Modeling and simulation of free-surface thin film flows with evaporation

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Type de contrat : CDD

Niveau de diplôme exigé : Bac + 4 ou équivalent

Fonction : Stagiaire de la recherche

Contexte et atouts du poste

COMMEDIA is a common project-team linked to the following research institutions: Sorbonne Université, CNRS and Inria. The research activity of COMMEDIA focuses on the numerical simulation of bio-fluid flows in the human body, more specifically, blood flows in the cardiovascular system and air flows in the respiratory system. These simulations are intended to complement available clinical data with the following purpose: help clinicians or bio-engineers to enhance the understanding of physiological phenomena, to improve diagnosis and therapy planning or to optimize medical devices.

The proposed internship work will be conducted within the context of an industrial collaboration, to foster innovation.

• Paid compensation 

• Option of PhD offer

Mission confiée

Free-surface thin film flows are ubiquitous in biological systems, for instance, in mucus transport within the respiratory tract, the tear film on the eye, or blood thin films. Such flows occur when two immiscible fluids (e.g., water and air) interact and one of them adheres to a solid substrate as a thin layer.

The goal of this internship is to investigate the numerical approximation of lubrication theory based mathematical models with evaporation describing these systems (see, e.g., [2, 1, 3]). These models are generally based on nonlinear fourth-order degenerate parabolic equations written on surfaces. Mixed finite elementmethods will be explored for their numerical approximation in combination with inequality contraints to guarantee the non-negativeness of the approximation. The non-linearity will be treated via Newton’s iterations. The numerical studies will be conducted using FreeFem++.

References:

[1] J.W. Barrett, J.F. Blowey, and H. Garcke. Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Numerische Mathematik, 80(4):525–556, 1998.

[2] H.P. Greenspan. On the motion of a small viscous droplet that wets a surface. Journal of Fluid Mechanics, 84(1):125–143, 1978.

[3] Hangjie Ji and Thomas P. Witelski. Instability and dynamics of volatile thin films. Phys. Rev. Fluids, 3:024001, Feb 2018.

Principales activités

• Contribute to the design and implementation of scientific computing software.

• Perform numerical simulations on selected test cases.

• Develop or optimize algorithms for high-performance computing.

• Collaborate with researchers in applied mathematics, physics, and computer science.

Compétences

 

• Background in applied mathematics.

• Experience with programming languages: C++.

• Familiarity with numerical methods: finite elements, finite differences.

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 and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage