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At least 667 records · Page 37

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Cowsar, Lawrence C.↗

Method of Real-Time Principal-Component Analysis

Dominant-element-based gradient descent and dynamic initial learning rate (DOGEDYN) is a method of sequential principal-component analysis (PCA) that is well suited for such applications as data compression and extraction of features from sets of data. In comparison with a prior method of gradient-descent-based sequential PCA, this method offers a greater rate of learning convergence. Like the prior method, DOGEDYN can be implemented in software. However, the main advantage of DOGEDYN over the prior method lies in the facts that it requires less computation and can be implemented in simpler hardware. It should be possible to implement DOGEDYN in compact, low-power, very-large-scale integrated (VLSI) circuitry that could process data in real time.

Duong, Tuan↗

Long term performance of vacuum insulation panels integrated into building components

Vacuum insulation panels provide much greater resistance to heat transfer than conventional insulation materials, making them ideal for building applications, especially where space is a constraint. Of particular interest is energy retrofits where high insulation values are required with very little or no modifications to existing building envelope elements such as fenestrations and service penetrations. To facilitate the use of vacuum insulation panels (VIPs) in residential and commercial construction, this study investigates the performance of VIPs integrated into polyisocyanurate foam board and vinyl siding after several years of service. Vacuum insulation panels integrated with polyisocyanurate boards were studied in mixed humid and cold climates. The integration of VIPs with vinyl siding was investigated in a mixed humid climate. Periods of service were between two and five years. In all cases, the integrated building components outperformed conventional materials by almost 40 percent during heating and cooling periods. However, the percent reduction in heat gains and losses of the integrated building components decreased with time at a rate between approximately 4% and 10% per year during the service period. In some cases, the rate seems to converge to a steady -state value. Measurements are ongoing to determine if a steady-state value is attained or the panel's insulation value continues to decrease with time. This study is critical in addressing the service life and durability of the building envelope with VIP integrated building components. The effect of these changes will be reviewed in the context of an exterior retrofit.

Aldykiewicz Jr, Antonio↗

Influences of Local Sea-Surface Temperatures and Large-scale Dynamics on Monthly Precipitation Inferred from Two 10-year GCM-Simulations

Two parallel sets of 10-year long: January 1, 1982 to December 31, 1991, simulations were made with the finite volume General Circulation Model (fvGCM) in which the model integrations were forced with prescribed sea-surface temperature fields (SSTs) available as two separate SST-datasets. One dataset contained naturally varying monthly SSTs for the chosen period, and the oth& had the 12-monthly mean SSTs for the same period. Plots of evaporation, precipitation, and atmosphere-column moisture convergence, binned by l C SST intervals show that except for the tropics, the precipitation is more strongly constrained by large-scale dynamics as opposed to local SST. Binning data by SST naturally provided an ensemble average of data contributed from disparate locations with same SST; such averages could be expected to mitigate all location related influences. However, the plots revealed: i) evaporation, vertical velocity, and precipitation are very robust and remarkably similar for each of the two simulations and even for the data from 1987-ENSO-year simulation; ii) while the evaporation increased monotonically with SST up to about 27 C, the precipitation did not; iii) precipitation correlated much better with the column vertical velocity as opposed to SST suggesting that the influence of dynamical circulation including non-local SSTs is stronger than local-SSTs. The precipitation fields were doubly binned with respect to SST and boundary-layer mass and/or moisture convergence. The analysis discerned the rate of change of precipitation with local SST as a sum of partial derivative of precipitation with local SST plus partial derivative of precipitation with boundary layer moisture convergence multiplied by the rate of change of boundary-layer moisture convergence with SST (see Eqn. 3 of Section 4.5). This analysis is mathematically rigorous as well as provides a quantitative measure of the influence of local SST on the local precipitation. The results were recast to examine the dependence of local rainfall on local SSTs; it was discernible only in the tropics. Our methodology can be used for computing relationship between any forcing function and its effect(s) on a chosen field.

Sud, Y. C.↗

Simulating combustion of a seven-component surrogate for a gasoline/ethanol blend including soot formation and comparison with experiments

Combustion of a seven-component surrogate for a research grade 87 octane gasoline mixed with 10% ethanol is investigated experimentally and numerically from the perspective of an isolated droplet burning under conditions that promote one-dimensional gas transport. The numerical analysis included a kinetic mechanism comprised of 398 species and 24,814 reactions and a soot model that accounted for nucleation, surface growth, coalescence/aggregation of soot particles, and luminous flame radiation. Measurements of droplet and flame diameters were made for an initial droplet diameter (D o ) of approximately 0.63 mm. The simulations agreed well with the measurements including the location of the soot shell. Preferential vaporization was revealed by simulations of the liquid concentrations in the droplet. Predicted peak soot volume fractions coincided with temperatures between 1300 K and 1400 K as a soot inception temperature. Simulations were also carried out for D o between 0.25 mm and 5 mm to explore the effect of radiation and D o on burning. Below 0.25 mm radiation was negligible and burning rates and flame temperatures converged to a single value. Increasing D o up to 1.8 mm lowered the burning rate with luminous radiation having a strong effect. When radiation was entirely removed from the model the burning rate was nearly constant. Above D o = 2 mm droplets extinguished almost immediately after ignition. The flame temperature decreased with increasing D o while it increased when radiation was omitted. As a result, the simulations show that soot precursors including polyaromatic hydrocarbons were concentrated around the soot shell.

42 ENGINEERING↗

Convergence Criteria for Multiphysics Simulations

The behavior of engineered systems is often influenced by multiple physical phenomena, such as mechanical deformation, heat transfer, and chemical species transport and reactions. There are often strong interactions between these phenomena, and there is increasing interest in applying coupled-physics models to improve understanding of physical behavior under complex environmental conditions. Multiple simulation frameworks that facilitate coupled-physics simulations are in widespread use, and these employ a variety of techniques to account for interactions between those physics. Many frameworks solve the physics models independently and transfer results between them. Alternatively, a single monolithic system of equations for every physics model can be formed and solved. Each of these approaches has its benefits and drawbacks, and the optimal approach varies depending on the nature of the problem. The open-source MOOSE framework was developed targeting solution of large-scale multiphysics problems. Although it provides options for all these coupling approaches, its standard approach for multiphysics solutions is to form and solve a single monolithic system of equations containing the unknowns for all physics models. MOOSE provides a streamlined approach for users to define the solution variables, the terms in the partial differential equations pertaining to each variable, and interactions between solution variables. One aspect of the monolithic solution approach that can be problematic, however, is defining appropriate convergence criteria for the nonlinear system. A standard approach is to determine convergence is to simply take a norm of the residual vector corresponding to the full vector of unknowns. However, if the residual vector contains variables for multiple physics models, the magnitudes of those variables can differ significantly, and the variables can converge at significantly different rates from each other. It is important to ensure that the variables for each of the physics are converged, and also ensure that the convergence criteria are not excessively stringent in cases when there is little change in the solution. This talk presents representative multiphysics problems to highlight these issues, and shows strategies for convergence criteria in MOOSE that are robust for multiphysics models under a variety of conditions.

97 - MATHEMATICS AND COMPUTING↗

A new design approach to achieve a minimum impulse limit cycle in the presence of significant measurement uncertainties

A new design was developed for the Space Shuttle Transition Phase Digital Autopilot to reduce the impact of large measurement uncertainties in the rate signal during attitude control. The signal source, which was dictated by early computer constraints, is characterized by large quantization, noise, bias, and transport lag which produce a measurement uncertainty larger than the minimum impulse rate change. To ensure convergence to a minimum impulse limit cycle, the design employed bias and transport lag compensation and a switching logic with hysteresis, rate deadzone, and 'walking' switching line. The design background, the rate measurement uncertainties, and the design solution are documented.

Martin, M. W.↗

Linear convergence of accelerated conditional gradient algorithms in spaces of measures

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding coefficients. Under general assumptions, a sub-linear [see formula in PDF] rate in the objective functional is obtained, which is sharp in most cases. To improve efficiency, one can fully resolve the finite-dimensional subproblems occurring in each iteration of the method. We provide an analysis for the resulting procedure: under a structural assumption on the optimal solution, a linear [see formula in PDF] convergence rate is obtained locally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Asymptotic Spreading Rate of Initially Compressible Jets: Experiment and Analysis

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing "jet Mach number" M(sub J). Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the "potential core length" of the jet occurring with increasing M(sub J), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Zaman, K. B. M. Q.↗

Asymptotic Spreading Rate of Initially Compressible Jets-Experiment and Analysis

Experimental results for the spreading and centerline velocity decay rates for round, compressible jets, from a convergent and a convergent-divergent nozzle, are presented. The spreading rate is determined from the variation of streamwise mass flux obtained from Pitot probe surveys. Results for the far asymptotic region show that both spreading and centerline velocity decay rates, when nondimensionalized by parameters at the nozzle exit, decrease with increasing "jet Mach number" M(sub j). Dimensional analysis with the assumption of momentum conservation, together with compressible flow calculations for the conditions at the nozzle exit, predict this Mach number dependence well. The analysis also demonstrates that an increase in the "potential core length" of the jet occurring with increasing M(sub j), a commonly observed trend, is largely accounted for simply by the variations in the density and static pressure at the nozzle exit. The effect of decreasing mixing efficiency with increasing compressibility is inferred to contribute only partially to the latter trend.

Zaman, K. B. M. Q.↗

Non-LTE radiative transfer with lambda-acceleration - Convergence properties using exact full and diagonal lambda-operators

We investigate the convergence properties of Lambda-acceleration methods for non-LTE radiative transfer problems in planar and spherical geometry. Matrix elements of the 'exact' A-operator are used to accelerate convergence to a solution in which both the radiative transfer and atomic rate equations are simultaneously satisfied. Convergence properties of two-level and multilevel atomic systems are investigated for methods using: (1) the complete Lambda-operator, and (2) the diagonal of the Lambda-operator. We find that the convergence properties for the method utilizing the complete Lambda-operator are significantly better than those of the diagonal Lambda-operator method, often reducing the number of iterations needed for convergence by a factor of between two and seven. However, the overall computational time required for large scale calculations - that is, those with many atomic levels and spatial zones - is typically a factor of a few larger for the complete Lambda-operator method, suggesting that the approach should be best applied to problems in which convergence is especially difficult.

Macfarlane, J. J.↗

High-throughput quantification of quasistatic, dynamic and spall strength of materials across 10 orders of strain rates

Abstract The response of metals and their microstructures under extreme dynamic conditions can be markedly different from that under quasistatic conditions. Traditionally, high strain rates and shock stresses are achieved using cumbersome and expensive methods such as the Kolsky bar or large spall experiments. These methods are low throughput and do not facilitate high-fidelity microstructure–property linkages. In this work, we combine two powerful small-scale testing methods, custom nanoindentation, and laser-driven microflyer (LDMF) shock, to measure the dynamic and spall strength of metals. The nanoindentation system is configured to test samples from quasistatic to dynamic strain-rate regimes. The LDMF shock system can test samples through impact loading, triggering spall failure. The model material used for testing is magnesium alloys, which are lightweight, possess high-specific strengths, and have historically been challenging to design and strengthen due to their mechanical anisotropy. We adopt two distinct microstructures, solutionized (no precipitates) and peak-aged (with precipitates) to demonstrate interesting upticks in strain-rate sensitivity and evolution of dynamic strength. At high shock-loading rates, we unravel an interesting paradigm where the spall strength vs. strain rate of these materials converges, but the failure mechanisms are markedly different. Peak aging, considered to be a standard method to strengthen metallic alloys, causes catastrophic failure, faring much worse than solutionized alloys. Our high-throughput testing framework not only quantifies strength but also teases out unexplored failure mechanisms at extreme strain rates, providing valuable insights for the rapid design and improvement of materials for extreme environments.

Eswarappa Prameela, Suhas (ORCID:0000000334530184)↗

Ab initio electron-two-phonon scattering in GaAs from next-to-leading order perturbation theory

Electron-phonon (e–ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e–ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-range e–ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles.

36 MATERIALS SCIENCE↗

Monte Carlo analysis of uncertainty propagation in a stratospheric model. 2: Uncertainties due to reaction rates

A concise stratospheric model was used in a Monte-Carlo analysis of the propagation of reaction rate uncertainties through the calculation of an ozone perturbation due to the addition of chlorine. Two thousand Monte-Carlo cases were run with 55 reaction rates being varied. Excellent convergence was obtained in the output distributions because the model is sensitive to the uncertainties in only about 10 reactions. For a 1 ppby chlorine perturbation added to a 1.5 ppby chlorine background, the resultant 1 sigma uncertainty on the ozone perturbation is a factor of 1.69 on the high side and 1.80 on the low side. The corresponding 2 sigma factors are 2.86 and 3.23. Results are also given for the uncertainties, due to reaction rates, in the ambient concentrations of stratospheric species.

Stolarski, R. S.↗

Human Rating the Orion Parachute System

Human rating begins with design. Converging on the requirements and identifying the risks as early as possible in the design process is essential. Understanding of the interaction between the recovery system and the spacecraft will in large part dictate the achievable reliability of the final design. Component and complete system full-scale flight testing is critical to assure a realistic evaluation of the performance and reliability of the parachute system. However, because testing is so often difficult and expensive, comprehensive analysis of test results and correlation to accurate modeling completes the human rating process. The National Aeronautics and Space Administration (NASA) Orion program uses parachutes to stabilize and decelerate the Crew Exploration Vehicle (CEV) spacecraft during subsonic flight in order to deliver a safe water landing. This paper describes the approach that CEV Parachute Assembly System (CPAS) will take to human rate the parachute recovery system for the CEV.

Machin, Ricardo A.↗

A preliminary study of relaxation methods for the inviscid conservative gasdynamics equations using flux splitting

Plus minus flux vector split schemes are combined with the multigrid relaxation method to obtain fast rates of iterative (or steady state) convergence. On model nonlifting biconvex airfoil flow, steady state convergence is obtained using multigrid in 40 iteractions for subsonic cases and in 120 iterations for transonic cases. A 65 x 33 stretched grid is used. However, the multigrid scheme used here (and there are numerous variations) sometimes could not be made to work for transonic cases with a large number of supersonic points. Moreover, the multigrid method is only several times faster than the conventional algorithm which itself could perhaps be accelerated by other means. Nethertheless, with proper adjustment the multigrid method will ultimately lead to very fast rates of iterative convergence.

Steger, J. L.↗

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗