Smoothed Particles Hydrodynamics pro interakci mezi tekutinou a pevnými tělesy

• Thesis title in Czech: Smoothed Particles Hydrodynamics pro interakci mezi tekutinou a pevnými tělesy
• Thesis title in English: Smoothed Particle Hydrodynamics for fluid-structure interactions
• Key words: SPH|FSI|numerické simulace|mechanika tekutin
• English key words: SPH|FSI|numerical simulations|fluid mechanics
• Academic year of topic announcement: 2023/2024
• Thesis type: diploma thesis
• Department: Mathematical Institute of Charles University (32-MUUK)
• Supervisor: doc. RNDr. Michal Pavelka, Ph.D.
• Advisors: RNDr. Jaroslav Hron, Ph.D.

Guidelines

The thesis should consist of the following steps:
1) Review of the SPH method and simple numerical tests using SmoothedParticles.jl framework [2].
2) Review of paper [1], where an SPH method for both fluids and solids was developed.
3) Review of fluid-structure interaction (FSI) problems in continuum mechanics, for instance the Turek-Hron benchmark.
4) An attempt to simulate an FSI problem using SPH.

References

[1] O. Kincl, I. Peshkov, M. Pavelka, V. Klika, Unified description of fluids and solids in Smoothed Particle Hydrodynamics, Applied Mathematics and Computation 439(15), 1275792022, 2023.
[2] https://github.com/OndrejKincl/SmoothedParticles.jl

Preliminary scope of work in English

Smoothed Particle Hydrodynamics (SPH) is a mesh-less numerical method that discretizes fluids and solids by seeing them as a collection of macroscopic quasi-particles. The quasi-particles then interact in such a way that they reconstruct behavior of continuous fluids and solids. The method is especially useful for problems with a free boundary, where other numerical methods based on meshes (finite elements and volumes) become complicated.

Recently, we have developed an SPH method suitable for both solids and fluids. A question remains open, however, whether the method could be useful in simulations of fluid-structure interactions. The goal of this thesis is to approach that questions.