Simulace Rayleigh-Bénardovy konvekce pomocí Smoothed Particle Hydrodynamics
| Název práce v češtině: | Simulace Rayleigh-Bénardovy konvekce pomocí Smoothed Particle Hydrodynamics |
|---|---|
| Název v anglickém jazyce: | Simulating Rayleigh-Bénard convection using Smoothed Particle Hydrodynamics |
| Klíčová slova: | Smoothed Particle Hydrodynamics|Rayleigh-Bénard|modelování|numerická simulace |
| Klíčová slova anglicky: | Smoothed Particle Hydrodynamics|Rayleigh-Bénard|modelling|numerical simulation |
| 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: | Matěj Lev Hart - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 03.10.2024 |
| Datum zadání: | 03.10.2024 |
| Datum potvrzení stud. oddělením: | 07.11.2024 |
| Konzultanti: | prof. RNDr. Ladislav Skrbek, DrSc. |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| [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 |
| Předběžná náplň práce v anglickém jazyce |
| 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. |