abstract: Compressible fluid flows involving multiple physical states of matter occur in both nature and technical applications such as underwater explosions and implosions, cavitation-induced bubble collapse in naval applications and Richtmyer-Meshkov type instabilities in inertial confinement fusion. Of particular interest is the atomization of fuels that enable shock-induced mixing of fuel and oxidizer in supersonic combustors. Due to low residence times and varying length scales, providing insight through physical experiments is both technically challenging and sometimes unfeasible. Numerical simulations can help provide detailed insight and aid in the engineering design of devices that can harness these physical phenomena. In this research, computational methods were developed to accurately simulate phase interfaces in compressible fluid flows with a focus on targeting primary atomization. Novel numerical methods which treat the phase interface as a discontinuity, and as a smeared region were developed using low-dissipation, high-order schemes. The resulting methods account for the effects of compressibility, surface tension and viscosity. To aid with the varying length scales and high-resolution requirements found in atomization applications, an adaptive mesh refinement (AMR) framework is used to provide high-resolution only in regions of interest. The developed methods were verified with test cases involving strong shocks, high density ratios, surface tension effects and jumps in the equations of state, in one-, two- and three dimensions, obtaining good agreement with theoretical and experimental results. An application case of the primary atomization of a liquid jet injected into a Mach 2 supersonic crossflow of air is performed with the methods developed. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2020

As ever more challenging designs are required in present-day industries, the traditional trial-and-error procedure frequently used for designing mechanical parts slows down the design process and yields suboptimal designs, so that new approaches are needed to obtain a competitive advantage. With the ascent of the Finite Element Method (FEM) in the engineering community in the 1970s, structural shape optimization arose as a promising area of application. However, due to the iterative nature of shape optimization processes, the handling of large quantities of numerical models along with the approximated character of numerical methods may even dissuade the use of these techniques (or fail to exploit their full potential) because the development time of new products is becoming ever shorter. This Thesis is concerned with the formulation of a 3D methodology based on the Cartesian-grid Finite Element Method (cgFEM) as a tool for efficient and robust numerical analysis. This methodology belongs to the category of embedded (or fictitious) domain discretization techniques in which the key concept is to extend the structural analysis problem to an easy-to-mesh approximation domain that encloses the physical domain boundary. The use of Cartesian grids provides a natural platform for structural shape optimization because the numerical domain is separated from a physical model, which can easily be changed during the optimization procedure without altering the background discretization. Another advantage is the fact that mesh generation becomes a trivial task since the discretization of the numerical domain and its manipulation, in combination with an efficient hierarchical data structure, can be exploited to save computational effort. However, these advantages are challenged by several numerical issues. Basically, the computational effort has moved from the use of expensive meshing algorithms towards the use of, for example, elaborate numerical integration schemes designed to capture the mismatch between the geometrical domain boundary and the embedding finite element mesh. To do this we used a stabilized formulation to impose boundary conditions and developed novel techniques to be able to capture the exact boundary representation of the models. To complete the implementation of a structural shape optimization method an adjunct formulation is used for the differentiation of the design sensitivities required for gradient-based algorithms. The derivatives are not only the variables required for the process, but also compose a powerful tool for projecting information between different designs, or even projecting the information to create h-adapted meshes without going through a full h-adaptive refinement process. The proposed improvements are reflected in the numerical examples included in this Thesis. These analyses clearly show the improved behavior of the cgFEM technology as regards numerical accuracy and computational efficiency, and consequently the suitability of the cgFEM approach for shape optimization or contact problems. / La competitividad en la industria actual impone la necesidad de generar nuevos y mejores diseños. El tradicional procedimiento de prueba y error, usado a menudo para el diseño de componentes mecánicos, ralentiza el proceso de diseño y produce diseños subóptimos, por lo que se necesitan nuevos enfoques para obtener una ventaja competitiva. Con el desarrollo del Método de los Elementos Finitos (MEF) en el campo de la ingeniería en la década de 1970, la optimización de forma estructural surgió como un área de aplicación prometedora. El entorno industrial cada vez más exigente implica ciclos cada vez más cortos de desarrollo de nuevos productos. Por tanto, la naturaleza iterativa de los procesos de optimización de forma, que supone el análisis de gran cantidad de geometrías (para las se han de usar modelos numéricos de gran tamaño a fin de limitar el efecto de los errores intrínsecamente asociados a las técnicas numéricas), puede incluso disuadir del uso de estas técnicas. Esta Tesis se centra en la formulación de una metodología 3D basada en el Cartesian-grid Finite Element Method (cgFEM) como herramienta para un análisis numérico eficiente y robusto. Esta metodología pertenece a la categoría de técnicas de discretización Immersed Boundary donde el concepto clave es extender el problema de análisis estructural a un dominio de aproximación, que contiene la frontera del dominio físico, cuya discretización (mallado) resulte sencilla. El uso de mallados cartesianos proporciona una plataforma natural para la optimización de forma estructural porque el dominio numérico está separado del modelo físico, que podrá cambiar libremente durante el procedimiento de optimización sin alterar la discretización subyacente. Otro argumento positivo reside en el hecho de que la generación de malla se convierte en una tarea trivial. La discretización del dominio numérico y su manipulación, en coalición con la eficiencia de una estructura jerárquica de datos, pueden ser explotados para ahorrar coste computacional. Sin embargo, estas ventajas pueden ser cuestionadas por varios problemas numéricos. Básicamente, el esfuerzo computacional se ha desplazado. Del uso de costosos algoritmos de mallado nos movemos hacia el uso de, por ejemplo, esquemas de integración numérica elaborados para poder capturar la discrepancia entre la frontera del dominio geométrico y la malla de elementos finitos que lo embebe. Para ello, utilizamos, por un lado, una formulación de estabilización para imponer condiciones de contorno y, por otro lado, hemos desarrollado nuevas técnicas para poder captar la representación exacta de los modelos geométricos. Para completar la implementación de un método de optimización de forma estructural se usa una formulación adjunta para derivar las sensibilidades de diseño requeridas por los algoritmos basados en gradiente. Las derivadas no son sólo variables requeridas para el proceso, sino una poderosa herramienta para poder proyectar información entre diferentes diseños o, incluso, proyectar la información para crear mallas h-adaptadas sin pasar por un proceso completo de refinamiento h-adaptativo. Las mejoras propuestas se reflejan en los ejemplos numéricos presentados en esta Tesis. Estos análisis muestran claramente el comportamiento superior de la tecnología cgFEM en cuanto a precisión numérica y eficiencia computacional. En consecuencia, el enfoque cgFEM se postula como una herramienta adecuada para la optimización de forma. / Actualment, amb la competència existent en la industria, s'imposa la necessitat de generar nous i millors dissenys . El tradicional procediment de prova i error, que amb freqüència es fa servir pel disseny de components mecànics, endarrereix el procés de disseny i produeix dissenys subòptims, pel que es necessiten nous enfocaments per obtindre avantatge competitiu. Amb el desenvolupament del Mètode dels Elements Finits (MEF) en el camp de l'enginyeria en la dècada de 1970, l'optimització de forma estructural va sorgir com un àrea d'aplicació prometedora. No obstant això, a causa de la natura iterativa dels processos d'optimització de forma, la manipulació dels models numèrics en grans quantitats, junt amb l'error de discretització dels mètodes numèrics, pot fins i tot dissuadir de l'ús d'aquestes tècniques (o d'explotar tot el seu potencial), perquè al mateix temps els cicles de desenvolupament de nous productes s'estan acurtant. Esta Tesi se centra en la formulació d'una metodologia 3D basada en el Cartesian-grid Finite Element Method (cgFEM) com a ferramenta per una anàlisi numèrica eficient i sòlida. Esta metodologia pertany a la categoria de tècniques de discretització Immersed Boundary on el concepte clau és expandir el problema d'anàlisi estructural a un domini d'aproximació fàcil de mallar que conté la frontera del domini físic. L'utilització de mallats cartesians proporciona una plataforma natural per l'optimització de forma estructural perquè el domini numèric està separat del model físic, que podria canviar lliurement durant el procediment d'optimització sense alterar la discretització subjacent. A més, un altre argument positiu el trobem en què la generació de malla es converteix en una tasca trivial, ja que la discretització del domini numèric i la seua manipulació, en coalició amb l'eficiència d'una estructura jeràrquica de dades, poden ser explotats per estalviar cost computacional. Tot i això, estos avantatges poden ser qüestionats per diversos problemes numèrics. Bàsicament, l'esforç computacional s'ha desplaçat. De l'ús de costosos algoritmes de mallat ens movem cap a l'ús de, per exemple, esquemes d'integració numèrica elaborats per poder capturar la discrepància entre la frontera del domini geomètric i la malla d'elements finits que ho embeu. Per això, fem ús, d'una banda, d'una formulació d'estabilització per imposar condicions de contorn i, d'un altra, desevolupem noves tècniques per poder captar la representació exacta dels models geomètrics Per completar la implementació d'un mètode d'optimització de forma estructural es fa ús d'una formulació adjunta per derivar les sensibilitats de disseny requerides pels algoritmes basats en gradient. Les derivades no són únicament variables requerides pel procés, sinó una poderosa ferramenta per poder projectar informació entre diferents dissenys o, fins i tot, projectar la informació per crear malles h-adaptades sense passar per un procés complet de refinament h-adaptatiu. Les millores proposades s'evidencien en els exemples numèrics presentats en esta Tesi. Estes anàlisis mostren clarament el comportament superior de la tecnologia cgFEM en tant a precisió numèrica i eficiència computacional. Així, l'enfocament cgFEM es postula com una ferramenta adient per l'optimització de forma. / Marco Alacid, O. (2017). Structural Shape Optimization Based On The Use Of Cartesian Grids [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86195 / TESIS

We present an Embedded Boundary with Adaptive Mesh Refinement technique for solving the compressible Navier Stokes equations in arbitrary complex domains; followed by a numerical studies for the effect of circular cylinders on the transient dynamics of the Richtmyer-Meshkov Instability. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The Navier Stokes equations are numerically solved by the second order multidimensional upwind method. Block-structured AMR, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the Embedded Boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The effects on the transient dynamics of the Richtmyer-Meshkov instability due to small scale perturbations introduced on the shock-wave or the material interface by a single or set of solid circular cylinders were computationally investigated using the developed technique. First, we discuss the RMI initiated on a flat interface by a rippled shock-wave that is disturbed by a single circular cylinder. Then, we study the effect of introducing a number of circular cylinders on the interface. The arrangement of the cylinders set mimic (in a two dimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in the experimental setup. We analyzed their effects on the mixing layer growth and the mixedness level, and qualitatively demonstrate the cylinders' perturbation effects on the mixing layer structure. We modeled the cylinders' influence based on their diameters; and showed the model ability to predict the variation of the mixing layer growth for different flow parameters.

Products manufactured by aluminium casting have become very popular and already replaced many parts that were once produced by iron and steel casting. This trends upwards especially in the automotive industry as it has become extremely important to reduce vehicle weight due to environmental requirements and economical aspects. This popularity of aluminium alloys could be ascribed to their light weights and many other advantages including excellent castability, good corrosion resistance, good thermal and electrical conductivity, good machinability, low melting temperatures and minimal gas solubility with the exception of hydrogen. The most important alloy group among casting alloys is Aluminium Silicon (Al - Si).   Al-Si alloys must undergo a specific melt treatment procedure prior to casting. This treatment consists of several steps including degassing of hydrogen, grain refinement and eutectic modification. The aim of this study is to make an assessment of the metal treatment process of an (Al-Si) casting alloy at Unnaryd Modell AB for the purpose of improving the melt conditions and thus the quality of the final product. A rotary degasser provided by Foseco is also tested instead of the traditional tablet degassing method to see if this technique would result in any significant improvement of the melt quality. The results show that Unnaryd modell AB follows a proper treatment routine. It shows moreover that the rotary degassing is superior to the tablet degassing in many aspects including the level of degassing achieved, time efficiency, environmental consideration and personnel security.

Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included.

We present an $hp$-adaptive strategy that is based on estimating the decay of the expansion coefficients when a function is expanded in $L^2$-orthogonal polynomails on a triangle or a tetrahedron. This method is justified by showing that the decay of the coefficients is exponential if and only if the function is analytic. Numerical examples illustrate the performance of this approach, and we compare it with two other $hp$-adaptive strategies.

In this thesis, a robust, reliable and efficient isogeometric analysis framework is presented that allows for an adaptive spatial discretization of non-linear and time-dependent multi-field problems. In detail, B\'ezier extraction of truncated hierarchical B-splines is proposed that allows for a strict element viewpoint, and in this way, for the application of standard finite element procedures. Furthermore, local mesh refinement and coarsening strategies are introduced to generate graded meshes that meet given minimum quality requirements. The different strategies are classified in two groups and compared in the adaptive isogeometric analysis of two- and three-dimensional, singular and non-singular problems of elasticity and the Poisson equation. Since a large class of boundary value problems is non-linear or time-dependent in nature and requires incremental solution schemes, projection and transfer operators are needed to transfer all state variables to the new locally refined or coarsened mesh. For field variables, two novel projection methods are proposed and compared to existing global and semi-local versions. For internal variables, two different transfer operators are discussed and compared in numerical examples. The developed analysis framework is than combined with the phase-field method. Numerous phase-field models are discussed including the simulation of structural evolution processes to verify the stability and efficiency of the whole adaptive framework and to compare the projection and transfer operators for the state variables. Furthermore, the phase-field method is used to develop an unified modelling approach for weak and strong discontinuities in solid mechanics as they arise in the numerical analysis of heterogeneous materials due to rapidly changing mechanical properties at material interfaces or due to propagation of cracks if a specific failure load is exceeded. To avoid the time consuming mesh generation, a diffuse representation of the material interface is proposed by introducing a static phase-field. The material in the resulting transition region is recomputed by a homogenization of the adjacent material parameters. The extension of this approach by a phase-field model for crack propagation that also accounts for interface failure allows for the computation of brittle fracture in heterogeneous materials using non-conforming meshes.

abstract: This dissertation introduces FARCOM (Fortran Adaptive Refiner for Cartesian Orthogonal Meshes), a new general library for adaptive mesh refinement (AMR) based on an unstructured hexahedral mesh framework. As a result of the underlying unstructured formulation, the refinement and coarsening operators of the library operate on a single-cell basis and perform in-situ replacement of old mesh elements. This approach allows for h-refinement without the memory and computational expense of calculating masked coarse grid cells, as is done in traditional patch-based AMR approaches, and enables unstructured flow solvers to have access to the automated domain generation capabilities usually only found in tree AMR formulations. The library is written to let the user determine where to refine and coarsen through custom refinement selector functions for static mesh generation and dynamic mesh refinement, and can handle smooth fields (such as level sets) or localized markers (e.g. density gradients). The library was parallelized with the use of the Zoltan graph-partitioning library, which provides interfaces to both a graph partitioner (PT-Scotch) and a partitioner based on Hilbert space-filling curves. The partitioned adjacency graph, mesh data, and solution variable data is then packed and distributed across all MPI ranks in the simulation, which then regenerate the mesh, generate domain decomposition ghost cells, and create communication caches. Scalability runs were performed using a Leveque wave propagation scheme for solving the Euler equations. The results of simulations on up to 1536 cores indicate that the parallel performance is highly dependent on the graph partitioner being used, and differences between the partitioners were analyzed. FARCOM is found to have better performance if each MPI rank has more than 60,000 cells. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2019

Dans le contexte de la dynamique moléculaire classique appliquée à la physique de la matière condensée, les chercheurs du CEA étudient des phénomènes physiques à une échelle atomique. Pour cela, il est primordial d'optimiser continuellement les codes de dynamique moléculaire sur les dernières architectures de supercalculateurs massivement parallèles pour permettre aux physiciens d'exploiter la puissance de calcul pour reproduire numériquement des phénomènes physiques toujours plus complexes. Cependant, les codes de simulations doivent être adaptés afin d'équilibrer la répartition de la charge de calcul entre les cœurs d'un supercalculateur.Pour ce faire, dans cette thèse nous proposons d'incorporer la méthode de raffinement de maillage adaptatif dans le code de dynamique moléculaire ExaSTAMP. L'objectif est principalement d'optimiser la boucle de calcul effectuant le calcul des interactions entre particules grâce à des structures de données multi-threading et vectorisables. La structure permet également de réduire l'empreinte mémoire de la simulation. La conception de l’AMR est guidée par le besoin d'équilibrage de charge et d'adaptabilité soulevé par des ensembles de particules se déplaçant très rapidement au cours du temps.Les résultats de cette thèse montrent que l'utilisation d'une structure AMR dans ExaSTAMP permet d'améliorer les performances de celui-ci. L'AMR permet notamment de multiplier par 1.31 la vitesse d'exécution de la simulation d'un choc violent entraînant un micro-jet d'étain de 1 milliard 249 millions d'atomes sur 256 KNLs. De plus, l'AMR permet de réaliser des simulations qui jusqu'à présent n'étaient pas concevables comme l'impact d'une nano-goutte d'étain sur une surface solide avec plus 500 millions d'atomes. / In the context of classical molecular dynamics applied to condensed matter physics, CEA researchers are studying complex phenomena at the atomic scale. To do this, it is essential to continuously optimize the molecular dynamics codes of recent massively parallel supercomputers to enable physicists to exploit their capacity to numerically reproduce more and more complex physical phenomena. Nevertheless, simulation codes must be adapted to balance the load between the cores of supercomputers.To do this, in this thesis we propose to incorporate the Adaptive Mesh Refinement method into the ExaSTAMP molecular dynamics code. The main objective is to optimize the computation loop performing the calculation of particle interactions using multi-threaded and vectorizable data structures. The structure also reduces the memory footprint of the simulation. The design of the AMR is guided by the need for load balancing and adaptability raised by sets of particles moving dynamically over time.The results of this thesis show that using an AMR structure in ExaSTAMP improves its performance. In particular, the AMR makes it possible to execute 1.31 times faster than before the simulation of a violent shock causing a tin microjet of 1 billion 249 million atoms on 256 KNLs. In addition, simulations that were not conceivable so far can be carried out thanks to AMR, such as the impact of a tin nanodroplet on a solid surface with more than 500 million atoms.

Uppsatsen tar sikte på att undersöka hur dagens aktörer arbetar med grön fastighetsförädling och vilka olika incitament som finns för aktörer att arbeta med detta. Vidare analyserar vi konkret vilka incitament som finns för ägaren av bostadsrättsfastigheter respektive hyresrättsfastigheter att investera i solceller. Vad finns det för likheter och skillnader mellan dessa två upplåtelseformer? Uppsatsen konkretiserar undersökningen genom en fallstudie i samarbete med HSB MälarDalarna. Där genomförs investeringar genom montering av solceller på fastigheten Adils 17 i Borlänge för att öka den ekonomiska lönsamheten. Målet är att uppnå självförsörjning av energiförbrukningen för fastigheten samtidigt som det skall vara ekonomiskt hållbart med återbetalningstid och nettonuvärde i åtanke. Grönfastighetsförädling är något som ligger i tiden för de flesta fastighetsbolagen idag. Flertalet av aktörerna och bolagen på fastighetsmarknaden blir mer och mer medvetna om miljövänliga investeringar och har högt satta miljömål. Där kommer bland annat investeringar i solceller som ett alternativ in vilket idag är något som såväl privatpersoner som kommersiella aktörer antingen redan arbetar med att montera eller strävar mot att investera i. Uppsatsen visat att incitamenten för att arbeta med grön fastighetsförädling för olika aktörer är många. Där de flesta incitamenten är av likartad karaktär även om det finns olikheter för de olika upplåtelseformerna vid grönförädling av befintliga fastigheter. Incitamenten för investeringar i solceller beror till stor del på upplåtelseformerna, vilket uppsatsen påvisar. Det föreligger såklart likheter och skillnader kring incitamenten även för solceller beroende på om det är en bostadsrättsfastighet eller hyresrättsfastighet. Detta utreder och förklara uppsatsen också. För fallstudien beräknades olika alternativa monterings möjligheter på Adils 17 där de mest lönsamma sedan tagits vidare och analyseras ytterligare innan någon slutsats och rekommendation kring montering av solceller på fastigheten har givits. Återbetalningstiderna varierar något beroende på vilket val av montering som väljs, samma gäller för nettonuvärdet. Viktigt är att båda dessa nyckeltal är inom ramen för vad en fastighetsägare likt HSB kan tänka sig för att det skall vara värt att investera, då besparingarna på just denna fastighet från solcellerna tillfaller fastighetsägaren i sin helhet. Två av monterings möjligheterna har i denna uppsats genom fallstudien funnits ligga inom ramen för vad som är en god investering. / The thesis aims to investigate how today's actors work with green property refinement and what different incentives are there for actors to work with this. This is then to analyse in concrete terms what incentives are available for tenant-owner properties and tenant-owner properties to invest in solar cells. What are the similarities and differences between these two forms of lending. The thesis furthermore concretises investments in solar cells in the form of a case study in collaboration with HSB where the financial profitability for the installation of solar cells on the Adils 17 a property in Borlange is carried out. The goal is to achieve self-sufficiency of the energy consumption of the property while being financially sustainable with repayment time and net present value in mind. Green property refinement is something that lays within the time and modern thinking of most real estate companies today. Where most of the actors and companies become more and more aware of environmentally friendly investments and have high environmental goals. There, among other things, investments in solar cells come as an alternative, which today is something that both private individuals and commercial actors are either already working on to assemble or strive to invest in. The thesis has shown that the incentives for working with green property refinement for various actors are many. Where most of the incentives are of a similar character, although there are differences for different forms of tenure in green refinement of existing properties. The incentives for investments in solar cells largely depend on the which form of tenure the property is, as the thesis demonstrates. Of course, there are similarities and differences regarding the incentives for solar cells, depending on whether it is a condominium or rental property. This is also something the thesis will straighten out and explain more in detail. For the case study, various alternative mounting options were calculated on Adils 17 where the most profitable options where further analysed before any conclusion and recommendation regarding the installation of solar cells on the property could be given. The repayment times vary slightly depending on the choice of assembly chosen, the same applies to the net present value. It is important that both of these key figures are within the scope of what a property owner, like HSB MalarDalarna, expects them to be to invest. As the savings on this particular property from the solar cells are due to the property owner. Two of the mounting possibilities in this essay have been calculated to lay within the scope of what could be considered a good investment through the fall study.