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At least 667 records · Page 37

Jupiter's Atmospheric Temperatures: From Voyager IRIS to Cassini CIRS

Retrievals run on Cassini Composite Infrared Spectrometer data obtained during the distant Jupiter flyby have been used to generate global temperature maps of the planet in the troposphere and stratosphere. Similar retrievals were performed on Voyager 1 IRIS data and have provided the first detailed IRIS map of the stratosphere. In both data sets, high latitude troposphere temperatures are presented for the first time, and the meridional gradients indicate the presence of circumpolar jets. Thermal winds were calculated for each data set and show strong vertical shears in the zonal winds at low latitudes. The temperatures retrieved from the two spacecraft were also compared with yearly ground-based data obtained over the intervening two decades. Tropospheric temperatures reveal gradual changes at low latitudes, with little obvious seasonal or short-term variation (Orton et al. 1994). Stratospheric temperatures show much more complicated behavior over short timescales, consistent with quasi-quadrennial oscillations at low latitudes, as suggested in prior analyses of shorter intervals of ground- based data (Orton et al. 1991, Friedson 1999). A scaling analysis indicates that meridional motions, mechanically forced by wave or eddy convergence, play an important role in modulating the temperatures and winds in the upper troposphere and stratosphere on seasonal and shorter time scales. At latitudes away from the equator, the mechanical forcing can be derived simply from a temporal record of temperature and its vertical derivative. Ground-based observations with improved vertical resolution and/or long-term monitoring from spacecraft are required for this purpose.

Simon-Miller, Amy A.↗

Computational Analysis of Shock Layer Emission Measurements in an Arc-Jet Facility

This paper reports computational analysis of radiation emission experiments in a high enthalpy arc-jet wind tunnel at NASA Ames Research Center. Recently, as part of ongoing arc-jet characterization work, spectroscopic radiation emission experiments have been conducted at the 20 MW NASA Ames arc-jet facility. The emission measurements were obtained from the arc-jet freestream and from a shock layer formed in front of flatfaced models. Analysis of these data is expected to provide valuable information about the thermodynamic state of the gas in the arc-jet freestream and in the shock layer as well as thermochemical equilibration processes behind the shock in arc-jet flows. Knowledge of the thermodynamic state of the gas in arc-jet test flows and especially within the shock layer is essential to interpret the heat transfer measurements such as in surface catalysis experiments. The present work is a continuation of previous work and focuses on analysis of the emission data obtained at relatively low-pressure conditions for which the arc-jet shock layer is expected to be in thermal and chemical nonequilibrium. Building blocks of the present computational analysis are: (1) simulation of nonequilibrium expanding flow in the converging-diverging conical nozzle and supersonic jet; (2) simulation of nonequilibrium shock layer formed in front of the flat-faced cylinder model; and (3) prediction of line-of-sight radiation from the computed flowfield. For computations of the nonequilibrium flow in the conical nozzle and shock layer, multi-temperature nonequilibrium codes with the axisymmetric formulation are used. For computations of line-of-sight radiation. a nonequilibrium radiation code (NEQAIR) is used to predict emission spectra from the computed flowfield. Computed line-of-sight averaged flow properties such as vibrational and rotational temperatures, species number densities within the shock layer will be compared with those deduced from the experimental spectra. Detailed comparisons of computational and experimental spectra will also be presented.

Gokcen, Tahir↗

Extended Forward Sensitivity Analysis for Uncertainty Quantification

This paper presents the extended forward sensitivity analysis as a method to help uncertainty qualification. By including time step and potentially spatial step as special sensitivity parameters, the forward sensitivity method is extended as one method to quantify numerical errors. Note that by integrating local truncation errors over the whole system through the forward sensitivity analysis process, the generated time step and spatial step sensitivity information reflect global numerical errors. The discretization errors can be systematically compared against uncertainties due to other physical parameters. This extension makes the forward sensitivity method a much more powerful tool to help uncertainty qualification. By knowing the relative sensitivity of time and space steps with other interested physical parameters, the simulation is allowed to run at optimized time and space steps without affecting the confidence of the physical parameter sensitivity results. The time and space steps forward sensitivity analysis method can also replace the traditional time step and grid convergence study with much less computational cost. Two well-defined benchmark problems with manufactured solutions are utilized to demonstrate the method.

99 GENERAL AND MISCELLANEOUS↗

Design and execution of a verification, validation, and uncertainty quantification plan for a numerical model of left ventricular flow after LVAD implantation

Left ventricular assist devices (LVADs) are implantable pumps that act as a life support therapy for patients with severe heart failure. Despite improving the survival rate, LVAD therapy can carry major complications. Particularly, the flow distortion introduced by the LVAD in the left ventricle (LV) may induce thrombus formation. While previous works have used numerical models to study the impact of multiple variables in the intra-LV stagnation regions, a comprehensive validation analysis has never been executed. The main goal of this work is to present a model of the LV-LVAD system and to design and follow a verification, validation and uncertainty quantification (VVUQ) plan based on the ASME V&V40 and V&V20 standards to ensure credible predictions. The experiment used to validate the simulation is the SDSU cardiac simulator, a bench mock-up of the cardiovascular system that allows mimicking multiple operation conditions for the heart-LVAD system. The numerical model is based on Alya, the BSC’s in-house platform for numerical modelling. Alya solves the Navier-Stokes equation with an Arbitrary Lagrangian-Eulerian (ALE) formulation in a deformable ventricle and includes pressure-driven valves, a 0D Windkessel model for the arterial output and a LVAD boundary condition modeled through a dynamic pressure-flow performance curve. The designed VVUQ plan involves: (a) a risk analysis and the associated credibility goals; (b) a verification stage to ensure correctness in the numerical solution procedure; (c) a sensitivity analysis to quantify the impact of the inputs on the four quantities of interest (QoIs) (average aortic root flow $Q^{avg}_{Ao}$, maximum aortic root flow $Q^{max}_{Ao}$, average LVAD flow $Q^{avg}_{VAD}$, and maximum LVAD flow $Q^{max}_{VAD}$; (d) an uncertainty quantification using six validation experiments that include extreme operating conditions. Numerical code verification tests ensured correctness of the solution procedure and numerical calculation verification showed a grid convergence index (GCI)95% <3.3%. The total Sobol indices obtained during the sensitivity analysis demonstrated that the ejection fraction, the heart rate, and the pump performance curve coefficients are the most impactful inputs for the analysed QoIs. The Minkowski norm is used as validation metric for the uncertainty quantification. It shows that the midpoint cases have more accurate results when compared to the extreme cases. The total computational cost of the simulations was above 100 [core-years] executed in around three weeks time span in Marenostrum IV supercomputer. This work details a novel numerical model for the LV-LVAD system, that is supported by the design and execution of a VVUQ plan created following recognised international standards. We present a methodology demonstrating that stringent VVUQ according to ASME standards is feasible but computationally expensive.

59 BASIC BIOLOGICAL SCIENCES↗

Verifying the interactive convergence clock synchronization algorithm using the Boyer-Moore theorem prover

The application of formal methods to the analysis of computing systems promises to provide higher and higher levels of assurance as the sophistication of our tools and techniques increases. Improvements in tools and techniques come about as we pit the current state of the art against new and challenging problems. A promising area for the application of formal methods is in real-time and distributed computing. Some of the algorithms in this area are both subtle and important. In response to this challenge and as part of an ongoing attempt to verify an implementation of the Interactive Convergence Clock Synchronization Algorithm (ICCSA), we decided to undertake a proof of the correctness of the algorithm using the Boyer-Moore theorem prover. This paper describes our approach to proving the ICCSA using the Boyer-Moore prover.

Young, William D.↗

Interpolation and extrapolation of creep rupture data by the minimum commitment method. III - Analysis of multiheats

An outline is presented of approaches for treating multiheats on the basis of the focal point convergence method. The method has been employed in the case of two highly characterized multiheats, including a 304 stainless steel studied in Japan and a low alloy carbon steel studied in England. The method makes use of the same functional form for all materials. Only the constants are varied for each multiheat. Completely computerized procedures are employed for the determination of the constants. Once the basic analysis has been performed, the representation of various members in the same system is achieved by adding linear expressions of log stress, changing only two constants in the equations to represent a selected heat.

Manson, S. S.↗

Dark Energy Survey Year 3 results: Cosmology with moments of weak lensing mass maps

We present a cosmological analysis using the second and third moments of the weak lensing mass (convergence) maps from the first three years of data (Y3) data of the Dark Energy Survey. The survey spans an effective area of 4139 square degrees and uses the images of over 100 million galaxies to reconstruct the convergence field. The second moment of the convergence as a function of smoothing scale contains information similar to standard shear 2-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The data is analyzed in the context of the Λ CDM model, varying five cosmological parameters and 19 nuisance parameters modeling astrophysical and measurement systematics. Our modeling of the observables is completely analytical, and has been tested with simulations in our previous methodology study. We obtain a 1.7% measurement of the amplitude of fluctuations parameter S 8 ≡ σ 8 ( Ω m / 0.3 ) 0.5 = 0.784 ± 0.013 . The measurements are shown to be internally consistent across redshift bins, angular scales, and between second and third moments. In particular, the measured third moment is consistent with the expectation of gravitational clustering under the Λ CDM model. The addition of the third moment improves the constraints on S 8 and Ω m by ∼ 15 % and ∼ 25 % compared to an analysis that only uses second moments. We compare our results with Planck constraints from the cosmic microwave background, finding a 2.2 – 2.8 σ tension in the full parameter space, depending on the combination of moments considered. The third moment, independently, is in 2.8 σ tension with Planck, and thus provides a cross-check on the analyses of 2-point correlations.

79 ASTRONOMY AND ASTROPHYSICS↗

Exact and approximate gas dynamics using the tangent gas

For the determination of aerodynamic characteristics such as lift, drag, and moment coefficients, it is crucial to compute the properties of steady flow past an airfoil. This investigation provides a set of flow dependent grid systems and initial flowfield guesses which substantially improve convergence rates when applied to the Euler equations for flows past an airfoil. The basic equations are examined, taking into account nonlinear equations which are difficult to solve. A good approximation to these equations under certain conditions can be obtained by introducing the so-called 'tangent gas approximation' considered by Woods (1961), in which the isentropic relation between rho and p is replaced by a tangent to a curve. Attention is given to the solution procedure, the analysis (direct) problem, and a comparison of the tangent gas solution with the converged Euler solution.

Daripa, P. K.↗

Assessment and improvement of the 2D/1D method stability in DeCART

As part of ongoing work with Consortium for Advanced Simulation of Light Water Reactors (CASL), the 2D/1D code, DeCART, has demonstrated some of the advantages of the 2D/1D method with respect to realistic, full-core analysis, particularly over explicit 3D transport methods, which generally have higher memory and computation requirements. The 2D/1D method performs 2D-radial transport sweeps coupled with ID-axial diffusion calculations to provide a full 3D simulation. DeCART employs the 2D method of characteristics for the radial sweeps and ID one-node nodal diffusion for the axial sweeps, coupling the two methods with transverse leakages to ensure a more consistent representation of the transport equation. It has been observed that refinement of the axial plane thickness leads to instabilities in the calculation scheme. This work assesses the sources of these instabilities and the approaches to improve them, especially with respect to negative scattering cross sections and the tightness of the 2D-radial/ID-axial coupling schemes. Fourier analyses show that the existing iteration scheme is not unconditionally stable, suggesting a tighter coupling scheme is required. For this reason 3D-CMFD has been implemented, among other developments, to ensure more stable calculation. A matrix of test cases has been used to assess the convergence, with the primary parameter being the axial plane thickness, which has been refined down to 1 cm. These cases demonstrate the issues observed and how the modification improve the stability. However, it is apparent that more work is necessary to ensure unconditional stability. (authors)

97 MATHEMATICS AND COMPUTING↗

Improving Solution Accuracy and Convergence for Stochastic Physics Parameterizations with Colored Noise

Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properties. Convergence issues can arise when time integration methods originally developed for deterministic differential equations are applied naively to stochastic problems. In previous studies, it has been demonstrated that a correction term, known in stochastic analysis as the Itô correction, can help improve solution accuracy for various deterministic numerical schemes and ensure convergence to the physically relevant solution without substantial computational overhead. The usual formulation of the Itô correction is valid only when the stochasticity is represented by white noise. In this study, a generalized formulation of the Itô correction is derived for noises of any color. The formulation is applied to a test problem described by an advection–diffusion equation forced with a spectrum of fast processes. We present numerical results for cases with both constant and spatially varying advection velocities to show that, for the same time step sizes, the introduction of the generalized Itô correction helps to substantially reduce time integration error and significantly improve the convergence rate of the numerical solutions when the forcing term in the governing equation is rough (fast varying); alternatively, for the same target accuracy, the generalized Itô correction allows for the use of significantly longer time steps and, hence, helps to reduce the computational cost of the numerical simulation.

54 ENVIRONMENTAL SCIENCES↗

Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering

Here we present an error analysis for the discontinuous Galerkin (DG) method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation with isotropic scattering. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.

97 MATHEMATICS AND COMPUTING↗

Extrapolation methods for vector sequences

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Smith, David A.↗

Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

Bramble, James H.↗

CROSS-CORRELATING THE γ -RAY SKY WITH CATALOGS OF GALAXY CLUSTERS

In this article, we report the detection of a cross-correlation signal between Fermi Large Area Telescope diffuse γ-ray maps and catalogs of clusters. In our analysis, we considered three different catalogs: WHL12, redMaPPer, and PlanckSZ. They all show a positive correlation with different amplitudes, related to the average mass of the objects in each catalog, which also sets the catalog bias. The signal detection is confirmed by the results of a stacking analysis. The cross-correlation signal extends to rather large angular scales, around 1°, that correspond, at the typical redshift of the clusters in these catalogs, to a few to tens of megaparsecs, i.e., the typical scale-length of the large-scale structures in the universe. Most likely this signal is contributed by the cumulative emission from active galactic nuclei (AGNs) associated with the filamentary structures that converge toward the high peaks of the matter density field in which galaxy clusters reside. In addition, our analysis reveals the presence of a second component, more compact in size and compatible with a point-like emission from within individual clusters. At present, we cannot distinguish between the two most likely interpretations for such a signal, i.e., whether it is produced by AGNs inside clusters or if it is a diffuse γ-ray emission from the intracluster medium. Lastly, we argue that this latter, intriguing, hypothesis might be tested by applying this technique to a low-redshift large-mass cluster sample.

79 ASTRONOMY AND ASTROPHYSICS↗

High-order shock-fitted detonation propagation in high explosives

In this paper, a highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich–von Neumann–Döring (ZND) detonation wave, and Taylor–Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m / s , which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott–Stewart–Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting strategy, in conjunction with a nonlinear optimizer, a new set of reaction rate parameters improves the correlation of the model to experimental results. In conclusion, this new model is tested against two dimensional slabs as a validation test.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Influence of Primary Gage Sensitivities on the Convergence of Balance Load Iterations

The connection between the convergence of wind tunnel balance load iterations and the existence of the primary gage sensitivities of a balance is discussed. First, basic elements of two load iteration equations that the iterative method uses in combination with results of a calibration data analysis for the prediction of balance loads are reviewed. Then, the connection between the primary gage sensitivities, the load format, the gage output format, and the convergence characteristics of the load iteration equation choices is investigated. A new criterion is also introduced that may be used to objectively determine if the primary gage sensitivity of a balance gage exists. Then, it is shown that both load iteration equations will converge as long as a suitable regression model is used for the analysis of the balance calibration data, the combined influence of non linear terms of the regression model is very small, and the primary gage sensitivities of all balance gages exist. The last requirement is fulfilled, e.g., if force balance calibration data is analyzed in force balance format. Finally, it is demonstrated that only one of the two load iteration equation choices, i.e., the iteration equation used by the primary load iteration method, converges if one or more primary gage sensitivities are missing. This situation may occur, e.g., if force balance calibration data is analyzed in direct read format using the original gage outputs. Data from the calibration of a six component force balance is used to illustrate the connection between the convergence of the load iteration equation choices and the existence of the primary gage sensitivities.

Ulbrich, Norbert Manfred↗

Testing dark matter halo properties using self-similarity

ABSTRACT We use self-similarity in N-body simulations of scale-free models to test for resolution dependence in the mass function and two-point correlation functions of dark matter haloes. We use 10243 particle simulations performed with abacus , and compare results obtained with two halo finders: friends-of-friends (fof ), and rockstar . The fof mass functions show a systematic deviation from self-similarity which is explained by resolution dependence of the fof mass assignment previously reported in the literature. Weak evidence for convergence is observed only starting from haloes of several thousand particles, and mass functions are overestimated by at least as much as $20-25{{\ \rm per\ cent}}$ for haloes of 50 particles. The mass function of the default rockstar halo catalogue (with bound virial spherical overdensity mass), on the other hand, shows good convergence of the order of 50 to 100 particles per halo, with no detectable evidence at the few percent level of any systematic dependence for larger particle number. Tests show that the mass unbinding procedure in rockstar is the key factor in obtaining this much improved resolution. Applying the same analysis to the halo–halo two point correlation function, we find again strong evidence for convergence only for rockstar haloes, at separations sufficiently large so that haloes do not overlap. At these separations, we can exclude dependence on resolution at the $5-10{{\ \rm per\ cent}}$ level once haloes have of the order of 50 to 100 particles. At smaller separations results are not converged even at significantly larger particle number, and bigger simulations would be required to establish the resolution required for convergence.

79 ASTRONOMY AND ASTROPHYSICS↗