Modelování interakce tekutin a pevných látek pomocí Smoothed Particle Hydrodynamics
| Název práce v češtině: | Modelování interakce tekutin a pevných látek pomocí Smoothed Particle Hydrodynamics |
|---|---|
| Název v anglickém jazyce: | Modelling Fluid-Structure Interaction using Smoothed Particle Hydrodynamics |
| Klíčová slova: | matematické modelování|interakce tekutin a pevných látekk|numerické výpočty|smoothed particle hydrodynamics |
| Klíčová slova anglicky: | mathematical modelling|fluid-structure interactions|numerics|smoothed particle hydrodynamics |
| Akademický rok vypsání: | 2024/2025 |
| Typ práce: | bakalářská práce |
| Jazyk práce: | |
| Ústav: | Matematický ústav UK (32-MUUK) |
| Vedoucí / školitel: | doc. RNDr. Michal Pavelka, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 23.09.2024 |
| Datum zadání: | 24.09.2024 |
| Datum potvrzení stud. oddělením: | 07.11.2024 |
| Konzultanti: | RNDr. Jaroslav Hron, Ph.D. |
| Zásady pro vypracování |
| The thesis should consist of the following steps:
1) Review of paper [1], where an SPH method for both fluids and solids was developed. 2) Review of the SPH method and simple numerical tests using SmoothedParticles.jl framework [2]. 3) Review of fluid-structure interaction (FSI) problems in continuum mechanics, for instance the Turek-Hron benchmark [3]. 4) An attempt to simulate an FSI problem using SPH. |
| Seznam odborné literatury |
| [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 [3] Turek, S., Hron, J. (2006). Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow. In: Bungartz, HJ., Schäfer, M. (eds) Fluid-Structure Interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34596-5_15 |
| Předběžná náplň práce v anglickém jazyce |
| 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 the behavior of continuous fluids and solids. The method is beneficial 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 (FSI). The goal of this thesis is to approach that questions. If SPH turns out to be useful for fluid-structure interactions, it could greatly simplify and speed up the simulations FSI. |