Phd Position F/m All-speed Schemes for Fluid-structure Interaction

Le descriptif de l’offre ci-dessous est en Anglais_

**Type de contrat**: CDD

**Niveau de diplôme exigé**: Bac + 5 ou équivalent

**Fonction**: Doctorant

**Contexte et atouts du poste**:
The aim of this project is to develop computationally efficient and robust numerical schemes for simulating multi-material interactions, including interfaces between fluids, gases, and solids. The project uses a monolithic hyperbolic model of partial differential equations to describe all materials within the same Eulerian framework. This allows simulations to be performed across a wide range of flow regimes — from compressible to nearly incompressible — without changing the solver. In addition to interface treatment, the model's multi-scale nature poses numerical challenges, particularly when stiff materials such as copper or fluids under high pressure are considered. This requires so-called all-speed schemes, which remain stable when large time steps are taken during deformation or transport of the interfaces while eliminating fast, negligible processes. This necessitates the use of semi-implicit time integrators, which yield non-linear implicit systems. To avoid computational overheads, suitable linearisations are considered that are compatible with the interface conditions, which are treated as immersed boundaries.

This PhD is part of the ANR project DELFIN which is dedicated to the development of efficient numerical schemes for fluid structure interaction.
Travel and research visits to international collaborating universities located in Bordeaux (France), Rome (Italy) and Aachen/Jülich (Germany) are forseen which are covered within the limits of the scale in force.

Supervisors: Prof. Philippe Helluy web page and CR Andrea Thomann, PhD, web page

**Applications only in english.**

**Earliest starting date 01/01/2026.**

**Mission confiée**:
The focus of this PhD is the construction of all-speed numerical solvers for compressible inviscid and viscous flows as well as compressible solids in a unified manner.
A focus will be on combining multi-scale semi-implicit solver with interface treatement. The objectives of the PhD are the following:

- Focus on high order finite volume schemes for single phase flows exploring the use of high order semi-implicit Runge-Kutta methods and high order space discretization methods for a multi-scale relaxation method.
- Modelling of viscous flows within a relaxation approach obtaining a unified relaxation model for inviscid and viscous materials
- Treatment of the interface by establishing interface conditions for the relaxation model based on physical and mathematical constraints
- Implementation in existing 2D code environment with level set methods and mesh refinement with the focus on efficient simulation in pre-exascale supercomputers.

**Literature and standard textbooks**

We invite the interested students to consult the standard text-books on fluid dynamics and specific literature on the topic.

**Textbooks**

Toro, E. F. **Riemann Solvers and Numerical Methods for Fluid Dynamics: a Practical Introduction.**2009
Hairer, E. / Wanner, G. **Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems**1991

**Research articles connected to the project**

Cravero, I. / Puppo, G. / Semplice, M. / Visconti, G. CWENO: uniformly accurate reconstructions for balance laws _Math. Comput._, Vol. 87, No. 312, p. 1689-1719, 2018.
Thomann, A. / Iollo, A. / Puppo, G. Implicit Relaxed All Mach Number Schemes for Gases and Compressible Materials_, _SIAM J. Sci. Comput._, Vol. 45, No. 5, p. A2632-A2656, 2023.
A. Thomann. Semi-implicit relaxed finite volume schemes for hyperbolic multi-scale systems of conservation laws, _J. Comput. Phys._, 539, 114263, 2025.
Abbate, E. / Iollo, A. / Puppo, G. An implicit scheme for moving walls and multi-material interfaces in weakly compressible materials, _Commun. Comput. Phys._, Vol. 27, No. 1, p. 116-144, 2020.

**Principales activités**:
The main activities of the student with the help of the supervisors regard
- Development and implementation of numerical methods
- Numerical analysis of the scheme with mathematical proofs of their properties
- Code development, simulations and benchmarks of the novel methods
- Presentation of results at international conferences and to the international collaborateurs
- Drafting of articles and reports of research results

**Compétences**:
Numerical analysis

(Hyperbolic) Partial differential equations

Very good knowledge of a basic programming language (Matlab, Phython, C)

Good knowledge in C++ and Fortan is advantageous

The research language will be english, thus a very good level of english is expected.

**Avantages**:

- 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 teleworking (after