Thèse Couplage des Méthodes des Volumes Finis et des Particules Lissées pour l'Hydrodynamique à Surface Libre avec Applications à la Modélisation des Inondations et à l'Évaluation des Risques Mult H/F

Université Paris-Saclay GS Sciences de l'ingénierie et des systèmes

Établissement : Université Paris-Saclay GS Sciences de l'ingénierie et des systèmes
École doctorale : Sciences Mécaniques et Energétiques, Matériaux et Géosciences
Laboratoire de recherche : LMPS - Laboratoire de Mécanique Paris-Saclay
Direction de la thèse : Faisal AMLANI ORCID 0000000340228088
Début de la thèse : 2026-09-08
Date limite de candidature : 2026-04-21T23:59:59

Le changement climatique augmente la fréquence et l'intensité des pluies extrêmes et des inondations en France [1], ce qui rend indispensable une évaluation fiable des risques d'inondation pour la planification des infrastructures et la prise de décisions éclairées en matière de risques. Les solveurs physiques haute fidélité sont essentiels pour prédire l'étendue des inondations, les caractéristiques des écoulements et les charges hydrodynamiques (forces) sur l'environnement bâti, tout en servant de base de calcul pour les cadres d'évaluation des risques multialéas utilisés dans l'adaptation des infrastructures [2,3]. La propagation des inondations est régie par des équations différentielles partielles non linéaires à surface libre (par exemple, les équations de Navier-Stokes pour les eaux peu profondes ou incompressibles) qui impliquent un transport hyperbolique, des termes sources non conservatifs, des transitions humides-secs et des régimes hautement transitoires tels que les chocs et le déferlement des vagues. Les méthodes des volumes finis (FV) [4,5] sont largement utilisées en raison de leur conservativité et de leur robustesse à grande échelle, tandis que l'hydrodynamique des particules lissées (SPH) [8,9] capture naturellement les grandes déformations et les interactions fluide-structure, mais reste exigeante sur le plan informatique.

L'objectif de cette thèse est de développer un cadre de calcul hybride FV-SPH pour les écoulements non linéaires à surface libre, adapté à la modélisation des inondations et capable de traiter de grandes régions en France. Le premier axe se concentre sur la construction d'un solveur couplé qui permet un échange d'informations cohérent et efficace entre les représentations eulériennes (FV) et lagrangiennes (SPH), tout en préservant la conservativité, la stabilité et la fidélité physique. La validation sera effectuée sur des benchmarks canoniques (par exemple, des problèmes de rupture de barrage et d'impact des vagues), avec une attention particulière portée à l'estimation des charges hydrodynamiques sur les structures immergées. Le deuxième axe développe une stratégie multi-échelle dans laquelle des simulations SPH localisées à haute résolution sont intégrées dans un modèle FV global, permettant une résolution précise des géométries urbaines complexes. L'accent sera mis sur l'intégration de données topographiques et urbaines haute résolution (e.g., DEM, LiDAR) des régions françaises dans les maillages et les distributions de particules. À terme, le projet vise à fournir un solveur d'inondations robuste et efficace, capable d'intégrer des topographies réalistes, de résoudre les impacts structurels localisés et de soutenir l'ingénierie tenant compte des risques climatiques.

Several consequences of climate change are already observable and possibly irreversible on engineering time scales. In France [1] (and Europe at large), the increasing frequency and intensity of extreme weather (e.g., rainfall) events, river overflow, and coastal flooding demonstrate that hydrological extremes are present and recurring challenges. Engineering design and infrastructure planning must therefore increasingly rely on quantitatively reliable flood hazard assessments. As such, high-fidelity physics-based flood solvers play a central facilitating role in this context, including for predicting inundation extent and flow characteristics as well as for quantifying hydrodynamic loading on the built environment/infrastructure. In particular, accurate and physically-faithful deterministic simulations are essential for emerging multihazard frameworks [2], serving as the underlying computational foundation of probabilistic and decision-support tools [3] employed in problems related to risk adaptation and associated infrastructure planning.

Flood propagation is governed by nonlinear free-surface partial differential equations (PDEs), typically the shallow-water equations or the incompressible Navier-Stokes equations with moving boundaries. These systems combine hyperbolic transport, non-conservative source terms, evolving wet-dry interfaces, and strongly transient (time-dependent) regimes such as jumps/discontinuities and wave breaking. Low-order finite volume- (FV-)based approaches [4,5] are most common for large-scale flood modeling due to their conservative structure, robustness, and relatively-low computational cost. However, demands for higher-order accuracy and for more general applicability introduce a number of classical numerical challenges: shock capturing, preservation of well-balanced steady states over irregular geometries, minimization of computational cost, mitigation of non-physical oscillations, and stability, among others. Although other methodologies have been proposed [6,7], they are less versatile in general contexts than those based on FV.

Smoothed Particle Hydrodynamics (SPH) [8, 9], on the other hand, provides a fully Lagrangian discretization based on kernel approximations of the governing equations. SPH naturally handles large free-surface deformation, impact phenomena, and complex fluid-structure interactions without many of these mesh issues. However, particle methods remain computationally expensive (in terms of time and memory) at large scales and require careful stabilization to ensure consistency/conservation.

Additionally, integration of high-resolution topographic and urban geographic data into computational geometries/domains, which is essential for the treatment of realistic scenarios, is not straightforward. Digital elevation models (DEMs), LiDAR scans, and detailed urban maps must be translated into discretizations suitable for both FV grids and particle distributions. Such requirements introduce a number of numerical challenges related to source-term discretization and the representation of sharp geometric features. For example, a specific topography enters into shallow water formulations via (non-conservative) source terms; hence discrete errors in its representation may compromise balance and induce spurious numerical artifacts. Furthermore, focused treatment is required for mesh generation over highly irregular topographies (including sharp urban features) and for particle initialization near complex boundaries.

Hybrid Eulerian-Lagrangian strategies have been explored in the context of free-surface Navier-Stokes flows and wave-structure interaction problems [8,9]. Such hybridized approaches typically depend on a domain decomposition or an overlapping configuration in which SPH is employed locally to resolve highly-complex free-surface dynamics, while grid-based solvers govern the larger-scale flow. However, these developments have not led to a conservative, fully-consistent coupling between FV shallow-water solvers and fully Lagrangian SPH tailored to multiscale flood propagation over complex and realistic topographies. Indeed, a general, dynamically-adaptive FV-SPH framework specifically designed for large-scale flood modeling has not been adequately developed.

Accordingly, the construction of a fast and efficient hybridized flood solver---that can simultaneously preserve accuracy, conservation, and stability (while incorporating realistic topographic data)---is the primary focus of this work.

The overarching goals of this project are two-fold:

1) **** Construction of a coupled finite FV-SPH flood solver for nonlinear free-surface flows. ****
Building on an existing FV solver, the objective is to develop and implement in code the complementary SPH component together with a consistent coupling mechanism enabling the fast and accurate exchange of information between Eulerian and Lagrangian representations. The overall solver will be designed to be physically-faithful and computationally efficient, as well as to remain conservative and robust in highly-dynamic regimes. Validation will be performed on canonical benchmarks that include dam breaking, wave breaking, and fluid-structure interaction problems, with particular attention geared towards hydrodynamic load (force) estimation on immersed obstacles (e.g., buildings, trees, etc.).

2) **** Hybrid multiscale algorithms & mesh generation for realistic configurations. ****
The second objective extends the coupled solver towards a multi-resolution framework in which localized SPH simulations are embedded within a global FV simulation, particularly near buildings and geometrically complex urban features. The FV solver will govern large-scale flood propagation, while SPH will provide localized high-fidelity solutions of fluid-structure interaction and force estimation. A particular challenge is the incorporation of elevation models and urban geographic data as well as their mesh and particle initializations on the corresponding irregular geometries. The methodology will be assessed on realistic flood scenarios representative of those found in various French regions.

A complementary research direction, contingent on progress within the above axes, is to explore how the developed solver may support surrogate or reduced-order modeling within broader multihazard risk assessment frameworks. In particular, high-fidelity simulations may serve as a basis for preliminary uncertainty propagation or data-driven approximation of hazard/risk and (force-based) engineering analysis metrics.

In short, such work is towards advancing hybrid numerical methodologies for nonlinear free-surface flows by developing a robust flood solver capable of integrating realistic topographies, resolving localized structural impacts, and supporting hazard-informed engineering in climate-related contexts (particularly in France).

**** Year 1: literature review & baseline/foundational development. ****
The first phase of the project consists of an in-depth bibliographic study on finite volume (FV) methods for shallow-water equations, Smoothed Particle Hydrodynamics (SPH) for free-surface flows, and existing hybrid Eulerian-Lagrangian strategies. Particular attention will be given to global conservation, well-balanced formulations, stability, and shock-capturing (treatment of discontinuities), as well as to SPH consistency and stabilization. Building on an existing FV solver, the SPH component will be developed and implemented in code, together with preliminary coupling strategies. Initial validation will be performed on canonical benchmarks (e.g., dam break, wave breaking).

**** Year 2: coupling strategy & a multiscale framework. ****
The second phase focuses on the construction of a consistent, conservative, and dynamically-adaptive FV-SPH coupling algorithm that enables efficient information exchange between Eulerian and Lagrangian domains. This will enable extensions of the overall solver toward a multiscale configuration in which localized high-fidelity SPH simulations are embedded within a global FV model. Validation will include fluid-structure interaction problems and hydrodynamic force estimation on immersed obstacles representative of urban environments.

**** Year 3: realistic configurations & risk-oriented extensions. ****
The final phase focuses on the integration of high-resolution topographic and urban geographic data (e.g., DEMs, LiDAR) into computational geometries, including mesh generation and particle initialization over irregular domains. The methodology will be assessed on realistic flood scenarios representative of French regions. Depending on progress, complementary developments may explore reduced-order or surrogate modeling strategies to support uncertainty propagation and multihazard risk assessment frameworks.