Performanse multigrid algoritma za linearni sustav brzina-tlak

master's thesis

• Title (english): Performance of the multigrid algorithm for the velocity-pressure linear system
• Author: Martina Nobilo
• Mentor: Hrvoje Jasak (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2022-12-16, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering; Process Energy Engineering

Abstract

S obzirom na sve veću upotrebu računalnih simulacija za rješavanje složenih problema u industriji i znanosti, potrebno je neprestano raditi na unaprjeđenju postojećih softvera kako bi matematičke jednadžbe koje opisuju stvarne fizikalne probleme bile što bolja reprezentacija stvarnosti. Zbog prirode matematičkih modela kojima se u računalnoj dinamici fluida (RDF) nastoje aproksimirati stvarni fizikalni problemi, prilikom pretvorbe diferencijalnih jednadžbi u diskretne jednadžbe i provođenja iterativnih postupaka javljaju se greške. U ovom radu proučavaju se performanse multigrid algoritma koji omogućava eliminiranje komponenti grešaka koje klasični iterativni algoritmi sporo eliminiraju. Izložena je teorijska pozadina klasičnih iterativnih algoritama i multigrid algoritma. Testirane su različite postavke multigrid algoritma na mrežama različitih gustoća i oblika kontrolnih volumena kako bi se donijeli zaključci o utjecaju veličine i oblika proračunske mreže na brzinu konvergencije multigrid algoritma. Također, testirana su dva različita algoritma u ulozi zaglađivača (algoritam koji zaglađuje rješenje prije i nakon multigrid ciklusa) - ILU i Gauss-Seidel - te su doneseni zaključci o njihovim performansama i uvjetima korištenja. Na kraju samog rada iznesena je sažeta tablica donesenih zaključaka kako bi se budućim korisnicima multigrid algoritma olakšalo njegovo korištenje.

Abstract (english)

Considering the increasing use of computer simulations to solve complex problems in industry and science, it is necessary to constantly work on the improvement of existing software so that the mathematical equations that describe real physical problems are a better representation of reality. Due to the nature of the mathematical models used in Computational Fluid Dynamics (CFD) to approximate real physical problems, errors occur when converting differential equations into discrete equations and performing iterative procedures. In this paper, the performance of the multigrid algorithm is studied, which enables the elimination of components of errors that classical iterative algorithms eliminate slowly. The theoretical background of classical iterative algorithms and the multigrid algorithm is presented. Different settings of the multigrid algorithm are tested on grids of different densities and shapes of control volumes in order to draw conclusions about the influence of the size and shape of the computational mesh on the speed of convergence of the multigrid algorithm. Also, two different algorithms were tested in the role of a smoother (an algorithm that smoothes the solution before and after the multigrid cycle) - ILU and Gauss-Seidel - and conclusions were drawn about their performance and conditions of use. At the end of the paper, a summary table of the conclusions was presented in order to make it easier for future users of the multigrid algorithm to use it.

• Keywords: RDF; selektivni algebarski multigrid; ILU; Gauss-Seidel
• Keywords (english): CFD; Selective Algebraic Multigrid; ILU; Gauss-Seidel
• Language: croatian
• URN:NBN: urn:nbn:hr:235:981002
• Study programme: Title: Mechanical Engineering; specializations in: Design, Process and Energy Engineering, Production Engineering, Engineering Modelling and Computer Simulation, Marine Engineering, Industrial Engineering and Management, Materials Engineering, Mechatronics and Robotics, Autonomous Systems; Course: Process and Energy Engineering; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka strojarstva (magistar/magistra inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-12-01 09:57:57