Calcium treatment is an established operation in the production of steels. Most importantly, it serves to modify detrimental inclusions in the melt for improved castability and superior product properties. Due to calcium’s low melting point and high vapour pressure, its addition to liquid steel is challenging and yields are generally low. The current standard method for addition is cored wire feeding, in which a calcium-bearing compound is injected into the melt inside a sacrificial metal tube. The depth at which the compound is released has a pronounced impact on its yield and depends on the rate at which the wire is injected. A mathematical model is constructed to predict the time after which release occurs and thus estimate injection depth. It is based on one-dimensional heat transfer and respects phase change effects, i.e., solidification of melt on the cold wire surface and subsequent melting of the wire and compound. Equations are derived using the finite difference method and the model is solved numerically using an implicit method. The model is applied to two different steel grades – one austenitic (AISI 316L), one super-duplex (SAF 2507) – and predictions are tested for the former grade in a 75-ton industrial ladle furnace. Results indicate that a decreased feeding rate (<100 m/min) leads to better calcium yield. Positive effects were also observed with downward melt stirring and a good slag coverage. Improved yield can lead to savings in process and material cost. The results also provide insights into the cored wire feeding process which may be useful for future process development, both for calcium and other additions. / Kalciumbehandling är en etablerad process vid tillverkning av stål. Framförallt används den för modifieringen av skadliga inneslutningar i smältan för att förbättra gjutbarheten och produktegenskaper. På grund av kalciums låga smältpunkt och höga ångtryck är det svårt att tillsätta det till flytande stål och utbytet är i allmänhet låg. Den nuvarande standardmetoden för tillsats är inmatning av tråd, där ett kalciumhaltig ämne matas in i smältan inuti en metallhölje som smälter bort. Djupet på vilket ämnet frigörs påverkar utbytet och beror på hur snabbt tråden matas. En matematisk modell konstrueras för att beräkna den tid efter vilken frisättning sker. Den bygger på endimensionell värmeöverföring och tar hänsyn till fasförändringseffekter, dvs. stelning av smältan på den kalla trådytan och smältning av tråd och kalciumämne efteråt. Ekvationer härleds med hjälp av finita differensmetoden och modellen löses numeriskt med hjälp av en implicit metod. Modellen tillämpas på två olika stålsorter – en austenitisk (AISI 316L) och en superduplex (SAF 2507) – och förutsägelser testas för den förstnämnda sorten i en 75-tons industriell skänkugn. Resultaten visar att en minskad matningshastighet (< 100 m/min) leder till ett ökat kalciumutbyte. Positiva effekter observerades med nedåtgående smältomrörning och god slaggtäckning. Ett förbättrat utbyte kan leda till besparingar i fråga om process- och materialkostnader. Resultaten ger också insikter i processen för inmatning av tråd, vilket kan vara användbart för framtida processutveckling, både för kalcium och andra tillsatser.

Electrical impedance imaging is an imaging technique which has the capability of revealing the spatial distribution of the electrical impedance inside biological tissues. Classical electrical impedance imaging including Electrical Impedance Tomography (EIT) typically has low resolution. Advances in electrical impedance imaging typically involve methods that either increase image resolution or image contrast. This study investigates the possibility of the resolution improvement for electrical impedance imaging using motion, and presents a novel high-resolution and calibrated impedance imaging method called Scanning electrical Impedance Imaging (SII). SII uses an electrical probe held at a known voltage and scanned over a thin sample immersed in a conductive medium on a grounded conducting plane to obtain high-resolution calibrated impedance images of samples. For system improvement and image reconstruction, a numerical model is developed to describe the SII system. This model simulates the measurement process by solving a 3-D electrostatic field at each scanning position using a modified approach of the finite difference method (FDM). The simulation consists of a quasi-statics problem involving inhomogeneous media with a complicated boundary condition. This 3-D model is used to optimize both the probe height and the shield-spacing for probe fabrication and also to evaluate system parameters including the frequency and the resistor in the peripheral circuit. Based on this model, an approach is also developed to quantifying conductivity values using the SII system. However, a large computational cost due to the motion involved in SII leads to challenges for a fast and accurate image reconstruction based on this 3-D model. Alternative fast models are derived as a replacement of the 3-D model for quick image reconstruction. In particular, the Modified Linear Approximation (MLA) involving two conductivity-weighted convolutions based on the reciprocity principle, explains the function of the special shield design introduced in the SII system reasonably well. Based on the MLA a nonlinear inverse method using total variation regularization and the Polak-Ribi'{e}re variant of the nonlinear conjugate-gradient method is developed for fast image reconstruction of the SII system. The inverse method is accelerated using convolution which eliminates the requirement of a numerical solver for the 3-D electrostatic field. 2-D images of small biological tissues and cells are measured using the SII system. The corresponding conductivity images are reconstructed using the MLA method. The successful improvement of resolution shown in both simulation and experimental results demonstrates that the idea of this approach can potentially be expanded to other imaging modalities for resolution improvement using motion.

The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were combined with Euler and fourth-order Runge-Kutta time differencing. In most cases, the order of convergence of the numerical solution to the exact solution was the same as the formal order of accuracy of the compact schemes employed.

Spread options are derivative securities, which are written on the difference between the values of two underlying market variables. They are very important tools to hedge the correlation risk. American style spread options allow the holder to exercise the option at any time up to and including maturity. Although they are widely used to hedge and speculate in financial market, the valuation of the American spread option is very challenging. Because even under the classic assumptions that the underlying assets follow the log-normal distribution, the resulting spread doesn't have a distribution with a simple closed formula. In this dissertation, we investigate the American spread option pricing problem. Several approaches for the geometric Brownian motion model and the stochastic volatility model are developed. We also implement the above models and the numerical results are compared among different approaches.

Wildfire modeling is a complex, computationally costly endeavor, but with droughts worsening and fires burning across the western United States, obtaining accurate wildfire predictions is more important than ever. In this paper, we present a novel approach to wildfire modeling using data assimiliation. We model wildfire spread with a modification of the partial differential equation model described by Mandel et al. in their 2008 paper. Specifically, we replace some constant parameter values with geospatial functions of fuel type. We combine deep learning and remote sensing to obtain real-time data for the model and employ the Nelder-Mead method to recover optimal model parameters with data assimilation. We demonstrate the efficacy of this approach on computer-generated fires, as well as real fire data from the 2021 Dixie Fire in California. On generated fires, this approach resulted in an average Jaccard index of 0.996 between the predicted and actual fire perimeters and an average Kulczynski measure of 0.997. On data from the Dixie Fire, the average Jaccard index achieved was 0.48, and the average Kulczynski measure was 0.66.

The heat transfer in the filling phase of injection moulding is studied, based on Gunnar Aronsson’s distance model for flow expansion ([Aronsson], 1996). The choice of a thermoplastic materials model is motivated by general physical properties, admitting temperature and pressure dependence. Two-phase, per-phase-incompressible, power-law fluids are considered. The shear rate expression takes into account pseudo-radial flow from a point inlet. Instead of using a finite element (FEM) solver for the momentum equations a general analytical viscosity expression is used, adjusted to current axial temperature profiles and yielding expressions for axial velocity profile, pressure distribution, frozen layer expansion and special front convection. The nonlinear energy partial differential equation is transformed into its conservative form, expressed by the internal energy, and is solved differently in the regions of streaming and stagnant flow, respectively. A finite difference (FD) scheme is chosen using control volume discretization to keep truncation errors small in the presence of non-uniform axial node spacing. Time and pseudo-radial marching is used. A local system of nonlinear FD equations is solved. In an outer iterative procedure the position of the boundary between the “solid” and “liquid” fluid cavity parts is determined. The uniqueness of the solution is claimed. In an inner iterative procedure the axial node temperatures are found. For all physically realistic material properties the convergence is proved. In particular the assumptions needed for the Newton-Mysovskii theorem are secured. The metal mould PDE is locally solved by a series expansion. For particular material properties the same technique can be applied to the “solid” fluid. In the circular plate application, comparisons with the commercial FEM-FD program Moldflow (Mfl) are made, on two Mfl-database materials, for which model parameters are estimated/adjusted. The resulting time evolutions of pressures and temperatures are analysed, as well as the radial and axial profiles of temperature and frozen layer. The greatest differences occur at the flow front, where Mfl neglects axial heat convection. The effects of using more and more complex material models are also investigated. Our method performance is reported. In the polygonal star-shaped plate application a geometric cavity model is developed. Comparison runs with the commercial FEM-FD program Cadmould (Cmd) are performed, on two Cmd-database materials, in an equilateral triangular mould cavity, and materials model parameters are estimated/adjusted. The resulting average temperatures at the end of filling are compared, on rays of different angular deviation from the closest corner ray and on different concentric circles, using angular and axial (cavity-halves) symmetry. The greatest differences occur in narrow flow sectors, fatal for our 2D model for a material with non-realistic viscosity model. We present some colour plots, e.g. for the residence time. The classical square-root increase by time of the frozen layer is used for extrapolation. It may also be part of the front model in the initial collision with the cold metal mould. An extension of the model is found which describes the radial profile of the frozen layer in the circular plate application accurately also close to the inlet. The well-posedness of the corresponding linearized problem is studied, as well as the stability of the linearized FD-scheme. / <p>Report code: LiU-TEK-LIC-2002:66.</p>

The modelling of the processes of advection and dispersion-diffusion is the most crucial factor in solute transport simulations. It is generally appreciated that the first order upwind difference scheme gives rise to excessive numerical diffusion, whereas the conventional second order central difference scheme exhibits severe oscillations for advection dominated transport, especially in regions of high solute gradients or discontinuities. Higher order schemes have therefore become increasingly used for improved accuracy and for reducing grid scale oscillations. Two such schemes are the QUICK (Quadratic Upwind Interpolation for Convective Kinematics) and TOASOD (Third Order Advection Second Order Diffusion) schemes, which are similar in formulation but different in accuracy, with the two schemes being second and third order accurate in space respectively for finite difference models. These two schemes can be written in various finite difference forms for transient solute transport models, with the different representations having different numerical properties and computational efficiencies. Although these two schemes are advectively (or convectively) stable, it has been shown that the originally proposed explicit QUICK and TOASOD schemes become numerically unstable for the case of pure advection. The stability constraints have been established for each scheme representation based upon the von Neumann stability analysis. All the derived schemes have been tested for various initial solute distributions and for a number of continuous discharge cases, with both constant and time varying velocity fields. The 1-D QUICKEST (QUICK with Estimated Streaming Term) scheme is third order accurate both in time and space. It has been shown analytically and numerically that a previously derived quasi 2-D explicit QUICKEST scheme, with a reduced accuracy in time, is unstable for the case of pure advection. The modified 2-D explicit QUICKEST, ADI-TOASOD and ADI-QUICK schemes have been developed herein and proved to be numerically stable, with the bility sta- region of each derived 2-D scheme having also been established. All these derived 2-D schemesh ave been tested in a 2-D domain for various initial solute distributions with both uniform and rotational flow fields. They were further tested for a number of 2-D continuous discharge cases, with the corresponding exact solutions having also been derived herein. All the numerical tests in both the 1-D and 2-D cases were compared with the corresponding exact solutions and the results obtained using various other difference schemes, with the higher order schemes generally producing more accurate predictions, except for the characteristic based schemes which failed to conserve mass for the 2-D rotational flow tests. The ADI-TOASOD scheme has also been applied to two water quality studies in the U. K., simulating nitrate and faecal coliform distributions respectively, with the results showing a marked improvement in comparison with the results obtained by the second order central difference scheme. Details are also given of a refined numerical representation of flooding and drying of tidal flood plains for hydrodynamic modelling, with the results showing considerable improvements in comparison with a number of existing models and in good agreement with the field measured data in a natural harbour study.

Deformation of materials due to heat exposure can be a challenge in vehicle design. Sun exposure and heat build up in the vehicle cabin contribute to accelerated aging of the materials used. To understand how this process affects the durability, numerical simulation is an important tool. This thesis work investigates whether it is possible to, with weather data and knowledge of how a car is used, simulate the deformation process of the trim parts due to heat exposure from the sun. To answer this question, two simulation methods have been compared: The first method is to only look at the aging of the material over time. This method is used today at Volvo Cars, but has been found to be insufficient from a number of aspects. The second method includes the effects of the reversible deformations. This method has not previously been tested in a similar context but was considered interesting as it models more true to life. In addition, the effects of modeling the car according to a virtual customer behavior, rather than stationary, were investigated. The main simulation tools used are TAITherm and Abaqus. The results show that modeling the vehicle with an imagined user routine yields a lower mean temperature as the car is cooled down when driven. The result of the comparison between the two methods shows that inclusion of the effects of the reversible deformations contribute to a better model of the aging of the trim parts due to heat exposure from the sun. / Deformation av material till följd av hög värmelast är ofta en utmaning inom fordonsdesign. Materialet i kupén exponeras både för direkt solljus och den värme som ackumuleras i det stängda utrymmet. För att få förståelse för hur denna process påverkar hållbarheten är numerisk analys ett viktigt verktyg. Föreliggande examensarbete undersöker om det är möjligt att, med väderdata och kunskap om hur en bil används, simulera deformationsprocessen i trim- delarna som uppkommer av värmexponering från solen. För att besvara denna fråga har två simuleringsmetoder jämförts: Den första metoden är att endast titta på materialets åldrande över tiden. Den används idag på Volvo Cars, men har befunnits vara otillräcklig utifrån ett antal aspekter. Den andra metoden inkluderar effekterna av de elastiska deformationerna av materialet. Denna metod har inte tidigare prövats i ett liknande sammanhang men bedömdes intressant då den modellerar mer verklighetstroget. Dessutom undersöktes effekterna av att modellera bilen enligt ett virtuellt kundbeteen- de snarare än som stillastående. De huvudsakliga simuleringsverktygen som använts här är TAITherm och Abaqus. Resultaten visar att modellering av fordonet med en tänkt användarrutin ger en lägre medeltemperatur eftersom bilen kyls ner när den körs. Resultatet av jämförelsen mellan de två metoderna visar att inkludering av effekterna av de elastiska deformationerna bidrar till en bättre modellering av åldrandet av trimdelarna till följd av värmexponering från solen.

No description available.

No description available.