[Internship postion] Study of thermo-poro viscous fingering instabilities: Single phase flow

Institute GeM is a Joint Research Unit supervised by Nantes Université, Centrale Nantes and the CNRS. Founded in 2004, the objective was to bring together within the same laboratory all the skills in the Nantes Saint-Nazaire area in the fields of civil engineering, materials and processes, modelling and simulation in structural mechanics.

The mission of our research institute is to propose innovative manufacturing processes and simulation tools adapted to the dimensioning and life cycle management of products, structures and works, taking into account the influence of severe stresses and environmental actions.

The research carried out at GeM is balanced between advanced and applied research. The unit is characterised by its significant and differentiating testing resources, with several technological platforms: civil engineering (test slab, durability characterisation, environment), manufacturing (bio-printing and additive manufacturing, composite processes), materials (X-ray diffraction, composite durability), structures (membrane structures, static and dynamic tests)

The projects are conducted in close collaboration with industry, project owners and companies specialising in mechanical and civil engineering. It is also the subject of scientific collaboration with other French and foreign research centres, in particular as part of European programmes or networks.

Context & problem statement

What happens when a hot fluid is injected into a porous media that is apriori saturated by a cold but same fluid ? In the case of immiscible fluids it is well-known that a low viscous fluid displaces the high viscous counterpart in a conditionally stable manner, forming viscous fingering instabilities with a range of possible finger sizes limited by surface tension. In the case of the single-phase flow a temperature gradient can still lead to viscosity contrasts, however in the absence of instability-limiting surface tension of the menisci. In such cases, would there still be a possibility for non-homogeneous flow, or rather non-homogeneous convection of heat, in the form of fingered thermal structures ? This is the question that this project aims to answer, with implications in a variety of applications including control of thermocline-based thermal energy storage systems and geo-thermal heat extraction. The tools will be continuum-scale thermo-hydro poromechanics, Darcy-like flow modeling, Traveling wave (TW) analysis and Linear stability analysis (LSA).

Scientific approach & internship objectives

The project is structured into 5 phases as follows:

1. Formulating a minimal model to describe the (i) fluid advection, (ii) thermal diffusion, (iii) hydrodynamic (Taylor) dispersion along the flow direction, and (iv) heat loss to the porous solid
2. Identifying and proper grouping of dimensionless numbers that govern the various phenomena.
3. Resolution of the coupled model using FD method to identify the regimes, (for instance for varying injection rates), of possible manifestation of TWs as diffused shocks or not.
4. Performing LSA on TW solutions to identify conditional stability and its consequence on thermal mixing.
5. Scaling laws and conception of laboratory-scale setup involving a porous Hele-Shaw cell to validate predictions. (Possibility of realizing qualitative experiments based on in-time acquisition of experimental setup.)

During the internship, the student will apply skills acquired in Numerical methods & analysis, be able to collaborate with a dynamic research group & have the opportunity to learn from leading researchers.

Internship advisors

• Siddhartha Harsha OMMI (Maître de Conférences), Institut de Génie Civil et Mécanique (GeM), Ecole Centrale de Nantes
• Giulio SCIARRA (Professeur des Universités), Institut de Génie Civil et Mécanique (GeM), Ecole Centrale de Nantes

Additional information

• The internship will be conducted in its entirety at the Institut de Génie Civil et Mécanique (GeM), Ecole Centrale de Nantes, 1, rue de la Noë, 44321 Nantes cedex 03, FRANCE.
• The internship will start on 23 February 2026 and lasts 6 months (possible extension to a PhD thesis).
• The gratification will be 4.35 €/hour (≈ 600 €/month) according to the French law.
• The internship is funded by the Projet STOLER (STOckage Littoral d’Énergie Renouvelable) backed by Institute Carnot MERS.

Required competences:

• We are looking for an enrolled master student in Civil Engineering or Mechanical Engineering or Physics (Computational, Applied, Mathematical) being interested in applied research activities and numerical methods for PDEs and numerical analysis. 
• Familiarity with numerical methods for coupled problems.
• Strong programming skills using Python and Matlab.
• Fluent in written/spoken English.