consortium federating the major universities of New Aquitaine and leading research organizations in the field of natural and environmental risks, already grouped around the regional research network (R3) RIVAGES, dedicated to the specific theme of coastal risks.

IMPT 2023

Participants: Nicolas Barral, Fabien Salmon.

• Title:
  Parallel mesh adaptation for sea ice dynamic
• Duration:
  24 months
• Starting Date:
  1st September 2023
• Coordinator:
  Nicolas Barral
• Abstract:
  In this project we work with the sea ice model neXtSIM, developed at Nansen Environmental and Remote Sensing Center (Bergen, Norway) and Institute of Environmental Geosciences (Grenoble, France). This new model aims at modelling complex sea ice dynamics accross scales, in order to be used for both local short-term predictions and global climate prediction simulations. The specificity of neXtSIM is the use of a purely Lagrangian advection formalism on fully unstructured meshes, coupled with a novel rheological framework, that has given promising results. Such a Lagrangian approach results in strongly deformed meshes over time, in particular in the vicinity of cracks in the ice resulting from the mechanical forces coming from winds and currents, and where large drift of the ice can occur. A remeshing step is thus necessary to locally replace stretched or invalid mesh elements and restore the quality of the mesh. However, unlike the rest of the code that was parallelised recently for distributed memory architectures using MPI, the remeshing stage remains sequential, thus strongly impacting the performance of the code. Besides, the current remeshing does not yet take advantage of modern anisotropic mesh adaptation techniques that aim at optimising the size and orientation of the mesh elements to minimise a certain numerical error estimate and makes it possible to reduce the computationnal cost while increasing the accuracy. The goal of the collaboration is to leverage these methods to accelerate simulations, and thus be able to perform ensembles of large-scale high-resolution (kilometric) simulations of the sea ice, and to study ice trajectories from a statistical perspective.

IMPT 2024

Participants: Martin Parisot, Tony Bonnet.

• Title:
• Duration:
  36 months
• Starting Date:
  1st octobre 2024
• Coordinator:
  Martin Parisot
• Abstract:
  This project is a collaboration with Mathieu Coquerelle, from I2M, to supervised the PdH of Tony Bonnet. The objective of this project is to propose a numerical tools for the analysis of the exchange between surface water and ground water. A 3D modeling is considerate based on the VANS (Volume Averaged Navier–Stokes) model. The scientific lock lies on the boundary condition that depends on the the direction of the flows (from surface to ground or the opposite), making simulations usually not robust. In a second time, we propose to analyse the evolution of the physical parameters of the ground media (porosity and permeability), recovering experimental data and ensuring the conservation of mass and energy.

10.1.1 Scientific events: organisation

10.1.2 Journal

10.1.3 Invited talks

• M. Ricchiuto has delilvered invited talks to the following events
  • Oberwolfach workshop “Hyperbolic Balance Laws: interplay between scales and randomness”, 21 February-01 March 2024, Oberwolfach (Germany);
  • Gold shark-FV - Sharing high order reserach know-how on Finite-Volume, May 26-31 2024, Minho (Portugal);
  • 2024 International Conference on Water Waves and Bores, Sptember 13-18, Ningbo University (China);

• M. Parisot has delilvered invited talks to the following events
  • Bourgeons ANR, January 2024, Paris;
  • Canum, June 2024, Ile de Ré;
  • Journées de Modélisation des Surfaces Continentales: JMSC24, Strasbourg.

10.1.4 Leadership within the scientific community

10.1.5 Research administration

M. Ricchiuto has been deputy head of science of the Inria center at University of Bordeaux until Arpil 2024.

10.2.1 Teaching

• Licence: Nicolas Barral, Calcul Scientifique en Fortran 90, 22h, L3, ENSEIRB-MATMÉCA, France
• Licence : Nicolas Barral, TP Fortran 90, 44h, L3, ENSEIRB-MATMÉCA, France
• Licence : Nicolas Barral, TP C++, 48h, M1, ENSEIRB-MATMÉCA, France
• Master : Nicolas Barral, Calcul Haute Performance (OpenMP-MPI), 45h, M1, ENSEIRB-MATMÉCA et Université de Bordeaux, France
• Master : Nicolas Barral, Meshing for computational science, 24h, M2, ENSEIRB-MATMÉCA et Université de Bordeaux, France
• Master : Nicolas Barral : projet professionnel et suivi de stages, 14 h, ENSEIRB-MATMÉCA, France
• Master : Nicolas Barral : responsable des stages 2A, 20 h, ENSEIRB-MATMÉCA, France
• Héloïse Beaugendre has been the Director of Research, Innovation, and Transfer at ENSEIRB-MATMECA since September 2024. 96 h.
• Licence: Héloïse Beaugendre, Encadrement de projets sur la modélisation du biomimétisme ou le chaos, 20h, L3, ENSEIRB-MATMÉCA, France
• Master : Héloïse Beaugendre, Calcul Haute Performance (OpenMP-MPI), 45h, M1, ENSEIRB-MATMÉCA et Université de Bordeaux, France
• Master : Héloïse Beaugendre, Responsable de filière de 3ème année, 20h, M2, ENSEIRB-MATMÉCA, France
• Master : Héloïse Beaugendre, Calcul parallèle (MPI), 39h, M2, ENSEIRB-MATMÉCA, France
• Master : Héloïse Beaugendre, Encadrement de projets de la filière Calcul Haute Performance, 10h, M2, ENSEIRB-MATMÉCA, France
• Master : Héloïse Beaugendre, Modélisation des écoulements turbulents, 36h, M2, ENSEIRB-MATMÉCA, France
• Master : Héloïse Beaugendre, Encadrement de projets sur la quantification d'incertitudes et la sensibilté au maillage, 20h, M1, ENSEIRB-MATMÉCA, France
• Master : Héloïse Beaugendre, Projet fin d'études, 4h, M2, ENSEIRB-MATMÉCA, France
• License: Martin Parisot, TP Fortran, 21h, M1, ENSEIRB-MATMÉCA, France
• Master : Martin Parisot, GeoPhysics course, 26h cours magistrale, M2, ENSEIRB-MATMÉCA, France
• Master and PhD: Elena Gaburro, Advanced Numerical Methods for the solution of Hyperbolic Equations, 12h (University of Verona, Italy)

10.2.2 Supervision

• PhD (defended in June 2024): J. Galaz Mora, Coupling of free surface coastal models, started in February 2021, co-supervised by M. Kazolea and A. Rousseau.
• PhD (up to April 2024): M. Carreau, Modeling, analysis and scientific computing for the simulation of geophysical flows with unified models, started in November 2020, co-supervised by M. Parisot and R. Masson.
• PhD (defended in December 2024): M. Romanelli, Deep Wall Models for Aerodynamic Simulations, started in october 2021, co-supervised by H. Beaugendre and M. Bergmann (MEMPHIS).
• PhD (defended in October 2024): B. Jouy, Simulation of Favre waves in channels with variable section, started in November 2021, co-supervised by M. Ricchiuto and D. Violeau (EDF).
• PhD in progress: V. Pilorget, High order DG modelling of global storm surges for very long term inundation simulations, started in January 2022, co-supervised by A.-G. Filippini (BRGM) and M. Ricchiuto.
• PhD in progress: A. Cas, Development of models and numerical methods for the degradation of a pyrolysable material , started in October 2023, co-supervised by C. Baranger and S. Peluchon (CEA) and H. Beaugendre.
• PhD in progress: F. Forte Tenreiro,On the design of an improved Boussinesq model for real applications: equilibrium between accuracy and performance, started in April 2024, co-supervised by A.-G. Filippini (BRGM) and M. Kazolea.
• PhD in progress: A. Del Piero, Advanced Discontinuous Galerkin Framework for Urban Flood Simulation: Sub-Cell Modeling and Integration with Real-World Dynamics, started in October 2024, co-supervised by A.-G. Filippini (BRGM) and M. Kazolea.
• PhD in progress: I. Tifouti, Mesh adaptation with model order reduction, started in October 2022, co-supervised by N. Barral and T. Taddei (Inria MEMPHIS).
• PhD in progress: T. Bonnet, started in October 2024, co-supervised by Martin Parisot and Mathieu Coquerelle (I2M).
• PhD in progress: S. Erdocio, started in November 2024, co-supervised by Martin Parisot and Benoit Chauveau (IFPEN).
• PhD in progress: C. Chabaud, Curvilinear Mesh Adaptation for Aircraft Design, co-supervised by N. Barral, M. Ricchiuto, and R. Laraufie (Airbus).
• PhD in progress: M. Janin, Numerical modelling of tsunami propagation with short crested waves, started in November 2024, co-supervised by P. Heinrich (CEA) and M. Ricchiuto.

10.2.3 Juries

• Heloise Beaugendre's participation in the selection committee for the MCF position in Rennes.
• Heloise Beaugendre's participation in the selection committee for the PR position in Poitiers.
• H. Beaugendre, On October 1, 2024, participation in Claire Roche's thesis defense. Thesis examiner. CEA Paris Saclay.
• H. Beaugendre, On November 29, participation in Benoit Cossart's thesis defense. Bordeaux University.
• H. Beaugendre, On December 10, participation in Alexis Dorange's thesis defense. ONERA Châtillon.
• H. Beaugendre, On December 12, participation in Michele Romanelli's thesis defense. PhD Supervisor. Bordeaux University.
• H. Beaugendre, On December 13, participation in Lucas Ménez's thesis defense. Thesis examiner. Poitiers ENSMA.
• H. Beaugendre, On December 17, participation in Ludovic Taguema's thesis defense. Thesis examiner. ONERA Toulouse.
• H. Beaugendre, On December 19, participation in Thomas Vigier's thesis defense. Bordeaux University.
• M. Ricchiuto has been member of the following juries:
  • PhD defense of C. Brutto, University of Trento, on June 18th, 2024. As thesis reviewer;
  • PhD defense of M. Nunez, Universitat Politècnica de Catalunya, on July 4th, 2024. As thesis reviewer;
  • PhD defense of M. Salihoglu, Sorbonne Université, on November 20th 2024. As thesis reviewer.

10.3.1 Participation in Live events

On June 24th 2024, in the framework of the cycle `Unithé ou Café” of the Inria center at Unviersity of Bordeaux, M. Ricchiuto has delivered a presentation on the “Continuum : modélisation, simulation, calcul”.

On October 7, 2024, H. Beaugendre participated in the Forum Emploi Math event at La Villette, Paris. She led and moderated the roundtable discussion on Mathematics and Space.

On September 9-14, 2024, M. Kazolea participated in the HONOM2024 conference, where she presented the European Project Rescuer as part of the project's communication and dissemination package 38.

International journals

• 4 articleN.Nicolas Barral, T.Tommaso Taddei and I.Ishak Tifouti. Registration-based model reduction of parameterized PDEs with spatio-parameter adaptivity.Journal of Computational Physics499February 2024, 112727HALDOIback to text
• 5 articleH.H. Beaugendre, A.A. Chan, V.V. Delmas, R.Raphaël Loubère, P.-H.P.-H. Maire, F.F. Morency and T.T. Vigier. Multidimensional aware subfaced-based Finite Volume scheme for the Eulerian droplet system of equation.Computers and Fluids279July 2024, 106326HALDOIback to text
• 6 articleS.Sourabh Bhat, N.Nicolas Barral and M.Mario Ricchiuto. Error-based efficient parameter space partitioning for mesh adaptation and local reduced order models.Computer Methods in Applied Mechanics and Engineering435February 2025, 117649HALDOIback to text
• 7 articleW.Walter Boscheri, F.Francisco Chinesta, R.Raphaël Loubère, S.Siddhartha Mishra, G.Gabriella Puppo, M.Mario Ricchiuto and C.-W.Chi-Wang Shu. Preface in Honour of Prof. Rémi Abgrall on the Occasion of His 61th Birthday.Communications on Applied Mathematics and Computation63July 2024, 1519-1520HALDOIback to text
• 8 articleM.Mirco Ciallella, S.Stephane Clain, E.Elena Gaburro and M.Mario Ricchiuto. Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data.Computers & Mathematics with Applications175December 2024, 1-18HALDOIback to text
• 9 articleB.Benjamin Constant, S.Stéphanie Péron, H.Heloise Beaugendre and C.Christophe Benoit. An improved immersed boundary method for turbulent flow simulations on Cartesian grids: extension of a global geometric approach for thin boundary layers and strong flow incidence.Journal of Computational Physics5192024, 113441HALDOIback to text
• 10 articleM.Michael Dumbser, O.Olindo Zanotti, E.Elena Gaburro and I.Ilya Peshkov. A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system.Journal of Computational Physics504May 2024, 112875HALDOIback to text
• 11 articleA. G.Andrea Gilberto Filippini, L.Luca Arpaia, V.Vincent Perrier, R.Rodrigo Pedreros, P.Philippe Bonneton, D.D. Lannes, F.Fabien Marche, S.Sebastien de Brye, S.Simon Delmas, S.Sophie Lecacheux, F.Faïza Boulahya and M.Mario Ricchiuto. An operational discontinuous Galerkin shallow water model for coastal flood assessment.Ocean Modelling192December 2024, 102447HALDOIback to text
• 12 articleE.Elena Gaburro, W.Walter Boscheri, S.Simone Chiocchetti and M.Mario Ricchiuto. Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: quasi-conservative formulation with subcell finite volume corrections.Computer Methods in Applied Mechanics and Engineering431June 2024, 117311HALDOIback to text
• 13 articleB.Bastien Jouy, D.Damien Violeau, M.Mario Ricchiuto and M. H.Ming Hoang Le. One dimensional modelling of Favre waves in channels.Applied Mathematical Modelling133September 2024, 170-194HALDOIback to text
• 14 articleY.Yogiraj Mantri, P.Philipp Öffner and M.Mario Ricchiuto. Fully well-balanced entropy controlled discontinuous Galerkin spectral element method for shallow water flows: global flux quadrature and cell entropy correction.Journal of Computational Physics498February 2024, 112673HALDOIback to textback to textback to text
• 15 articleL.Lorenzo Micalizzi, M.Mario Ricchiuto and R.Rémi Abgrall. Novel well-balanced continuous interior penalty stabilizations.Journal of Scientific Computing1001February 2024, 14HALDOIback to text
• 16 articleM.Martin Parisot. Thick interfaces coupling technique for weakly dispersive models of waves.ESAIM: Mathematical Modelling and Numerical Analysis584August 2024, 1497-1522HALDOIback to text
• 17 articleJ.Jens Visbech, A.Allan Engsig-Karup and M.Mario Ricchiuto. A spectral element solution of the Poisson equation with shifted boundary polynomial corrections: influence of the surrogate to true boundary mapping and an asymptotically preserving Robin formulation.Journal of Scientific Computing10212025, 11HALDOIback to text

Invited conferences

• 18 inproceedingsM.Maria Kazolea, C.Carlos Parés-Madronal and M.Mario Ricchiuto. Discrete fully well balanced WENO finite difference schemes via a global-flux quadrature method.9th European Congress on Computational Methods in Applied Sciences and EngineeringLisbon, PortugalJune 2024HALDOIback to text

International peer-reviewed conferences

• 19 inproceedingsH.H Beaugendre, A.A Benoit, F.F Morency and M.M Parisot. A Multi-layered Integral Approach to the de-icing process.Volume Advances in Numerical Methods for Solution Of PDEs, 2024DOI: 10.23967/eccomas.2024.0319th European Congress on Computational Methods in Applied Sciences and EngineeringAdvances in Numerical Methods for Solution Of PDEs, 2024Lisbon, PortugalOctober 2024HALback to text
• 20 inproceedingsB.Benjamin Constant, H.Heloise Beaugendre, S.Stéphanie Péron and C.Christophe Benoit. Amélioration des méthodes de frontières immergées pour la simulation d'écoulements turbulents sur grilles cartésiennes.CANUM 2024 - 46ème Congrès National d'Analyse NumériqueLe-Bois-Plage-en-Ré, FranceMay 2024HAL
• 21 inproceedingsJ.José Galaz, M.Maria Kazolea and A.Antoine Rousseau. Coupling Dispersive Shallow Water Models by Deriving Asymptotic Interface Operators.Domain Decomposition Methods in Science and Engineering XXVII27th International Conference on Domain Decomposition Methods in Science and Engineering - DD27149Lecture Notes in Computational Science and EngineeringPrague, Czech RepublicSpringer Nature SwitzerlandJanuary 2024, 181-188HALDOIback to text
• 22 inproceedingsJ.Jens Visbech, A. P.Allan Peter Engsig-Karup, H. B.Harry B Bingham, M.Mostafa Amini-Afshar and M.Mario Ricchiuto. A high-order shifted boundary method for water waves and floating bodies.IWWWFB 2024 - 39th International Workshop on Water Waves and Floating BodiesSt Andrews, Scotland, United KingdomApril 2024HALback to text

Conferences without proceedings

• 23 inproceedingsM. G.Michele Giuliano Carlino and E.Elena Gaburro. Second Order Finite Volume Scheme for Shallow Water Equations on Manifolds.ICNAAM 2022 - 20th International Conference of Numerical Analysis and Applied Mathematics30941Heraklion (CR), GreeceAIP Conference ProceedingsJune 2024HALDOIback to text
• 24 inproceedingsM.Maria Kazolea, R.Ralph Lteif and M.Martin Parisot. High order ImEx method for the shallow water model.HONOM 2024 - High-Order NOnlinear numerical Methods for evolutionary PDEs: theory and applications.Chania Crete, GreeceSeptember 2024HALback to text

Edition (books, proceedings, special issue of a journal)

• 25 proceedingsSerre and Boussinesq Models for Favre Waves in Trapezoidal Cross-Sectional Channels.Advances in Hydroinformatics—SimHydro 2023 Volume 2Springer WaterSpringer Nature Singapore2024, 473 - 483HALDOIback to text

Doctoral dissertations and habilitation theses

• 26 thesisJ.José Galaz. Coupling methods of phase-resolving coastal wave models.Université de montpellierJune 2024HALback to text
• 27 thesisM.Maria Kazolea. Advanced Numerical Methods for Nonlinear Water Wave dynamics and Breaking in Boussinesq-type models.Université de BordeauxOctober 2024HALback to text
• 28 thesisM.Martin Parisot. Some modeling and computational aspects of water waves action.Université de BordeauxNovember 2024HALback to text

Reports & preprints

• 29 miscW.Wasilij Barsukow, M.Mario Ricchiuto and D.Davide Torlo. Structure preserving nodal continuous Finite Elements via Global Flux quadrature.July 2024HALback to textback to text
• 30 miscS.Sergey Gavrilyuk and M.Mario Ricchiuto. A geometrical Green-Naghdi type system for dispersive-like waves in prismatic channels.December 2024HALback to textback to text
• 31 miscM.Maria Kazolea, C.Carlos Parés-Madronal and M.Mario Ricchiuto. APPROXIMATE WELL-BALANCED WENO FINITE DIFFERENCE SCHEMES USING A GLOBAL-FLUX QUADRATURE METHOD WITH MULTI-STEP ODE INTEGRATOR WEIGHTS.January 2025HALback to text
• 32 miscR.Ralph Lteif, M.Maria Kazolea and M.Martin Parisot. An efficient second order ImEx scheme for the shallow water model in low Froude regime.December 2024HALback to text
• 33 miscM.Martin Parisot. Derivation of weakly hydrodynamic models in the Dupuit-Forchheimer regime.March 2024HALback to text
• 34 miscH.Hendrik Ranocha and M.Mario Ricchiuto. Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form.August 2024HALback to textback to textback to text
• 35 miscF.Fabien Salmon. Unifying all physics with a single postulate.July 2024HAL

Other scientific publications

• 36 inproceedingsJ.José Galaz, M.Maria Kazolea and A.Antoine Rousseau. The linear hybrid Boussinesq-SaintVenant model is well-posed and produces O(h^2/L^2) reflections: Couplin phase-resolving coastal wave models.PhD day 2024Montpellier, FranceMarch 2024HALback to text
• 37 miscM.Maria Kazolea, M.Martin Parisot and R.Ralph Lteif. High order ImEx method for the shallow water model.Bilbao, SpainJune 2024HALback to text
• 38 inproceedingsM.Maria Kazolea. Resilient Solutions for Coastal, Urban, Estuarine and Riverine Environments.HONOM 2024 - High-Order NOnlinear numerical Methods for evolutionary PDEs: theory and applications.Chania, GreeceSeptember 2024HALback to text