Shocks in the Illustris Universe and Discontinuous Galerkin Hydrodynamics

Die Erforschung hochgradig nichtlinearer astrophysikalischer Systeme und Prozesse hängt in zunehmender Weise von numerischen Simulationverfahren ab. Die Ziele dieser Arbeit liegen in der Entwicklung neuartiger Analysemethoden für kosmologische Simulationen und der Einführung neuer numerischer Methoden zur Verbesserung ihrer Genauigkeit. Wir stellen die Implementierung eines Algorithmus zur Stoßwellendetektierung für den AREPO-Code mit bewegtem Gitter vor. Damit analysieren wir Stoßwellen in Illustris, einer hochmodernen kosmologischen Galaxienentstehungssimulation. Wir identifizieren Stoßwellen verschiedenster Art, zum Beispiel aufgrund von Akkretionsprozessen, Strukturkollisionen, schwarzen Löchern, und galaktischen Winden. Die stärksten Stoßwellen werden hierbei durch schwarze Löcher hervorgerufen. Zu späten Zeiten messen wir eine spezifische Stoßwellendissipationsrate, die relativ umgebungsunabhängig ist, von 0.1 erg / g / s. In einem weiteren Projekt beschreiben und implementieren wir eine diskontinuierliche Galerkin (DG) Methode höherer Ordnung zur Lösung der idealen Gasgleichungen auf einem strukturierten Gitter, welches lokal verfeinert werden kann. Durch Vergleich mit einem traditionellen Finiten-Volumen-Verfahren finden wir, dass DG geringere Diffusions- und Advektionsfehler aufweist, sowie für rotierende Systeme zu bevorzugen ist. Unsere Ergebnisse belegen ein großes Potenzial dieser Methode für astrophysikalische Anwendungen

Reionization in the Illustris Universe and Novel Numerical Methods

Numerical simulation methods provide powerful tools to study astrophysical processes in cosmic structure formation. Further advancing their utility requires to improve their accuracy and to account for more of the relevant physics. In this thesis, we pursue this goal by developing novel numerical approaches for studying the epoch of cosmic reionization and for simulating hydrodynamical flows with accurate higher-order methods. We introduce a novel GPU-based radiative transfer code designed to study cosmic reionization. Our implementation of radiative transfer uses either a cone-based or a moment-based advection method and is able to accurately follow the epoch of cosmic reionization in postprocessing. To validate our methods, we consider a number of standard reionization test problems. We then apply our implementation to the state-of-the-art Illustris simulation of galaxy formation. We find that the stellar populations of the galaxies forming in Illustris are able to reionize the universe at an epoch consistent with observations. In particular, our results reproduce Lyman-alpha constraints for the reionization history and yield an optical depth towards the surface of last scattering of tau = 0.065, which is in reassuring agreement with recent Planck observations. In our simulations, reionization proceeds ‘inside-out’ and predicts an evolving size distribution of ionized bubbles that is characterized by ever larger maximum sizes of the bubbles with time, whereas the abundance of small bubbles stays relatively constant over an extended period until reionization is completed. The results obtained with both of our radiative transfer schemes are rather similar, suggesting that the details of these methods are not a major source of uncertainty. We also present the implementation of a novel hydrodynamics solver based on a discontinuous Galerkin method. To this end we design and add an adaptive mesh refinement module to the hydrodynamical moving-mesh code AREPO. As a first application of this new tool, we discuss simulations of driven subsonic turbulence. There, we find an enlarged inertial range for our discontinuous Galerkin simulations compared with finite volume methods for an equal number of degrees of freedom. Furthermore, the overall compute time to solution at a prescribed accuracy is shorter as well for the new discontinuous Galerkin code, demonstrating the potential of this technique for future astrophysical applications

Magnetic Field Amplification in Galaxy Clusters and its Simulation

We review the present theoretical and numerical understanding of magnetic field amplification in cosmic large-scale structure, on length scales of galaxy clusters and beyond. Structure formation drives compression and turbulence, which amplify tiny magnetic seed fields to the microGauss values that are observed in the intracluster medium. This process is intimately connected to the properties of turbulence and the microphysics of the intra-cluster medium. Additional roles are played by merger induced shocks that sweep through the intra-cluster medium and motions induced by sloshing cool cores. The accurate simulation of magnetic field amplification in clusters still poses a serious challenge for simulations of cosmological structure formation. We review the current literature on cosmological simulations that include magnetic fields and outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure

Cosmological Simulations of Galaxy Formation

Over the last decades, cosmological simulations of galaxy formation have been instrumental for advancing our understanding of structure and galaxy formation in the Universe. These simulations follow the non-linear evolution of galaxies modeling a variety of physical processes over an enormous range of scales. A better understanding of the physics relevant for shaping galaxies, improved numerical methods, and increased computing power have led to simulations that can reproduce a large number of observed galaxy properties. Modern simulations model dark matter, dark energy, and ordinary matter in an expanding space-time starting from well-defined initial conditions. The modeling of ordinary matter is most challenging due to the large array of physical processes affecting this matter component. Cosmological simulations have also proven useful to study alternative cosmological models and their impact on the galaxy population. This review presents a concise overview of the methodology of cosmological simulations of galaxy formation and their different applications.Comment: To appear in Nature Reviews Physics. 34 pages, 2 figures, 2 table

Discontinuous Galerkin Spectral Element Methods for Astrophysical Flows in Multi-physics Applications

In engineering applications, discontinuous Galerkin methods (DG) have been proven to be a powerful and flexible class of high order methods for problems in computational fluid dynamics. However, the potential benefits of DG for applications in astrophysical contexts is still relatively unexplored in its entirety. To this day, a decent number of studies surveying DG for astrophysical flows have been conducted. But the adoption of DG by the astrophysics community is just beginning to gain traction and integration of DG into established, multi-physics simulation frameworks for comprehensive astrophysical modeling is still lacking. It is our firm believe, that the full potential of novel approaches for numerically solving the fluid equations only shows under the pressure of real-world simulations with all aspects of multi-physics, challenging flow configurations, resolution and runtime constraints, and efficiency metrics on high-performance systems involved. Thus, we see the pressing need to propel DG from the well-trodden path of cataloguing test results under "optimal" laboratory conditions towards the harsh and unforgiving environment of large-scale astrophysics simulations. Consequently, the core of this work is the development and deployment of a robust DG scheme solving the ideal magneto-hydrodynamics equations with multiple species on three-dimensional Cartesian grids with adaptive mesh refinement. We chose to implement DG within the venerable simulation framework FLASH, with a specific focus on multi-physics problems in astrophysics. This entails modifications of the vanilla DG scheme to make it fit seamlessly within FLASH in such a way that all other physics modules can be naturally coupled without additional implementation overhead. A key ingredient is that our DG scheme uses mean value data organized into blocks - the central data structure in FLASH. Having the opportunity to work on mean values, allows us to rely on a rock-solid, monotone Finite Volume (FV) scheme as "backup" whenever the high order DG method fails in cases when the flow gets too harsh. Finding ways to combine the two schemes in a fail-safe manner without loosing primary conservation while still maintaining high order accuracy for smooth, well-resolved flows involves a series of careful considerations, which we document in this thesis. The result of our work is a novel shock capturing scheme - a hybrid between FV and DG - with smooth transitions between low and high order fluxes according to solution smoothness estimators. We present extensive validations and test cases, specifically its interaction with multi-physics modules in FLASH such as (self-)gravity and radiative transfer. We also investigate the benefits and pitfalls of integrating end-to-end entropy stability into our numerical scheme, with special focus on highly compressible turbulent flows and shocks. Our implementation of DG in FLASH allows us to conduct preliminary yet comprehensive astrophysics simulations proving that our new solver is ready for assessments and investigations by the astrophysics community

Numerical Methods for Simulating and Understanding the Universe

Only within the past century have we discovered the existence of external galaxies outside our own Milky Way. The study of the formation and evolution of galaxies is now an entire field unto itself, with a key part of this field being the direct numerical simulation of galaxy formation. These simulations naturally depend heavily on an assortment of numerical methods, from fluid solvers to detailed prescriptions for metal evolution in stars. This thesis explores existing numerical methods and develops novel methods for simulating astrophysical fluids and analysing the baryon cycle in galaxies. We first show how the commonly used Pressure-SPH (Smoothed Particle Hydrodynamics) method leads to large integration errors when coupled to galaxy formation physics, before developing a new SPH method called Sphenix that does not suffer from the same errors. Sphenix is based on Density-SPH, and employs a novel artificial conduction scheme to reduce errors at contact discontinuities. Sphenix is then shown to solve a number of challenging problems for SPH, including vorticity conservation and fluid mixing, thanks to its conduction and viscosity schemes. Finally, we develop two new numerical schemes to study the baryon cycle in the Simba simulations. The spread metric is used to show that matter can be transported huge distances (≫ 10 Mpc) by redshift z = 0, primarily due to AGN feedback. By comparing the Lagrangian region that gas resides in at the initial state of the simulation to its resident halo at z = 0 we show how matter can be transported between bound haloes at the end of the simulation. Notably, we show that 5-10% of the baryonic mass in a typical Milky Way mass halo originated in the region defined by the dark matter of another halo, leading to potential difficulties for so-called ‘zoom-in’ simulations

Accurate, Meshless Methods for Magneto-Hydrodynamics

Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics (SPH) and adaptive mesh-refinement (AMR) schemes. Here, we extend these to include ideal magneto-hydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains div*B~0 to high accuracy. We implement these in the code GIZMO, together with a state-of-the-art implementation of SPH MHD. In every one of a large suite of test problems, the new methods are competitive with moving-mesh and AMR schemes using constrained transport (CT) to ensure div*B=0. They are able to correctly capture the growth and structure of the magneto-rotational instability (MRI), MHD turbulence, and the launching of magnetic jets, in some cases converging more rapidly than AMR codes. Compared to SPH, the MFM/MFV methods exhibit proper convergence at fixed neighbor number, sharper shock capturing, and dramatically reduced noise, div*B errors, and diffusion. Still, 'modern' SPH is able to handle most of our tests, at the cost of much larger kernels and 'by hand' adjustment of artificial diffusion parameters. Compared to AMR, the new meshless methods exhibit enhanced 'grid noise' but reduced advection errors and numerical diffusion, velocity-independent errors, and superior angular momentum conservation and coupling to N-body gravity solvers. As a result they converge more slowly on some problems (involving smooth, slowly-moving flows) but more rapidly on others (involving advection or rotation). In all cases, divergence-control beyond the popular Powell 8-wave approach is necessary, or else all methods we consider will systematically converge to unphysical solutions.Comment: 35 pages, 39 figures. MNRAS. Updated with published version. A public version of the GIZMO MHD code, user's guide, test problem setups, and movies are available at http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm

The impact of feedback on galactic and extra-galactic scales

Recent cosmological hydrodynamical simulations were for the first time able to produce galaxy populations with realistic sizes and morphologies. This success can be attributed to the inclusion of subgrid models for supernovae winds and active galactic nuclei (AGN) feedback. In this thesis, we investigate the impact of feedback driven galactic outflows. First, the expulsion of gas proves to be crucial for the rotational support of haloes hosting realistic galaxies. We employ the state-of-the-art hydrodynamical simulation suites Illustris and IllustrisTNG to characterise the amount of specific angular momentum in the baryonic component of haloes. We find the baryonic spin at z = 0 to be a factor of ∼ 2 higher than the dark matter spin, which is due to the transfer of a constant cumulative spin of Δλ = 0.0013 by z = 0 from dark matter to the gas during mergers, and to the preferential expulsion of low angular momentum gas by mostly AGN feedback. Second, galactic outflows impact the state of the diffuse gas on large scales. We employ the Lyman-α forest to examine the feedback induced changes in the inter-galactic medium (IGM) that serves as gas reservoir for accretion onto galaxies. For a clean comparison, we have run a suite of simulations with both galaxy formation physics and with the Quick Lyman-α (QLA) technique yielding an unperturbed IGM. We find the Lyman-α flux power spectrum to exhibit increasingly more power at large scales and correspondingly less power at small scales in the presence of outflows, as well as the IGM to be generally hotter. Employing IllustrisTNG we investigate the excess Lyman-α absorption as a function of impact parameter for haloes exhibiting strong and weak feedback and find significant differences that can largely be explained by the higher temperature of the perturbed gas

GEAR-RT: Towards Exa-Scale Moment Based Radiative Transfer For Cosmological Simulations Using Task-Based Parallelism And Dynamic Sub-Cycling with SWIFT

The development and implementation of GEAR-RT, a radiative transfer solver using the M1 closure in the open source code SWIFT, is presented, and validated using standard tests for radiative transfer. GEAR-RT is modeled after RAMSES-RT (Rosdahl et al. 2013) with some key differences. Firstly, while RAMSES-RT uses Finite Volume methods and an Adaptive Mesh Refinement (AMR) strategy, GEAR-RT employs particles as discretization elements and solves the equations using a Finite Volume Particle Method (FVPM). Secondly, GEAR-RT makes use of the task-based parallelization strategy of SWIFT, which allows for optimized load balancing, increased cache efficiency, asynchronous communications, and a domain decomposition based on work rather than on data. GEAR-RT is able to perform sub-cycles of radiative transfer steps w.r.t. a single hydrodynamics step. Radiation requires much smaller time step sizes than hydrodynamics, and sub-cycling permits calculations which are not strictly necessary to be skipped. Indeed, in a test case with gravity, hydrodynamics, and radiative transfer, the sub-cycling is able to reduce the runtime of a simulation by over 90%. Allowing only a part of the involved physics to be sub-cycled is a contrived matter when task-based parallelism is involved, and is an entirely novel feature in SWIFT. Since GEAR-RT uses a FVPM, a detailed introduction into Finite Volume methods and Finite Volume Particle Methods is presented. In astrophysical literature, two FVPM methods are written about: Hopkins (2015) have implemented one in their GIZMO code, while the one mentioned in Ivanova et al. (2013) isn't used to date. In this work, I test an implementation of the Ivanova et al. (2013) version, and conclude that in its current form, it is not suitable for use with particles which are co-moving with the fluid, which in turn is an essential feature for cosmological simulations.Comment: PhD Thesi