20.500.12556/DKUM-97800 Simulacija dinamike fluidov z mrežno Boltzmannovo metodo v programskem okolju Python magistrsko delo Simulation of fluid dynamics using the lattice Boltzmann method in a Python programming environment Delo obravnava razvoj, implementacijo in analizo simulacij toka fluidov z uporabo mrežne Boltzmannove metode (LBM) v programskem okolju Python. Delo se osredotoča na razvoj numeričnih modelov na podlagi mrežnega Bhatnagar-Gross-Krook (LBGK) modela ter njegove razširitve s Shan-Chenovim (SC) modelom, pri čemer sta bila modela implementirana iz osnovnih enačb. Razvita modela sta bila validirana s simulacijami klasičnih testnih primerov, ki obsegajo Poiseuillov tok, Couettejev tok, tok ob valju ter pokrovno-gnano votlino. Za Poiseuillov in Couettejev tok so bili rezultati primerjani z analitičnimi rešitvami, kar je pokazalo visoko stopnjo natančnosti ter pravilno obravnavo robnih pogojev. Pri zahtevnejših primerih, kot sta tok ob valju in pokrovno-gnana votlina sta modela uspešno reproducirala značilne tokovne pojave. Analiza je pokazala, da modela dobro simulirata tokove pri nižjih Reynoldsovih številih, vendar postaneta numerično nestabilna pri višjih vrednostih. Med primerjanima modeloma je SC model kazal izboljšano numerično stabilnost ter večjo natančnost. Dodatno je bila za Poiseuillov tok izvedena analiza občutljivosti na ločljivost mreže, ki je pokazala konvergenčno obnašanje metode ter izpostavila vpliv diskretizacije na natančnost in obravnavo robnih pogojev. Rezultati kažejo na to, da Python predstavlja prilagodljivo in učinkovito okolje za implementacijo LBM, primerno za uporabo kljub računsko zmogljivostnim omejitvam. Razviti modeli predstavljajo dobro osnovo za nadaljnje razširitve in optimizacije, ki bi bile primerne za kompleksnejše tokovne probleme. This work presents the development, implementation and analysis of fluid simulations using the lattice Boltzmann method (LBM) in a Python programming environment. The work focuses on the construction of numerical models based on the Bhatnagar-Gross-Krook (LBGK) model and its extension with the Shan-Chen (SC) model, both implemented from first principles. The developed models were validated by classic benchmark cases, including Poiseuille flow, Couette flow, flow past a cylinder and lid-driven cavity. For Poiseuille and Couette flows, the results were compared with analytical solutions, demonstrating a high degree of accuracy and a correct handling of boundary conditions. For more complex cases, such as flow past a cylinder and lid-driven cavity, the models successfully reproduced characteristic flow features. Analysis shows that the models simulate flows well at lower Reynolds numbers but become numerically unstable at higher values. Among the compared models, the SC model exhibited improved numerical and greater accuracy. Additionally, a grid resolution sensitivity analysis was performed for Poiseuille flow, demonstrating convergence behaviour and highlighting the effect of discretization on accuracy and the handling of boundary conditions. Results show that Python provides a flexible and effective environment for the implementation of LBM, suitable for use despite computational limitations. The developed models provide a good framework for further extensions and optimizations, which would be suitable for more complex flow cases mrežna Boltzmannova metoda (LBM) računska dinamika fluidov (CFD) Python Shan-Chenov model simulacija fluidov Lattice Boltzmann method (LBM) computational fluid dynamics (CFD) Python Shan-Chen model fluid simulation true true false [J. Konjar] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2026-04-15 10:17:12 2026-05-05 13:40:36 2026-05-23 03:05:39 0000-00-00 00:00:00 2026 0 Maribor 0 Maribor 1 spletni vir (1 datoteka PDF (XII, 87 str.)) 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.876.5:532.51/.54(043.2) 279034371 MAG_Konjar_Jure_2026.pdf MAG_Konjar_Jure_2026.pdf 1 B77B8707AA0F2A6A2C216BD07DF3373A 117556b38d0cc09f5d2ee2d6042091eb628fb88d453f1737c264fe252bdcfdeb 75ff0a9d-4732-11f1-8089-00155d0001a1 https://dk.um.si/Dokument.php?lang=slv&id=205707 Fakulteta za kemijo in kemijsko tehnologijo 0 0 0