18 research outputs found

    HIGHER ACCURACY METHODS FOR FLUID FLOWS IN VARIOUS APPLICATIONS: THEORY AND IMPLEMENTATION

    Get PDF
    This dissertation contains research on several topics related to Defect-deferred correction (DDC) method applying to CFD problems. First, we want to improve the error due to temporal discretization for the problem of two convection dominated convection-diffusion problems, coupled across a joint interface. This serves as a step towards investigating an atmosphere-ocean coupling problem with the interface condition that allows for the exchange of energies between the domains. The main diffuculty is to decouple the problem in an unconditionally stable way for using legacy code for subdomains. To overcome the issue, we apply the Deferred Correction (DC) method. The DC method computes two successive approximations and we will exploit this extra flexibility by also introducing the artificial viscosity to resolve the low viscosity issue. The low viscosity issue is to lose an accuracy and a way of finding a approximate solution as a diffusion coeffiscient gets low. Even though that reduces the accuracy of the first approximation, we recover the second order accuracy in the correction step. Overall, we construct a defect and deferred correction (DDC) method. So that not only the second order accuracy in time and space is obtained but the method is also applicable to flows with low viscosity. Upon successfully completing the project in Chapter 1, we move on to implementing similar ideas for a fluid-fluid interaction problem with nonlinear interface condition; the results of this endeavor are reported in Chapter 2. In the third chapter, we represent a way of using an algorithm of an existing penalty-projection for MagnetoHydroDynamics, which allows for the usage of the less sophisticated and more computationally attractive Taylor-Hood pair of finite element spaces. We numerically show that the new modification of the method allows to get first order accuracy in time on the Taylor-Hood finite elements while the existing method would fail on it. In the fourth chapter, we apply the DC method to the magnetohydrodynamic (MHD) system written in Elsásser variables to get second order accuracy in time. We propose and analyze an algorithm based on the penalty projection with graddiv stabilized Taylor Hood solutions of Elsásser formulations

    Particle scattering in turbulent plasmas with amplified wave modes

    Get PDF
    Our calculations show a good agreement of particle simulations and the QLT for broad-band turbulent spectra; for higher turbulence levels and particle beam driven plasmas, the QLT approximation gets worse. Especially the resonance gap at mu = 0 poses a well-known problem for QLT for steep turbulence spectra, whereas test-particle computations show no problems for the particles to scatter across this region. The reason is that the sharp resonant wave-particle interactions in QLT are an oversimplification of the broader resonances in test-particle calculations, which result from nonlinear effects not included in the QLT. We emphasise the importance of these results for both numerical simulations and analytical particle transport approaches, especially the validity of the QLT

    Modelling solar coronal magnetic field evolution

    Get PDF
    Footpoint motions at the photosphere can inject energy into the magnetic field in the solar corona. This energy is then released in the corona as heat. There are many mathematical approaches to model the evolution of these magnetic fields. Magnetohydrodynamics (MHD) provides the most convenient and practical approach. However, there are many alternative approximate methods. It is difficult to know when an approximate method is valid and how well the assumptions need to be satisfied for the solutions to be accurate enough. To illustrate this, a simple experiment is performed. Four approximate methods, including Reduced MHD (RMHD), are used to model the evolution of a footpoint driven coronal loop through sequences of equilibria. The predicted evolution from each method is compared to the solution from full MHD simulations to test the accuracy of each method when the relevant assumptions are adjusted. After this initial test, the validity of RMHD is investigated for the particular case of the magnetic field evolution involving the development of the tearing instability. Full MHD simulations are used to argue the applicability of the assumptions and conditions of RMHD for this evolution. The potential of this setup to heat the corona is considered by performing full MHD simulations including thermodynamic processes of optically thin radiation and thermal conduction. These additional processes are not included in RMHD

    Alfvén Wave Turbulence as a Coronal Heating Mechanism: Simultaneously Predicting the Heating Rate and the Wave-induced Emission Line Broadening

    Get PDF
    We test the predictions of the Alfvén Wave Solar Model (AWSoM), a global wave-driven magnetohydrodynamic (MHD) model of the solar atmosphere, against high-resolution spectra emitted by the quiescent off-disk solar corona. AWSoM incorporates Alfvén wave propagation and dissipation in both closed and open magnetic field lines; turbulent dissipation is the only heating mechanism. We examine whether this mechanism is consistent with observations of coronal EUV emission by combining model results with the CHIANTI atomic database to create synthetic line-of-sight spectra, where spectral line widths depend on thermal and wave-related ion motions. This is the first time wave-induced line broadening is calculated from a global model with a realistic magnetic field. We used high-resolution SUMER observations above the solar west limb between 1.04 and 1.34 R o at the equator, taken in 1996 November. We obtained an AWSoM steady-state solution for the corresponding period using a synoptic magnetogram. The 3D solution revealed a pseudo-streamer structure transversing the SUMER line of sight, which contributes significantly to the emission; the modeled electron temperature and density in the pseudo-streamer are consistent with those observed. The synthetic line widths and the total line fluxes are consistent with the observations for five different ions. Further, line widths that include the contribution from the wave-induced ion motions improve the correspondence with observed spectra for all ions. We conclude that the turbulent dissipation assumed in the AWSoM model is a viable candidate for explaining coronal heating, as it is consistent with several independent measured quantities.National Science Foundation (U.S.) (Grant AGS-1322543

    Fully kinetic simulations of microscale turbulence in space and astrophysical plasmas

    Get PDF

    Characterising 3D Small-scale Reconnection in Kinetic Simulations of Space Plasma Turbulence

    Get PDF
    Magnetic reconnection and turbulence are two of the most important and enigmatic phenomena in plasma physics. Although they have been widely studied individually in a wide range of configurations, the research about the links between turbulence and reconnection is still in its early stages. It is accepted that there is a bi-directional feedback between the two phenomena, and understanding it is crucial to solve the longstanding problem of energy dissipation in collisionless plasmas. In this thesis, I present my contribution to this research field. I use 3D fully kinetic particle-in-cell simulations to explore reconnection that occurs from the turbulent interaction of anisotropic fluctuations consistent with the plasma conditions in the solar wind. I characterise the turbulence in the simulation and propose a set of indicators to find reconnection sites in the simulation. I select one reconnection event and study its geometry, magnetic field configuration, and the associated particle flows. I also explore the profiles of plasma and magnetic-field fluctuations recorded along artificial-spacecraft trajectories passing near and through the reconnection region. Furthermore, I develop and apply a mathematical framework to explore the reversible and irreversible energy density transfer rates. I compare my results with previous studies of turbulent and laminar reconnection. The results presented in this thesis suggest that turbulent reconnection presents a complex three-dimensional problem, and the use of two-dimensional laminar or turbulent models to describe this type of reconnection does not accurately capture its energy transfer properties. Finally, I use my turbulent simulations for the preparation of a new multi-spacecraft mission concept (MagneToRE) to study the magnetic field topology in space plasmas

    A Model for Dissipation of Solar Wind Turbulence with Damping by Kinetic Alfvén Waves: Comparison with Observations and Implications for the Dissipation Process in the Solar Wind

    Get PDF
    The aim of this work is to improve the characterization of small scale processes in the solar wind, particularly, the dissipation process of the turbulent energy. Although some statistical properties of solar wind turbulence are comparable to those of hydrodynamic turbulence, the presence of the interplanetary magnetic field and the composition of the solar wind of charged particles result in important differences. We present a dissipation model, which is based on a combination of the nonlinear energy transport from large to small scales and the damping process, which becomes important at small scales. We assume that damping is caused by interactions between kinetic Alfvén waves (KAW) and solar wind particles. The first part of this thesis presents a one-dimensional model in wavenumber space, which is compared with solar wind observations. With the help of this model, the following conclusions can be drawn about the dissipation process: assuming an anisotropic energy transport, which follows the critical balance theory, the background turbulence is driven by KAWs and not by whistler waves. This KAW driven cascade results in a quasi-exponentially shaped dissipation range and a dissipation length which corresponds to the electron gyroradius. The model provides an answer to the question as to why the dissipation length in the solar wind is independent of the energy injected at large scales, which is a clear difference compared to hydrodynamic turbulence. The anisotropic nature of the solar wind turbulence influences the transport of energy in such a way that the damping becomes more effective with a larger amount of injected energy. The expansion of the one-dimensional dissipation model to three dimensions and the thereon based calculation of reduced power spectra in the frequency space lead to the following conclusions: Damping due to KAW is able to explain the steep spectral index in the sub-ion range, which is observed in the solar wind plasma but could not be explained by any theory. However, a direct comparison with a set of solar wind observations shows that the spectral index is still steeper in the observations than the spectral index in the model. We conclude that the KAW driven cascade is present in all the observed spectra, but that other effects or wave modes can additionally influence the slope
    corecore