Verification of mesoscale objective analyses of VAS and rawinsonde data using the March 1982 AVE/VAS special network data

Various combinations of VAS (Visible and Infrared Spin Scan Radiometer Atmospheric Sounder) data, conventional rawinsonde data, and gridded data from the National Weather Service's (NWS) global analysis, were used in successive-correction and variational objective-analysis procedures. Analyses are produced for 0000 GMT 7 March 1982, when the VAS sounding distribution was not greatly limited by the existence of cloud cover. The successive-correction (SC) procedure was used with VAS data alone, rawinsonde data alone, and both VAS and rawinsonde data. Variational techniques were applied in three ways. Each of these techniques was discussed

Buoyancy-driven flow and fluid-structure interaction with moving boundaries

We deploy the residual-based variational multi-scale (VMS) method in the sense of large-eddy simulation (LES) in finite element method to buoyancy-driven flow in enclosures and consider an extensive range of Rayleigh number from laminar ($10^3$) to turbulent ($10^{10}$) in a 2D benchmark Rayleigh--B\\u27enard problem. 3D simulations for a laminar and a turbulent case are performed and comparisons including mean profiles as well as fluctuation profiles with other numerical and experimental results are successfully carried out. A weakly imposed boundary conditions method is employed for both velocity and temperature, and it produces reasonable results with a much coarser mesh compared with the traditional imposition of boundary conditions. This suggests that the VMS framework with the weak imposition of boundary conditions is a computationally efficient approach to model buoyancy-driven flows in complex indoor environments. In addition to the flow fields, we deploy the immersogeometric analysis (IMGA) method in the sense of the immersed boundary method (IBM) for objects moving in fluids onto an unstructured framework. The finite element formulation is stabilized by the VMS method in an unstructured background mesh. Weak imposition of boundary conditions is used to impose no-slip boundary condition on the immersed boundary. Adaptively refined quadrature rules are used to better capture the geometry of the immersed boundary and accurately integrate the background elements that intersect the immersed boundary. Treatment for the freshly-cleared nodes is considered. We assess the accuracy of the moving IMGA framework by analyzing object motion in a variety of flow structures, including freely dropping cylinder/sphere in viscous fluids and particle focusing in (un)obstructed channels. We show the quantities of interests are in good agreements with other analytical, numerical and experimental solutions. Advantages of this moving IMGA framework in computational cost and efficiency are indicated by the comparison with the body-fitted method using a commercial computational fluid dynamic (CFD) software. The framework of moving IMGA is capable to be deployed in applications of particle control and manipulation in microfluidic channels. The moving IMGA on the unstructured framework is further deployed to a scalable, adaptively refined, octree-based finite element approach for a better computational performance to track object motion. This enables using a parallel, hierarchically refined octree mesh as the background mesh, with a variationally consistent IMGA formulation on this background mesh. We integrate the unstructured framework of moving IMGA to the octree-based framework. We show good scaling results of the coupled framework on Stampede2, TACC. This illustrates the potential of the moving IMGA on the coupled framework to efficiently track complex particles in flows

A variational framework for mathematically nonsmooth problems in solid and structure mechanics

This dissertation presents a new paradigm for addressing multi-physics problems with interfaces in the field of Additive Manufacturing and the modeling of fibrous composite materials. The unique process of adding the material layer by layer in the AM techniques raises the issue about the stability of the interfaces between the layers and along the boundaries of multi-constituent materials. A stabilized interface formulation is developed to model debonding in monotonic loading, fatigue effects in cyclic loading, and thermal effects at interfaces which severely impact the functional life of those materials and structures. The formulation is based on embedding Discontinuous Galkerin (DG) ideas in a Continuous Galerkin (CG) framework. Starting from a mixed method incorporating the Lagrange multiplier along the interface, a pure displacement formulation is derived using the Variational Multiscale Method (VMS). From a mathematical and computational perspective, the key factor influencing the accuracy and robustness of the interface formulation is the design of the numerical flux and the penalty or stability terms. Analytical expressions that are free from user-defined parameters are naturally derived for the numerical flux and stability tensor which are functions of the evolving geometric and material nonlinearity. The proposed framework is extended for debonding at finite strains across general bimaterial interfaces. An interfacial gap function is introduced that evolves subject to constraints imposed by opening and/or sliding interfaces. An internal variable formalism is derived together with the notion of irreversibility of damage results in a set of evolution equations for the gap function that seamlessly tracks interface debonding by treating damage and friction in a unified way. Tension debonding, compression damage, and frictional sliding are accommodated, and return mapping algorithms in the presence of evolving strong discontinuities are developed. This derivation variationally embeds the interfacial kinematic models that are crucial to capturing the physical and mathematical properties involving large strains and damage. The framework is extended for monolithic coupling of thermomechanical fields in the class of problems that have embedded weak and strong discontinuities in the mechanical and thermal fields. Since the derived expressions are a function of the mechanical and thermal fields, the resulting stabilized formulation contains numerical flux and stability tensors that provide an avenue to variationally embed interfacial kinetic and kinematic models for more robust representation of interfacial physics. Representative numerical tests involving large strains and rotations, damage phenomena, and thermal effects are performed to confirm the robustness and accuracy of the method. Comparison of the results with both experimental and numerical results from literature are presented.Ope

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings

Numerical Methods in Shape Spaces and Optimal Branching Patterns

The contribution of this thesis is twofold. The main part deals with numerical methods in the context of shape space analysis, where the shape space at hand is considered as a Riemannian manifold. In detail, we apply and extend the time-discrete geodesic calculus (established by Rumpf and Wirth [WBRS11, RW15]) to the space of discrete shells, i.e. triangular meshes with fixed connectivity. The essential building block is a variational time-discretization of geodesic curves, which is based on a local approximation of the squared Riemannian distance on the manifold. On physical shape spaces this approximation can be derived e.g. from a dissimilarity measure. The dissimilarity measure between two shell surfaces can naturally be defined as an elastic deformation energy capturing both membrane and bending distortions. Combined with a non-conforming discretization of a physically sound thin shell model the time-discrete geodesic calculus applied to the space of discrete shells is shown to be suitable to solve important problems in computer graphics and animation. To extend the existing calculus, we introduce a generalized spline functional based on the covariant derivative along a curve in shape space whose minimizers can be considered as Riemannian splines. We establish a corresponding time-discrete functional that fits perfectly into the framework of Rumpf and Wirth, and prove this discretization to be consistent. Several numerical simulations reveal that the optimization of the spline functional—subject to appropriate constraints—can be used to solve the multiple interpolation problem in shape space, e.g. to realize keyframe animation. Based on the spline functional, we further develop a simple regression model which generalizes linear regression to nonlinear shape spaces. Numerical examples based on real data from anatomy and botany show the capability of the model. Finally, we apply the statistical analysis of elastic shape spaces presented by Rumpf and Wirth [RW09, RW11] to the space of discrete shells. To this end, we compute a Fréchet mean within a class of shapes bearing highly nonlinear variations and perform a principal component analysis with respect to the metric induced by the Hessian of an elastic shell energy. The last part of this thesis deals with the optimization of microstructures arising e.g. at austenite-martensite interfaces in shape memory alloys. For a corresponding scalar problem, Kohn and Müller [KM92, KM94] proved existence of a minimizer and provided a lower and an upper bound for the optimal energy. To establish the upper bound, they studied a particular branching pattern generated by mixing two different martensite phases. We perform a finite element simulation based on subdivision surfaces that suggests a topologically different class of branching patterns to represent an optimal microstructure. Based on these observations we derive a novel, low dimensional family of patterns and show—numerically and analytically—that our new branching pattern results in a significantly better upper energy bound

Observations of aerosol particles and deep convective updrafts and the modeling of their interactions

2020 Spring.Includes bibliographical references.Within cloud updrafts, cloud droplets form on aerosol particles that serve as cloud condensation nuclei (CCN). Varying the concentrations of CCN alters the concentrations of cloud droplets, which in turn modifies subsequent microphysical processes within clouds. In this dissertation, both observational and modeling studies are presented that reduce the uncertainties associated with these aerosol-induced feedback processes in deep convective clouds. In the first study, five years of observations of aerosol particle size distributions from central Oklahoma are compared, and useful metrics are provided for implementing aerosol size distributions into models. Using these unique, long-term observations, power spectra analyses are also completed to determine the most relevant cycles (from hours to weeks) for different aerosol particle sizes. Diurnal cycles produce the strongest signals in every season, most consistently in the accumulation mode and the smallest (diameters < 30 nm) particles. The latter result suggests that these smallest particles may play a more important role in the CCN budget than previously thought. Ultimately, in understanding which, when and why different aerosol particles are present in the atmosphere, we can better assess the impacts that they have on clouds. The types and number of aerosol particles that can serve as CCN depend on the amount of supersaturation, and thus the magnitude of the cloud updraft vertical velocities. However, in situ updraft observations in deep convective clouds are scarce, and other vertical velocity estimates often have uncertainties that are difficult to characterize. In the next study, novel, in situ observations of deep convective updraft vertical velocities from targeted radiosonde launches during the CSU Convective Cloud Outflows and Updrafts Experiment (C3LOUD-Ex) are presented. Vertical velocities of over 50 m s-1 are estimated from radiosonde observations taken in Colorado. Radar data are used to contextualize the radiosonde measurements and to provide an independent estimate of the updraft magnitudes for comparison. These observations are valuable in that they: 1) contribute novel estimates of the vertical velocities within deep convective clouds, 2) demonstrate that in situ observations of vertical velocities complement estimates from other platforms and 3) will allow for better assessments of the supersaturation magnitudes, and thus the amount of CCN that are present within deep convective clouds. While the first two studies focus on observing aerosol particles and updrafts separately, the third study within this dissertation presents simulations of their interactions from an international model intercomparison project. Seven models from different institutions simulated the same case study of isolated deep convective clouds with both high and low CCN concentrations. The range of the responses in updrafts to varying CCN concentrations are calculated for this model suite. Despite the various physical parameterizations that these models utilize, all the models simulate stronger updrafts in the High-CCN simulations from near cloud base through ~8 km AGL, with diverging results above this altitude. The vertical velocity tendency equation is analyzed to explain which processes are causing the consistent and inconsistent updraft responses to varying CCN concentrations amongst the models. The three studies in this dissertation each reduce the uncertainties related to aerosol effects on deep convective cloud updrafts. This work also assisted in motivating the DOE Tracking Aerosol Convection Interactions Experiment (TRACER), which will further connect observational and modeling research to reduce the uncertainties in aerosol-cloud interactions

CYBER 200 Applications Seminar

Applications suited for the CYBER 200 digital computer are discussed. Various areas of application including meteorology, algorithms, fluid dynamics, monte carlo methods, petroleum, electronic circuit simulation, biochemistry, lattice gauge theory, economics and ray tracing are discussed

Metal droplet entrainment by solid particles in slags : a combined phase field-experimental approach

This doctoral work investigated metal droplet entrainment by solid particles in slags with a combination of two experimental set-ups and two phase field models. The binary model with limited complexity already clarified our view of the interaction between metal droplets and nonreacting solid particles to a great extent. For example, the fact that the movement of one phase with respect to the others influenced the apparent wetting regime is very interesting for the interpretation of experimentally obtained results. Moreover, the two different types of experiments confirmed that a chemical reaction might lay at the origin of the attachment, but that it requires nucleation sites in the form of metal droplets before it takes place. However, the first phase field model assumed nonreactive solid particles. Thus, a model concerning the growth of the solid phase in a realistic quaternary oxide system was also considered. Future work needs to consider the interaction of reacting metal droplets with reacting solid particles in a realistic liquid slag

Data analysis and data assimilation of Arctic Ocean observations

Thesis (Ph.D.) University of Alaska Fairbanks, 2019Arctic-region observations are sparse and represent only a small portion of the physical state of nature. It is therefore essential to maximize the information content of observations and bservation-conditioned analyses whenever possible, including the quantification of their accuracy. The four largely disparate works presented here emphasize observation analysis and assimilation in the context of the Arctic Ocean (AO). These studies focus on the relationship between observational data/products, numerical models based on physical processes, and the use of such data to constrain and inform those products/models to di_erent ends. The first part comprises Chapters 1 and 2 which revolve around oceanographic observations collected during the International Polar Year (IPY) program of 2007-2009. Chapter 1 validates pan- Arctic satellite-based sea surface temperature and salinity products against these data to establish important estimates of product reliability in terms of bias and bias-adjusted standard errors. It establishes practical regional reliability for these products which are often used in modeling and climatological applications, and provides some guidance for improving them. Chapter 2 constructs a gridded full-depth snapshot of the AO during the IPY to visually outline recent, previouslydocumented AO watermass distribution changes by comparing it to a historical climatology of the latter 20th century derived from private Russian data. It provides an expository review of literature documenting major AO climate changes and augments them with additional changes in freshwater distribution and sea surface height in the Chukchi and Bering Seas. The last two chapters present work focused on the application of data assimilation (DA) methodologies, and constitute the second part of this thesis focused on the synthesis of numerical modeling and observational data. Chapter 3 presents a novel approach to sea ice model trajectory optimization whereby spatially-variable sea ice rheology parameter distributions provide the additional model flexibility needed to assimilate observable components of the sea ice state. The study employs a toy 1D model to demonstrate the practical benefits of the approach and serves as a proof-of-concept to justify the considerable effort needed to extend the approach to 2D. Chapter 4 combines an ice-free model of the Chukchi Sea with a modified ensemble filter to develop a DA system which would be suitable for operational forecasting and monitoring the region in support of oil spill mitigation. The method improves the assimilation of non-Gaussian asynchronous surface current observations beyond the traditional approach.Chapter 1: Sea-surface temperature and salinity product comparison against external in situ data in the Arctic Ocean -- Chapter 2: Changes in Arctic Ocean climate evinced through analysis of IPY 2007-2008 oceanographic observations -- Chapter 3: Toward optimization of rheology in sea ice models through data assimilation -- Chapter 4: Ensemble-transform filtering of HFR & ADCP velocities in the Chukchi Sea -- General conclusion