PhD M/F Development of Numerical Methods for Simulating Two-Phase Flows with Interface Resolution and Property Jumps

Job Description

Thesis Subject

PhD Title: Development of Numerical Methods for Simulating Two-Phase Flows with Interface Resolution and Property Jumps

Keywords: Fluid mechanics, numerical methods, two-phase flow, numerical simulation

Your Work Environment

Context and Motivation
Two-phase flows with resolved interfaces (e.g., particles, bubbles, droplets, liquid films) are ubiquitous in industrial (energy, concentrated solar power, chemical, nuclear, etc.) and environmental applications. Their accurate numerical simulation remains a major challenge due to strong discontinuities at interfaces (material property jumps, surface tension). Classical methods, such as the one-fluid approach or front-tracking methods (used in TrioCFD), introduce regularization errors that degrade the convergence order of numerical schemes, limiting simulation accuracy, especially at high Reynolds or Weber numbers.
The ANR REGIME project aims to develop innovative regularization models to quantify and reduce these errors by combining:
1. A theoretical analysis of errors introduced by regularization methods.
2. Their discrete implementation in open-source codes (Basilisk, TrioCFD, JADIM).
3. Validation on academic and applied test cases.
This PhD focuses on the implementation, validation, and evaluation of these methods within the TrioCFD software.

Objectives
• Development of hybrid cut-cell and one-fluid methods.
• Implementation of these methods in TrioCFD (CEA's front-tracking code).
• Validation and evaluation of these methods, particularly for problems involving heat transfer.

Methodology
This PhD will use the Front-Tracking method in TrioCFD to account for the two-phase nature of the flow. This method employs a mobile surface mesh that explicitly represents interfaces, enabling precise description of arbitrary geometries and their interactions with the surrounding fluid. Recently, this method—originally developed with a one-fluid approach—was modified to use a cut-cell approach. Jump conditions are explicitly enforced at interfaces, and the method is intrinsically conservative. Generally, the cut-cell approach yields higher precision for equivalent mesh resolution. However, it remains computationally more expensive, and in some cases, precision may be slightly degraded.
The main objective of the PhD is to improve numerical methods for two-phase flow resolution by finding the best trade-off between cost and precision. To achieve this, the PhD candidate will:
• Conduct a comparative study of existing methods.
• Propose hybridizations between these methods.
• Develop corrections to mitigate errors due to regularization.

Candidate Profile
• Education: Master's degree in computational fluid mechanics, applied mathematics, or computational engineering.
• Skills:
o Proficiency in numerical methods (finite volumes, finite elements).
o Experience in scientific programming (C++, Python, Fortran).
o Knowledge of fluid-fluid two-phase flows and HPC (a plus).
• Qualities: Independence, ability to work in a team (multi-site collaborations).

Funding and Duration
• Funding: PhD grant via the ANR REGIME project.
• Duration: 3 years (starting January 2027).
• Primary Location: PROMES (Perpignan), with regular stays at D'Alembert (Paris).

Constraints and risks

Computer work

Compensation and benefits

Compensation

2300 € gross monthly

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

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