Bridging Scales in 2- and 3-Dimensional Atmospheric Modeling with Adaptive Mesh Refinement

Complex multi-scale atmospheric phenomena, like tropical cyclones, challenge conventional weather and climate models, which use relatively coarse uniform-grid resolutions to cope with computational costs. Adaptive Mesh Refinement (AMR) techniques mitigate these challenges by dynamically and transiently placing high-resolution grids over salient features, thus providing sufficient local resolution while limiting the computational burden. This thesis explores the development of AMR, a technique that has been featured only sporadically in the atmospheric science literature, within a new nonhydrostatic, finite-volume dynamical core and demonstrates AMR's effectiveness in improving model accuracy and ability to resolve multi-scale features. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique developed with the Chombo AMR library. The AMR dynamical core is implemented in a hierarchy of models of increasing complexity, from an idealized 2D shallow water configuration to the nonhydrostatic 3D equation set with subgrid-scale parameterizations schemes. AMR's numerical accuracy, computational efficiency, and ability to track and resolve multifaceted and evolving features are assessed with a variety of existing and new test cases, implemented within each model iteration. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity, or minimum pressure based thresholds, in order to achieve the best accuracy for cost. Simulations show that the model's AMR can accurately resolve key local features in both shallow water and 3D test cases without requiring global high-resolution grids, as the adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse-fine interfaces. Furthermore, the AMR grids keep degradation of the large-scale smooth flows to a minimum. 2D and 3D physics parameterizations are able to function effectively over multiple levels of refinement, though the parameterizations are sensitive to grid resolution. AMR is most effective when refinement is triggered early or when the base uniform resolution can partially resolve the features of interests. Very coarse base resolutions lead to large initial errors that cannot be overcome by AMR. However, the addition of refinement later in the simulation still results in significant improvements, especially in resolving small-scale features. The research showed that flow properties, such as strong gradients or rainbands, can be sensitive to small changes in AMR criteria. These may delay the onset of the refinement or alter the shape of the refined area, which impacts the evolution of the flow. With coarse base resolutions, the tagging criteria must therefore be uniquely tailored to capture the early growth phases of the feature of interest. A promising refinement technique is a combination of some initial refinement and AMR. The initial refinement limits error growth at the base resolution and ensures that the model can resolve the feature of interest. Overall, AMR is shown to be a powerful modeling approach that bridges the resolution gap for extreme weather events.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147504/1/joferg_1.pd

Effects of Varying the Three-Body Molecular Hydrogen Formation Rate in Primordial Star Formation

The transformation of atomic hydrogen to molecular hydrogen through three-body reactions is a crucial stage in the collapse of primordial, metal-free halos, where the first generation of stars (Population III stars) in the Universe are formed. However, in the published literature, the rate coefficient for this reaction is uncertain by nearly an order of magnitude. We report on the results of both adaptive mesh refinement (AMR) and smoothed particle hydrodynamics (SPH) simulations of the collapse of metal-free halos as a function of the value of this rate coefficient. For each simulation method, we have simulated a single halo three times, using three different values of the rate coefficient. We find that while variation between halo realizations may be greater than that caused by the three-body rate coefficient being used, both the accretion physics onto Population III protostars as well as the long-term stability of the disk and any potential fragmentation may depend strongly on this rate coefficient.Comment: 29 pages, 7 figures; Accepted for publication in The Astrophysical Journa

Improving Performance of M-to-N Processing and Data Redistribution in In Transit Analysis and Visualization

In an in transit setting, a parallel data producer, such as a numerical simulation, runs on one set of ranks M, while a data consumer, such as a parallel visualization application, runs on a different set of ranks N. One of the central challenges in this in transit setting is to determine the mapping of data from the set of M producer ranks to the set of N consumer ranks. This is a challenging problem for several reasons, such as the producer and consumer codes potentially having different scaling characteristics and different data models. The resulting mapping from M to N ranks can have a significant impact on aggregate application performance. In this work, we present an approach for performing this M-to-N mapping in a way that has broad applicability across a diversity of data producer and consumer applications. We evaluate its design and performance with a study that runs at high concurrency on a modern HPC platform. By leveraging design characteristics, which facilitate an “intelligent” mapping from M-to-N, we observe significant performance gains are possible in terms of several different metrics, including time-to-solution and amount of data moved

IllinoisGRMHD: An Open-Source, User-Friendly GRMHD Code for Dynamical Spacetimes

In the extreme violence of merger and mass accretion, compact objects like black holes and neutron stars are thought to launch some of the most luminous outbursts of electromagnetic and gravitational wave energy in the Universe. Modeling these systems realistically is a central problem in theoretical astrophysics, but has proven extremely challenging, requiring the development of numerical relativity codes that solve Einstein's equations for the spacetime, coupled to the equations of general relativistic (ideal) magnetohydrodynamics (GRMHD) for the magnetized fluids. Over the past decade, the Illinois Numerical Relativity (ILNR) Group's dynamical spacetime GRMHD code has proven itself as a robust and reliable tool for theoretical modeling of such GRMHD phenomena. However, the code was written "by experts and for experts" of the code, with a steep learning curve that would severely hinder community adoption if it were open-sourced. Here we present IllinoisGRMHD, which is an open-source, highly-extensible rewrite of the original closed-source GRMHD code of the ILNR Group. Reducing the learning curve was the primary focus of this rewrite, with the goal of facilitating community involvement in the code's use and development, as well as the minimization of human effort in generating new science. IllinoisGRMHD also saves computer time, generating roundoff-precision identical output to the original code on adaptive-mesh grids, but nearly twice as fast at scales of hundreds to thousands of cores.Comment: 37 pages, 6 figures, single column. Matches published versio

Some Revised Observational Constraints on the Formation and Evolution of the Galactic Disk

A set of 76 open clusters with abundances based upon DDO photometry and/or moderate dispersion spectroscopy has been transformed to a common [Fe/H] scale and used to study the local structure and evolution of the galactic disk. The metallicity distribution of clusters with R_GC is best described by two distinct zones. Between R_GC = 6.5 and 10 kpc, the distribution has a mean [Fe/H] = 0.0 and a dispersion of 0.1 dex; there is only weak evidence for a shallow abundance gradient over this distance range. Beyond R_GC = 10 kpc, the metallicity distribution has a dispersion between 0.10 and 0.15 dex, but with a mean [Fe/H] = -0.3, implying a sharp discontinuity at R_GC = 10 kpc. After correcting for the discontinuity, no evidence is found for a gradient perpendicular to the plane. Adopting the clusters interior to 10 kpc as a representative sample of the galactic disk over the last 7 Gyr, the cluster metallicity range is found to be about half that of the field stars. When coupled with the discontinuity in the galactocentric gradient, the discrepancy in the metallicity distribution is interpreted as an indication of significant diffusion of field stars into the solar neighborhood from beyond 10 kpc. These results imply that the sun is NOT atypical of the stars formed in the solar circle 4.6 Gyr ago. It is suggested that the discontinuity reflects the edge of the initial galactic disk as defined by the disk globular cluster system and the so-called thick disk; the initial offset in [Fe/H] created by the differences in the chemical history on either side of the discontinuity has carried through to the current stage of galactic evolution. If correct, diffusion coupled with the absence of an abundance gradient could make the separation of field stars on the basis of galactocentric origin difficult.Comment: 41 pages, 9 figure files, LaTex. Appendix section and tables (tex or postscript) available at http://kubarb.phsx.ukans.edu/ ~twarog/ Submitted to Astronomical Journal July 199