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Boltzmann Equation and Discrete Velocity Models: A discrete velocity model for polyatomic molecules
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
2019 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Boltzmannekvationen och diskreta hastighetsmodeller : En diskret hastighetsmodell för polyatomiska molekyler (Swedish)
Abstract [en]

In the study of kinetic theory and especially in the study of rarefied gas dynamics one often turns to the Boltzmann equation. The mathematical theory developed by Ludwig Boltzmann was at first sight applicable in aerospace engineering and fluid mechanics. As of today, the methods in kinetic theory are extended to other fields, for instance, molecular biology and socioeconomics, which makes the need of finding efficient solution methods still important. In this thesis, we study the underlying theory of the continuous and discrete Boltzmann equation for monatomic gases. We extend the theory where needed, such that, we cover the case of colliding molecules that possess different levels of internal energy. Mainly, we discuss discrete velocity models and present explicit calculations for a model of a gas consisting of polyatomic molecules modelled with two levels of internal energy.

Abstract [sv]

I studiet av kinetisk teori och speciellt i studiet av dynamik för tunna gaser vänder man sig ofta till Boltzmannekvationen. Den matematiska teorien utvecklad av Ludwig Boltzmann var vid första anblicken tillämpbar i flyg- och rymdteknik och strömningsmekanik. Idag generaliseras metoder i kinetisk teori till andra områden, till exempel inom molekylärbiologi och socioekonomi, vilket gör att vi har ett fortsatt behov av att finna effektiva lösningsmetoder. Vi studerar i denna uppsats den underliggande teorin av den kontinuerliga och diskreta Boltzmannekvationen för monatomiska gaser. Vi utvidgar teorin där det behövs för att täcka fallet då kolliderande molekyler innehar olika nivåer av intern energi. Vi diskuterar huvudsakligen diskreta hastighetsmodeller och presenterar explicita beräkningar för en modell av en gas bestående av polyatomiska molekyler modellerad med två lägen av intern energi.

Place, publisher, year, edition, pages
2019. , p. 39
Keywords [en]
Boltzmann equation, Discrete velocity models, Polyatomic molecules
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-76143OAI: oai:DiVA.org:kau-76143DiVA, id: diva2:1383586
Subject / course
Mathematics
Educational program
Mathematics Programme (180 ECTS credits)
Supervisors
Examiners
Available from: 2020-01-08 Created: 2020-01-08 Last updated: 2020-01-08Bibliographically approved

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