Effects of city-size heterogeneity on epidemic spreading in a metapopulation: A reaction-diffusion approach

We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolising cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metaopoluation in the long time limit, as well as the relevant parameters characterising the epidemic threshold that separates an epidemic from a non-epidemic phase. Within this model, we investigate the effect of a heterogeneous network topology and a heterogeneous subpopulation size distribution. Such a system is suited for epidemic modeling where small villages and big cities exist simultaneously in the metapopulation. We find that the heterogeneous conditions cause the epidemic threshold to be a non-trivial function of the reaction rates (local parameters), the network's topology (global parameters) and the cross-over population size that separates "village dynamics" from "city dynamics".Comment: 17 pages, 3 figure

Relaxation models for two-phase flow with applications to CO2 transport

This thesis presents mathematical models for two-phase pipeline flow, with an emphasis on applications to CO2 pipeline flow, as well as numerical methods suitable for solving these models. The considered models form a hierarchy of homogeneous (single-velocity) two-phase flow models with relaxation terms that account for transfer processes between the two phases. The relaxation terms model heat, mass and volume transfer caused by differences in temperature, chemical potential and pressure, respectively. The basis of the model hierarchy is a six-equation model with all three relaxation processes present. The rest of the hierarchy is then derived by assuming that one or more of the relaxation processes are infinitely rapid, which results in equilibrium in pressure, temperature and/or chemical potential, which makes a total of eight models. The models are formulated using conservation laws for mass, momentum and energy as well as an advection equation for the gas volume fraction. It is shown that the subcharacteristic condition, which is related to the stability of such models, translates to the requirement that the speed of sound is reduced when a new equilibrium condition is introduced. Expressions for the speeds of sound in the eight models are derived and proven to satisfy the subcharacteristic condition. A mass-transfer model for pipeline flow based on statistical rate theory is derived and formulated as a chemical-potential relaxation term in the pressure-temperature equilibrium model of the hierarchy. The model is used to simulate depressurization of a CO2 pipeline, and the results are found to be quite close to those of the full-equilibrium model. An exponential time-differencing scheme tailor-made for relaxation terms is applied to the model and compared to the Backward Euler method. The exponential time-differencing scheme is an explicit method, but it relies on knowledge of the equilibrium of the relaxation process. The mass-transfer equilibrium value has to be calculated using a Newton-Raphson iteration, which essentially makes both methods implicit, and comparable in both computational cost and accuracy. Finally, the Rankine-Hugoniot-Riemann (RHR) solver is presented, which aims to solve multidimensional conservation laws with source terms. The solver introduces the novel idea of treating flux gradients in other dimensions as additional source terms. The source term and cross-flux term is placed as a singular source in the centre of each cell, which causes a jump in the solution according to a Rankine-Hugoniot condition. The states on either side of a cell interface then define a Riemann problem that is solved by an approximate Riemann solver. The RHR solver is shown to be of second order in space for a 2D scalar advection equation, the 2D isothermal Euler equations and the 2D shallow water equations.PhD i energi- og prosessteknikkPhD in Energy and Process Engineerin

Fluid-Structure-Interaction Coupling between Project Chrono and REEF3D

Numerisk fluiddynamikk (CFD) utmerker seg primært for å løse hydrodynamiske problemer og simulere komplekse væskestrømninger. Programvaren mangler derimot en sterk modell for å gjennomføre strukturelle beregninger. Det er ofte interaksjonen mellom en væske og en struktur som er interessant i anvendte problemer. Denne masteroppgaven forslår derfor en koblingsstrategi mellom CFD-rammeverket REEF3D og en «Multi-Body Physics Engine» kalt Project Chrono, i et forsøk på å forbedre numerisk modellering av Fluid-Struktur-Interaksjoner (FSI). Både REEF3D og Chrono er rammeverk med åpen kildekode, skrevet i programmeringsspråket C++. Hvor REEF3D løser fluidets frie overflate, modellerer Chrono kollisjoner og strukturelle deformasjoner. Begge rammeverkene er validert i denne avhandlingen, med deformasjons-simuleringer i Chrono og stive innspente FSI i REEF3D. De overordnede resultatene er presise, og legger grunnlaget for kombinerte koblingssimuleringer mellom de to rammeverkene. Det settes innledende begrensninger på koblingsrammeverket for å prioritere utviklingen av kommunikasjonsfunksjonene i koblingen. Koblingen er utviklet med egenskaper innen «Single-Body» Dynamikk. Dette er oppnådd med dynamikk-algoritmer og stive kollisjonsalgoritmer i Chrono, ved hjelp av stive triangulære nett som representerer strukturer. REEF3D er det styrende programmet i koblingsrammeverket, og dikterer tidssteg og informasjonsutveksling. Under en simulering sender REEF3D de hydrodynamiske kreftene som virker på sitt strukturnett til Chrono, som anvender kreftene på sitt eget-definerte strukturnett. Chrono iterer med sitt eget interne tidssteg og beregner bevegelser og hastigheter av strukturen fram til REEF3D’s tidssteg er nådd. I dette øyeblikket sendes hastighetene og strukturposisjonene til REEF3D. REEF3D oppdaterer sin konfigurasjon med denne informasjonen før neste REEF3D-tidssteg kjører, eller avslutter simuleringen hvis den maksimale kjøretiden er nådd. Ved simulering med det utviklede koblingsrammeverket har informasjonsutvekslingen av krefter, hastigheter og posisjoner være vellykket. To ulike simuleringstilfeller ble utformet for å teste de grunnleggende egenskapene til koblingsrammeverket. I det første tilfellet ble de interne FSI-algoritmene med Euler-parametere i REEF3D benyttet. Denne interne simuleringen sammenlignes med Chronos strukturberegninger i koblingsnettverket mellom REEF3D og Chrono. Koblingssimuleringen var vellykket og samsvarer i stor grad med den interne FSI REEF3D-simuleringen. Videre har et annet tilfelle blitt simulert for å teste kollisjonsalgoritmene i koblingsrammeverket. Ved å slippe en kube ned på en fast struktur i vannet, oppstod en vellykket kollisjon med komplekse rotasjoner og bevegelser. Både den flytende koblingssimuleringen og kollisjonssimuleringen var derimot ustabile. Slike feil er forventet for et såpass nyutviklet koblingsrammeverk, og må undersøkes nærmere i fremtidig forskning og utvikling.Computational Fluid Dynamics (CFD) frameworks naturally excel in solving hydrodynamic problems and simulating complex fluid flows, but lack powerful structural solvers. In real-world engineering applications, the point of interest is often between a fluid and a structure. This master's thesis, therefore, proposes a coupling strategy between the CFD framework REEF3D and the Multi-Body Physic Engine Project Chrono, attempting to improve numerical modelling of Fluid-Structure-Interactions. Both REEF3D and Chrono are open-source frameworks, written in the programming language C++. While REEF3D solves the free surface of the fluid, Chrono models collisions and structural deformations. Both frameworks are validated in this thesis, simulating structural deformations in Chrono and rigid fixed FSI in REEF3D. The overall results are precise, preparing the frameworks for combined coupling simulations. Initial limitations are put on the coupling framework to focus on developing the coupling communication capabilities. Single-Body Dynamics with rigid collision algorithms in Chrono, utilizing a rigid triangular mesh, have been developed. REEF3D is the master in the coupling, dictating timesteps and information exchange. During a simulation, REEF3D will send the hydrodynamic forces working on the vertices in the mesh to Chrono, which will apply these forces in its own defined triangular Chrono mesh. Chrono iterates with its own internal timestep, calculating movements and velocities, until the REEF3D timestep is reached. At this moment, the velocities on the mesh vertices and the body positions will be sent to REEF3D. REEF3D updates its configuration before running the next REEF3D timestep, or ends the simulation if the maximum run-time limit is reached. When simulating with the developed coupling framework, the information exchange of forces, velocities and positions has been successful. Two different simulation cases were designed to test the initial capabilities of the coupling framework. The first case utilized the internal FSI algorithms with Euler parameters. This internal case is compared with Chrono's body calculations in the coupling framework. The coupling simulation ran successfully and broadly corresponds with the internal REEF3D simulation. Furthermore, a second case has been simulated to test the collision detection in the coupling framework. By dropping a cube on a fixed structure in the water, collision successfully occurred with resulting complex rotations and movements. However, in both the floating coupling case and the collision coupling case, the results aren't fully stable. Errors like this are expected for such a newly developed coupling framework and need to be investigated in future research and developments

FoU som arbeidsform i yrkesfaglærerutdanningen

Denne artikkelen bygger på et FoU prosjekt gjennomført ved yrkesfaglærerutdanning i restaurant- og matfag (YFL RM-fag) ved Høgskolen i Oslo og Akershus i perioden april 2011 til mai 2012. Prosjektet hadde flere formål: 1) styrke FoU kompetansen blant lærere som leder yrkesfaglærerutdanningen i restaurant- og matfag ved HiOA. 2) samle og systematisere grunnleggende kunnskap (baseline) om forhold ved den skolebaserte delen av yrkesopplæringen i restaurant- og matfag (RM-fag), 3) knytte yrkesfaglærerstudentenes bachelorarbeider til den innsamlede empirien slik at resultatene fra baselineundersøkelsen utdypes gjennom studentenes bacheloroppgaver, og 4) utvikle yrkesfaglærerstudentenes FoU kompetanse gjennom aktiv deltakelse i konkrete forskningsoppgaver. Erfaringene så langt er at FoU-prosjektet har gitt mer systematisk kunnskap om den skolebaserte delen av yrkesopplæringen i restaurant- og matfag, økt kompetanse i å gjennomføre forskningsprosesser og samtidig utviklet en arbeidsform der yrkesfaglærerstudentene er medforskere på en naturlig måt

Thermodynamic modeling with equations of state: present challenges with established methods

Equations of state (EoS) are essential in the modeling of a wide range of industrial and natural processes. Desired qualities of EoS are accuracy, consistency, computational speed, robustness and predictive ability outside of the domain where they have been fitted. In this work, we review present challenges associated with established models, and give suggestions on how to overcome them in the future. The most accurate EoS available, multiparameter EoS, have a second artificial Maxwell loop in the two-phase region that gives problems in phase-equilibrium calculations and exclude them from important applications such as treatment of interfacial phenomena with mass based density functional theory. Suggestions are provided on how this can be improved. Cubic EoS are among the most computationally efficient EoS, but they often lack sufficient accuracy. We show that extended corresponding state EoS are capable of providing significantly more accurate single-phase predictions than cubic EoS with only a doubling of the computational time. In comparison, the computational time of multiparameter EoS can be orders of magnitude larger. For mixtures in the two-phase region, however, the accuracy of extended corresponding state EoS has a large potential for improvement. The molecular-based SAFT family of EoS are preferred when predictive ability is important, e.g. for systems with strongly associating fluids or polymers where few experimental data are available. We discuss some of their benefits and present challenges. A discussion is presented on why predictive thermodynamic models for reactive mixtures such as CO2-NH3 and CO2-H2O-H2S must be developed in close combination with phase- and reaction equilibrium theory, regardless of the choice of EoS. After overcoming present challenges, a next-generation thermodynamic modeling framework holds the potential to improve the accuracy and predictive ability in a wide range of applications such as process optimization, computational fluid dynamics, treatment of interfacial phenomena and processes with reactive mixtures.publishedVersionCopyright © 2017 American Chemical Society. This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes

A Two-Fluid Model for Vertical Flow Applied to CO2 Injection Wells

Flow of CO2 in wells is associated with substantial variations in thermophysical properties downhole, due to the coupled transient processes involved: complex flow patterns, density changes, phase transitions, and heat transfer to and from surroundings. Large temperature variations can lead to thermal stresses and subsequent loss of well integrity, and it is therefore crucial to employ models that can predict this accurately. In this work, we present a model for vertical well flow that includes both two-phase flow and heat conduction. The flow is described by a two-fluid model, where mass transfer between the phases is modelled by relaxation source terms that drive the phases towards thermodynamic equilibrium. We suggest a new formulation of the mass transfer process that satisfies the second law of thermodynamics, and that is also continuous in the single-phase limit. This provides a more robust transition from two-phase to single-phase flow than the previous formulation. The model predicts which flow regimes are present downhole, and calculates friction and heat transfer depending on this. Moreover, the flow model is coupled with a heat conduction model for the layers that comprise the well, including tubing, packer fluid, casing, cement or drilling mud, and rock formation. This enables prediction of the temperature in the well fluid and in each layer of the well. The model is applied to sudden shut-in and blowout cases of a CO2 injection well, where we employ the highly accurate Span-Wagner reference equation-of-state to describe the thermodynamics of CO2. We predict pressure, temperature and flow regimes during these cases and discuss implications for well integrity. © 2016 Elsevier Ltd.acceptedVersio

Relaxation models for two-phase flow with applications to CO2 transport

This thesis presents mathematical models for two-phase pipeline flow, with an emphasis on applications to CO2 pipeline flow, as well as numerical methods suitable for solving these models. The considered models form a hierarchy of homogeneous (single-velocity) two-phase flow models with relaxation terms that account for transfer processes between the two phases. The relaxation terms model heat, mass and volume transfer caused by differences in temperature, chemical potential and pressure, respectively. The basis of the model hierarchy is a six-equation model with all three relaxation processes present. The rest of the hierarchy is then derived by assuming that one or more of the relaxation processes are infinitely rapid, which results in equilibrium in pressure, temperature and/or chemical potential, which makes a total of eight models. The models are formulated using conservation laws for mass, momentum and energy as well as an advection equation for the gas volume fraction. It is shown that the subcharacteristic condition, which is related to the stability of such models, translates to the requirement that the speed of sound is reduced when a new equilibrium condition is introduced. Expressions for the speeds of sound in the eight models are derived and proven to satisfy the subcharacteristic condition. A mass-transfer model for pipeline flow based on statistical rate theory is derived and formulated as a chemical-potential relaxation term in the pressure-temperature equilibrium model of the hierarchy. The model is used to simulate depressurization of a CO2 pipeline, and the results are found to be quite close to those of the full-equilibrium model. An exponential time-differencing scheme tailor-made for relaxation terms is applied to the model and compared to the Backward Euler method. The exponential time-differencing scheme is an explicit method, but it relies on knowledge of the equilibrium of the relaxation process. The mass-transfer equilibrium value has to be calculated using a Newton-Raphson iteration, which essentially makes both methods implicit, and comparable in both computational cost and accuracy. Finally, the Rankine-Hugoniot-Riemann (RHR) solver is presented, which aims to solve multidimensional conservation laws with source terms. The solver introduces the novel idea of treating flux gradients in other dimensions as additional source terms. The source term and cross-flux term is placed as a singular source in the centre of each cell, which causes a jump in the solution according to a Rankine-Hugoniot condition. The states on either side of a cell interface then define a Riemann problem that is solved by an approximate Riemann solver. The RHR solver is shown to be of second order in space for a 2D scalar advection equation, the 2D isothermal Euler equations and the 2D shallow water equations