Magnetohydrodynamic modeling of large-amplitude waves in the solar corona

Solar eruptions are a consequence of the complex dynamics occurring in the tenuous, hot magnetized plasma that characterizes the solar corona. From a socio-economic viewpoint, solar eruptions can be argued to be the most important manifestation of the magnetic activity of the Sun due to their role as the main drivers of space weather, i.e., conditions in space that can have an adverse impact on space- as well as ground-based technologies such as telecommunication, electric power systems and satellite navigation. The launch of new space-based solar observatories during the past two decades has resulted in a dramatic improvement of the instrumentation monitoring the inner heliosphere. In spite of the advances in the observational capabilities, the physics of the solar eruptions as well as the nature of the various transient large-scale coronal phenomena observationally associated with the eruptions remain elusive. Constructing models capable of simulating the coronal and heliospheric dynamics is a viable path for gaining a more complete understanding of these phenomena. This thesis is concerned with developing a simulation tool based on the magnetohydrodynamic (MHD) description of plasmas and employing it for studying the characteristics of large-scale waves and shocks launched into the solar corona by the lift-off of a solar eruption such as a coronal mass ejection (CME). A particular focus is on discussing the role of large-amplitude waves in producing transient phenomena such as EIT waves and solar energetic particle (SEP) events that are known to appear in conjunction with CMEs. A suite of MHD models of the solar corona are constructed that allow the study of the coronal dynamics in varying environments at several stages of the eruption. For this purpose, novel robust numerical methods for solving the equations of magnetohydrodynamics in orthogonal curvilinear geometries in multiple dimensions are derived, forming the basis of the numerical simulation tool developed for the thesis. The results show that a dynamically intricate global shock front degenerating to a fast-mode MHD wave towards the surface of the Sun is an essential and natural part of the eruption complex that plays a key role in the generation of eruption-related transient phenomena. For instance, the close resemblance between the on-disk signatures produced by the fast-mode wave and EIT waves suggest a wave interpretation of the latter. The simulations also reveal that a highly non-trivial evolution of the shock properties on coronal field lines occurs even for simple coronal conditions, highlighting the need for more sophisticated models of particle acceleration than generally used so far. The results of the thesis are of particular importance for the continuing efforts to construct reliable physics-based models of the inner heliosphere for use in space weather applications.I det tunna och heta magnetiserade plasmat, som kännetecknar solens korona, uppkommer soleruptioner som en följd av den komplicerade dynamiken i plasmat. I och med eruptionernas roll som huvudorsakaren av rymdvädret kan man ur en socioekonomisk synvinkel anse att soleruptioner är den viktigaste manifestationen av solens magnetiska aktivitet. Med begreppet rymdväder förstås sådana förhållanden i rymden som negativt kan påverka teknologiska system såväl i rymden som på jorden, till exempel telekommunikation, elsystem och satellitnavigering. I och med att nya rymdbaserade solobservatorier tagits i bruk de senaste två decennierna har instrumentationen som observerar den inre heliosfären förbättrats dramatiskt. Trots framstegen i observationsmöjligheterna är fysiken bakom soleruptionerna samt karaktären av diverse tillfälliga storskaliga fenomen som observeras i koronan i samband med eruptionerna fortfarande svårfångad. Ett sätt att uppnå en mera komplett förståelse av dessa fenomen är att konstruera modeller som kan simulera koronans och heliosfärens dynamik. I denna avhandling har ett simulationsverktyg utvecklats och tillämpats för att studera globala vågor och chockvågor i solens korona orsakade av soleruptioner så som koronamassutkast. Simulationsverktyget grundar sig på den magnetohydrodynamiska (MHD) beskrivningen av plasmor. Ett bärande tema är att diskutera rollen av dessa vågor i uppkomsten av fenomen som observeras i samband med koronamassutkast, exempelvis så kallade EIT vågor samt utbrott av energetiska partiklar. En svit av MHD modeller av solens korona har konstruerats i avhandlingen. Modellerna möjliggör studiet av koronans dynamik i varierande förhållanden och olika skeden av eruptionen. För detta ändamål har numeriska metoder som löser magnetohydrodynamikens ekvationer i ortogonala kroklinjiga geometrier i flera dimensioner utvecklats. Dessa numeriska metoder utgör grunden för det nya simulationsverktyget. Resultaten av modelleringen visar att en dynamiskt invecklad global chockfront, som övergår till en snabb magnetosonisk våg i närheten av solens yta, är en väsentlig och naturlig del av eruptionskomplexet. Dessa spelar en avgörande roll för uppkomsten av fenomen relaterade till eruptionen. Ett exempel är likheten mellan EIT vågen och den snabba magnetosoniska vågen på solens skiva. Detta antyder en vågtolkning av EIT vågorna. Simulationerna visar också att en icke-trivial evolution av chockvågens egenskaper på magnetiska fältlinjer i koronan förekommer även under relativt enkla omständigheter, vilket belyser behovet av att utveckla mera sofistikerade modeller för partikelacceleration i chockvågor i koronan. Avhandlingens resultat är av särskild betydelse för de fortsatta ansträngningarna att konstruera pålitliga fysikbaserade modeller av den inre heliosfären för applikationer med anknytning till rymdvädret

MHD Simulation of the Inner-Heliospheric Magnetic Field

Maps of the radial magnetic field at a heliocentric distance of ten solar radii are used as boundary conditions in the MHD code CRONOS to simulate a 3D inner-heliospheric solar wind emanating from the rotating Sun out to 1 AU. The input data for the magnetic field are the result of solar surface flux transport modelling using observational data of sunspot groups coupled with a current sheet source surface model. Amongst several advancements, this allows for higher angular resolution than that of comparable observational data from synoptic magnetograms. The required initial conditions for the other MHD quantities are obtained following an empirical approach using an inverse relation between flux tube expansion and radial solar wind speed. The computations are performed for representative solar minimum and maximum conditions, and the corresponding state of the solar wind up to the Earths orbit is obtained. After a successful comparison of the latter with observational data, they can be used to drive outer-heliospheric models.Comment: for associated wmv movie files accompanying Figure 7, see http://www.tp4.rub.de/~tow/max.wmv and http://www.tp4.rub.de/~tow/min.wm

Sensitivity Analysis and Optimization of Aerodynamic Configurations With Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition

Finite element methods for surface PDEs

In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit surface methods using level set descriptions of the surface, unfitted finite element methods and diffuse interface methods. In order to formulate the methods we present the necessary geometric analysis and, in the context of evolving surfaces, the necessary transport formulae. A wide variety of equations and applications are covered. Some ideas of the numerical analysis are presented along with illustrative numerical examples

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Pulsar magnetospheres in general relativity

The main contribution to the pulsar power can be calculated by assuming a rotating magnetically dominated magnetosphere described by the force-free approximation. Although this simple model has been used thoroughly to study pulsar magnetospheres in the flat spacetime regime, only a few works have considered the relativistic corrections introduced by the curvature and frame-dragging effects induced by a rotating neutron star. Here, we revisit the problem and describe pulsar magnetospheres within full general relativity, quantifying the corrections as a function of the angular velocity, the compactness of the star, and the misalignment angle between the spin and the magnetic dipole. We provide analytical expressions for the pulsar luminosity by fitting our numerical results. Finally, we also analyze the effect of the relativistic corrections on the braking index, which indicates a slight increment in its value.Fil: Carrasco, Federico León. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Palenzuela, Carlos. Universidad de las Islas Baleares; EspañaFil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin