Matematické modelování dvoufázového proudění pomocí mřížkové Boltzmannovy metody

Michal Malík

Mathematical modelling of two-phase flow using the lattice Boltzmann method

Type of document

diplomová práce
master thesis

Author

Michal Malík

Supervisor

Eichler Pavel

Opponent

Straka Robert

Study program

Matematické inženýrství

Institutions assigning rank

katedra matematiky

Rights

A university thesis is a work protected by the Copyright Act. Extracts, copies and transcripts of the thesis are allowed for personal use only and at one?s own expense. The use of thesis should be in compliance with the Copyright Act http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf and the citation ethics http://knihovny.cvut.cz/vychova/vskp.html
Vysokoškolská závěrečná práce je dílo chráněné autorským zákonem. Je možné pořizovat z něj na své náklady a pro svoji osobní potřebu výpisy, opisy a rozmnoženiny. Jeho využití musí být v souladu s autorským zákonem http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf a citační etikou http://knihovny.cvut.cz/vychova/vskp.html

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Abstract

Tato práce se zabývá užitím mřížkové Boltzmannovy metody (LBM) k simulaci vícefázového proudění. V rámci této práce byly popsány dva numerické modely řešící tuto problematiku. První řeší mísitelné proudění a skládá se z vícekomponentní vícefázové Shanovy-Doolenovy LBM (MCMP SD

This work addresses the use of the lattice Boltzmann method (LBM) for the simulation of the multiphase flow. Two numerical models, which solve this problem, were described in this thesis. The first model can be used to simulate miscible flows and consists of the multicomponent multiphase Shan-Doolen LBM (MCMP SD LBM). The second model is used to solve immiscible flow and is composed of the LBM for the Allen-Cahn equation and the LBM for the Navier-Stokes equations. The asymptotic analysis of MCMP SD LBM and LBM for the Allen-Cahn equation was performed. Both numerical models were implemented in CUDA C++ and tested for convergence and the conservation of mass. It turned out that the order of convergence depends on the adhesion parameter in the case of the miscible fluid model and the problem investigating wettable fluid adhesion. The method for immiscible fluids has experimental order of convergence higher than two for the simulations of heterogeneous systems without external forces. Nevertheless, the numeric solution does not converge to the solution of the Young-Laplace equation cited in the available literature. Next, the influence of the boundary conditions on the mass conservation of both methods was observed. However, the total mass is conserved when the periodic boundary conditions are applied