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Project Overview:

This PhD/postdoc position is part of a larger project focused on understanding and simulating the behaviour of cavitation bubbles near biomedical surfaces, such as kidney stones [1, 2]. In treatments like lithotripsy, cavitation bubbles form due to shock waves and undergo violent oscillations and collapses, producing high-speed jets that impact nearby surfaces. These interactions are crucial in medical and industrial applications but pose significant modelling challenges due to the complex physics involved, such as phase change and viscoelastic solids [3].
The selected candidate will contribute to advancing the phase-change capabilities of ECOGEN (https://code-mphi.github.io/ECOGEN/), an open-source CFD software designed for compressible multiphase flows [4]. ECOGEN is written in C++ and employs finite volume schemes, specifically Godunov-type schemes with Riemann solvers to determine fluxes. The objective is to enhance ECOGEN’s ability to simulate cavitation bubble dynamics near kidney stones.

PhD/Postdoc objectives:

The primary objectives of this position include:

  • Modelling and implementing phase-change processes, building on previous work [5], with a focus on incorporating non-condensable gases into relaxation processes. These processes drive the system toward equilibrium at each time step of the simulation.
  • Developing relaxation processes for both infinite and finite relaxation rates towards phase equilibrium.
  • Validating the models against an extensive set of test cases.
  • Conducting 2D axisymmetric and 3D simulations of cavitation bubble dynamics near kidney stones.
  • Collaborating with other project members working on solid material modelling and high-performance computing (HPC).

Candidate Profile:

For PhD applicants:

  • Master’s degree (M2 level) or an engineering diploma in mechanical engineering, applied mathematics, or a related field.
    For postdoctoral applicants:
  • PhD in Mechanical Engineering, Applied Mathematics, or a closely related discipline.
    Required skills (for both):
  • Strong background in fluid dynamics, with a solid understanding of compressible fluid mechanics.
  • Experience in numerical simulation methods for fluid flows.
  • Strong inclination toward software and numerical development, particularly for high-performance computing applications.
  • Proficiency in C/C++ programming is a plus.

Contact: Kevin Schmidmayer kevin.schmidmayer@inria.fr

References:

[1] Pishchalnikov Y. A., Behnke-Parks W. M., Schmidmayer K., Maeda K., Colonius T., Kenny T. W., Laser D. J. (2019). High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone. J. Acoust. Soc. Am., 146, 516-531.
[2] Sieber A., Shakya G., Bokman G. T., Belau M., Schlötter M., Kühl A., Lukić B., Schmidmayer K., Supponen O. (2024). Discovering the contribution of cavitation damage in kidney stone ablation through X-ray high-speed imaging and microtomography. 12th International Cavitation Symposium, CAV2024, Chania, Greece.
[3] Ndanou S., Favrie N., Gavrilyuk S. (2015). Multi-solid and multi-fluid diffuse interface model: Applications to dynamic fracture and fragmentation. J. Comp. Phys., 295, 523-555.
[4] Schmidmayer K., Petitpas F., Le Martelot S., Daniel. E. (2020b). ECOGEN: An open-source tool for multiphase, compressible, multiphysics flows. Comp. Phys. Com., 251, 107093.
[5] Cazé J., Petitpas F., Daniel E., Queguineur M., Le Martelot S. (2024). Modeling and simulation of the cavitation phenomenon in turbopumps. J. Comp. Phys., 502, 112817.