Simulace Rayleigh-Bénardovy konvekce pomocí Smoothed Particle Hydrodynamics
| Thesis title in Czech: | Simulace Rayleigh-Bénardovy konvekce pomocí Smoothed Particle Hydrodynamics |
|---|---|
| Thesis title in English: | Simulating Rayleigh-Bénard convection using Smoothed Particle Hydrodynamics |
| Key words: | Smoothed Particle Hydrodynamics|Rayleigh-Bénard|modelování|numerická simulace |
| English key words: | Smoothed Particle Hydrodynamics|Rayleigh-Bénard|modelling|numerical simulation |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | čeština |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | doc. RNDr. Michal Pavelka, Ph.D. |
| Author: | Bc. Matěj Lev Hart - assigned and confirmed by the Study Dept. |
| Date of registration: | 03.10.2024 |
| Date of assignment: | 03.10.2024 |
| Confirmed by Study dept. on: | 07.11.2024 |
| Date and time of defence: | 24.06.2025 08:30 |
| Date of electronic submission: | 07.05.2025 |
| Date of submission of printed version: | 07.05.2025 |
| Date of proceeded defence: | 24.06.2025 |
| Opponents: | Mgr. Ondřej Kincl, Ph.D. |
| Advisors: | prof. RNDr. Ladislav Skrbek, DrSc. |
| Guidelines |
| The thesis should consist of the following steps:
1) Review of Smoothed Particle Hydrodynamics with entropy [2], using code the [3] 2) Review the Rayleigh-Bénards convection (RBC), including the current experiments [3] 3) SPH simulation of RBC using an equation of state of choice 4) Try to bring the simulation closer to the real experiments [4], especially using a more realistic equation of state for cryogenic helium. |
| References |
| [1] G. Ahlers, S. Grossmann and D. Lohse, Heat transfer and large-scale dynamics in turbulent Rayleigh-Bénard convection, Rev. Mod. Phys. 81, 503 (2009). https://doi.org/10.1103/RevModPhys.81.503
[2] Michal Pavelka, Vaclav Klika, Ondrej Kincl, Approaches to conservative Smoothed Particle Hydrodynamics with entropy, https://arxiv.org/abs/2406.14229 [3] https://github.com/OndrejKincl/SmoothedParticles.jl [4] Urban, P., Králík, T., Musilová, V. et al. Modulated turbulent convection: a benchmark model for large scale natural flows driven by diurnal heating. Sci Rep 14, 15987 (2024). https://doi.org/10.1038/s41598-024-66882-5 |
| Preliminary scope of work in English |
| Rayleigh-Bénard convection (RBC), a special case of thermal convection, is caused by heating a slab of fluid from below. Typically, the fluid motion is simulated using the Oberbeck-Boussinesq approximation, where the fluid is assumed to have constant properties except its density varying linearly with the temperature. At high Rayleigh numbers, direct numerical simulation of confined RBC is notoriously difficult [1]. Smoothed Particle Hydrodynamics (SPH) is a particle-based method for simulating fluid dynamics that may be advantageous in tackling this problem. |