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At least 325 records · Page 18

Recent developments in quasi-Newton methods for structural analysis and synthesis

Unlike the Newton-Raphson method, quasi-Newton methods by virture of the updates and step length control procedures are globally convergent and hence better suited for the solution of nonlinear problems of structural analysis and synthesis. Extension of quasi-Newton algorithms to large scale problems has led to the development of sparse update algorithms and to economical strategies for evaluating sparse Hessians. Ill-conditioning problems have led to the development of self-scaled variable metric and conjugate gradient algorithms, as well as the use of the singular perturbation theory. This paper emphasizes the effectiveness of such quasi-Newton algorithms for nonlinear structural analysis and synthesis.

Kamat, M. P.↗

Implementation and Use of a Convergence Test for Iterative Wind Tunnel Balance Load Predictions

A modified and extended version of a convergence test for wind tunnel strain-gage balance load iterations was implemented. The test uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions if the Iterative Method is applied. Convergence is expected within the use envelope of the balance whenever this upper bound is less than the threshold of one. It is explained in great detail how the convergence test can be applied to the two load iteration equation types that are currently being used in the aerospace testing community. In addition, the application of the test to balances with bi-directional output characteristics is discussed. It is also shown how numerical differentiation can be used in order to obtain partial derivatives that are needed for the calculation of the Lipschitz constant. Finally, machine calibration data of NASA's MC60E six-component force balance is selected to demonstrate both implementation and use of the convergence test.

calibration analysis↗

New free-wake analysis of rotorcraft hover performance using influence coefficients

Free-wake analyses of helicopter rotor wakes in hover using time stepping have been shown to encounter instabilities which preclude convergence to valid free-vortex solutions for rotor-wake geometries. Previous work has demonstrated that these convergence difficulties can be overcome by implementing a new free-wake analysis method based on the use of influence coefficients. The present paper reviews this approach and documents its incorporation into a hover performance analysis called Evaluation of Hover Performance using Influence Coefficients (EHPIC). The technical principles underlying the EHPIC code are described with emphasis on steps taken to develop the single-filament wake models used in previous work into a multifilament wake valid for realistic hover performance predictions. The coupling of the wake model to a lifting surface loads analysis is described, and sample problems are solved that illustrate the robustness of the method. Performance calculations are also undertaken for hover to illustrate the utility of EHPIC in the analysis of rotorcraft performance.

Quackenbush, Todd R.↗

Improving the convergence rate of parabolic ADI methods

The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.

Abarbanel, S. S.↗

Model of Inverter-Based Resources

Blackbox modelling for SC analysis is a possible solution. Accuracy can be acceptable even without having vendor control diagrams. Is an NDA required to share a vendor Blackbox model for SC analysis? Differences in VRT detection and injection logics. Angle rotation is not addressed in control logics of most vendors. Current limitation logic during unbalanced faults is not clear. Model IBR as a current source with shunt to improve convergence

IBRs, Model of IBRs, Short Circuit Analysis, Class↗

Self-similarity of k -nearest neighbour distributions in scale-free simulations

ABSTRACT We use the k-nearest neighbour probability distribution function (kNN-PDF; Banerjee & Abel 2021a) to assess convergence in a scale-free N-body simulation. Compared to our previous two-point analysis, the kNN-PDF allows us to quantify our results in the language of haloes and numbers of particles, while also incorporating non-Gaussian information. We find good convergence for 32 particles and greater at densities typical of haloes, while 16 particles and fewer appear unconverged. Halving the softening length extends convergence to higher densities, but not to fewer particles. Our analysis is less sensitive to voids, but we analyse a limited range of underdensities and find evidence for convergence at 16 particles and greater even in sparse voids.

79 ASTRONOMY AND ASTROPHYSICS↗

The Structure and Dynamics of an Observed Moist Front

The structure and dynamics of the moist cold front of 25 and 26 April 1979, the third observing day of the Severe Environmental Storms and Mesoscale experiment (SESAME), are investigated through the use of a three-dimensional mesoscale numerical model. This work is one of the first studies in which model results are compared, in a one-to-one manner, with a detailed observational analysis, namely that of Ogura and Portis (1982) as taken from the SESAME observations. In addition, frontogenetical effects, both adiabatic and diabatic, are studied on a vertical cross-section through the front; similarities and differences with the adiabatic analysis of Ogura and Portis are discussed. Many similarities exist between the modeled and analyzed fields, although the analysis tends to have weaker horizontal gradients due to the coarseness of the observational network. Vorticity and convergence near the surface were found to have the same magnitude in both the model solution and the analysis, in contrast to idealized frontogenesis models which predict vorticity to be much larger than convergence.

Orlanski, I.↗

Aerosol Deposition Inside a Spent Fuel Transportation and Storage Canister (Interim Report)

This report documents the progress in preparing the ANSYS/Fluent ® and MELCOR models to perform characterization studies of aerosols dispersal and deposition within a select spent fuel cask system. Steady state thermal-hydraulic cask response is modeled with both codes, at present, while the MELCOR source code is being modified to allow imposed thermal-hydraulic conditions with aerosol physics calculations. This will allow the MELCOR model to assume the thermal-hydraulic calculation from the ANSYS/Fluent ® , while only computing the aerosol physics. Detailed results are presented on the thermal-hydraulic analysis of the MAGNASTOR ® cask for the current ANSYS/Fluent ® model, with convergent conditions observed over two fidelities. While the MELCOR computation computes the steady state conditions, they differ sufficiently from that computed with ANSYS/Fluent ® . The MELCOR analysis include a set of UO 2 sources to investigate system response for interim reporting. The airborne concentrations and evolving distributions are presented. Model development is anticipated to continue as additional components impacting flow conditions or aerosol deposition within the MAGNASTOR ® cask and Westinghouse fuel assemblies are identified.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Convergence properties of modal costs for certain distributed parameter systems

A complete modal cost analysis is presented for the vibration of various kinds of simple continua with different boundary conditions. Explicit formulas for the norm of the response (called the 'cost') are derived for these distributed parameter systems. The convergence theorems developed are useful in the model reduction of the equivalent continuum models of large space structures as well as in the selection of finite-element code for control design.

Hu, A.↗

Helicopter trim analysis by shooting and finite element methods with optimally damped Newton iterations

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Achar, N. S.↗

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

Atkins, H. L.↗

Reliability enhancement of Navier-Stokes codes through convergence enhancement

Reduction of total computing time required by an iterative algorithm for solving Navier-Stokes equations is an important aspect of making the existing and future analysis codes more cost effective. Several attempts have been made to accelerate the convergence of an explicit Runge-Kutta time-stepping algorithm. These acceleration methods are based on local time stepping, implicit residual smoothing, enthalpy damping, and multigrid techniques. Also, an extrapolation procedure based on the power method and the Minimal Residual Method (MRM) were applied to the Jameson's multigrid algorithm. The MRM uses same values of optimal weights for the corrections to every equation in a system and has not been shown to accelerate the scheme without multigriding. Our Distributed Minimal Residual (DMR) method based on our General Nonlinear Minimal Residual (GNLMR) method allows each component of the solution vector in a system of equations to have its own convergence speed. The DMR method was found capable of reducing the computation time by 10-75 percent depending on the test case and grid used. Recently, we have developed and tested a new method termed Sensitivity Based DMR or SBMR method that is easier to implement in different codes and is even more robust and computationally efficient than our DMR method.

Choi, K.-Y.↗

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

ABSTRACT We present a simulated cosmology analysis using the second and third moments of the weak lensing mass (convergence) maps. The second moment, or variances, of the convergence as a function of smoothing scale contains information similar to standard shear two-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The analysis is geared towards the third year (Y3) data from the Dark Energy Survey (DES), but the methodology can be applied to other weak lensing data sets. We present the formalism for obtaining the convergence maps from the measured shear and for obtaining the second and third moments of these maps given partial sky coverage. We estimate the covariance matrix from a large suite of numerical simulations. We test our pipeline through a simulated likelihood analyses varying 5 cosmological parameters and 10 nuisance parameters and identify the scales where systematic or modelling uncertainties are not expected to affect the cosmological analysis. Our simulated likelihood analysis shows that the combination of second and third moments provides a 1.5 per cent constraint on S8 ≡ σ8(Ωm/0.3)0.5 for DES Year 3 data. This is 20 per cent better than an analysis using a simulated DES Y3 shear two-point statistics, owing to the non-Gaussian information captured by the inclusion of higher order statistics. This paper validates our methodology for constraining cosmology with DES Year 3 data, which will be presented in a subsequent paper.

79 ASTRONOMY AND ASTROPHYSICS↗

On the Representativity of Electrode Microstructure Parameters and Their Electrochemical Response for Lithium Ion Batteries

Lithium-ion battery electrochemical models require an accurate description of the electrodes microstructures to be predictive that can be achieved through nanoscale imaging. Such observations are however limited by their field of view (FOV), as they provide only a subset of the whole electrode volume that does not necessarily represent the whole electrode microstructure heterogeneity, and therefore can bias the microstructure analysis. A microstructure scale electrochemical model was used to investigate lithium plating onset, material non-uniform utilization, and in-plane heterogeneities for an NMC-graphite full cell. To evaluate the representativeness, and thus relevance, of these model predictions, a coupled representativity analysis has been performed on the microstructure parameters and, in a novel way, on the full cell electrochemical response. Electrode microstructure parameters representativeness has been first quantified using the representative volume element (RVE) methodology. The RVE major flaw is that ultimately it can only conclude if a FOV contains representative subvolumes of the FOV, but not if the FOV itself is representative of the electrode volume. Analysis can conclude negatively ('FOV is not representative'), but not positively ('FOV is representative'). One major contribution of this work was to quantify the convergence of the RVE size with the FOV, to actually investigate the FOV representativeness and thus partly remedy this intrinsic limitation. The analysis determined that performing a standard RVE calculation, without exploring its FOV convergence, is likely to strongly underestimate the actual RVE size. The new RVE methodology has been automated in the NREL open-source Microstructure Analysis Toolbox (MATBOX) and is available to the battery community. Representativeness of microstructure parameters is however only an intermediate step, as the end-results of an electrochemical model are performances predictions. Indeed, what is the practical consequence of a given deviation for a microstructure parameter? The microstructure parameter deviation propagations to the 3D microstructure scale electrochemical response have been then quantified for different charge rates. This defines a threshold for the microstructure parameters FOV for a desired maximum deviation of the electrochemical response. Such deviation propagation analysis is analogous to error propagation analysis and is necessary to determine the relevance of microstructure scale model predictions for macroscale predictions. Electrochemical model shows cell representative section areas are increasing with C-rate, due to higher in-plane heterogeneities, indicating larger FOVs are required specifically for fast charge modeling. Therefore, we introduced the novel concept of electrochemical RVE (eRVE) that is a function of the operating conditions (thus defined as a dynamic RVE), with an increasing dependence with the C-rate. Representativity analysis of the investigated cell determined a FOV of 144.4 x 54.4 m2 is large enough to establish a convergence on the representative section areas for low to intermediate C-rate (=2.5C), but not large enough to conclude for higher rates. This work aims to emphasize the importance of representativity analysis for LIB electrode microstructures, as it is required to estimate the error, and thus the relevance, of microstructure parameters intended to be used in macroscale models. The methodology and results can help researchers to select the relevant imaging and associated FOV required to provide accurate enough microstructure parameters.

ADVANCED PROPULSION SYSTEMS↗

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Liou, M.-S.↗

Water Dielectric Function at Finite Wavelength and the Convergence of Its Large Wavelength Limit (Static Dielectric) by Fluctuation Formulas

Here we provide a general analysis of the longitudinal dielectric function ε l (k) via fluctuation formulas at finite wavelength k, including the static dielectric constant ε w = ε l (k → 0), and analyze the different sources of errors, deriving explicit formulas. Simulations with the SPC/E water model show that the convergence of fluctuation formulas to compute the static dielectric constant is slow and requires long simulations. The analysis of ε l (k) allows us to identify the long- and short-wavelength limits and provide a precise determination of the location of the poles as well as the zeros in the complex plane, which determine the short-distance form of the electrostatic (Coulomb) interaction among charged particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Dose of Reality: Radiation Analysis for Realistic Human Spacecraft

INTRODUCTION As with most computational analyses, a tradeoff exists between problem complexity, resource availability and response accuracy when modeling radiation transport from the source to a detector. The largest amount of analyst time for setting up an analysis is often spent ensuring that any simplifications made have minimal impact on the results. The vehicle shield geometry of interest is typically simplified from the original CAD design in order to reduce computation time, but this simplification requires the analyst to "re-draw" the geometry with a limited set of volumes in order to accommodate a specific radiation transport software package. The resulting low-fidelity geometry model cannot be shared with or compared to other radiation transport software packages, and the process can be error prone with increased model complexity. The work presented here demonstrates the use of the DAGMC (Direct Accelerated Geometry for Monte Carlo) Toolkit from the University of Wisconsin, to model the impacts of several space radiation sources on a CAD drawing of the US Lab module. METHODS The DAGMC toolkit workflow begins with the export of an existing CAD geometry from the native CAD to the ACIS format. The ACIS format file is then cleaned using SpaceClaim to remove small holes and component overlaps. Metadata is then assigned to the cleaned geometry file using CUBIT/Trelis from csimsoft (Registered Trademark). The DAGMC plugin script removes duplicate shared surfaces, facets the geometry to a specified tolerance, and ensures that the faceted geometry is water tight. This step also writes the material and scoring information to a standard input file format that the analyst can alter as desired prior to running the radiation transport program. The scoring results can be transformed, via python script, into a 3D format that is viewable in a standard graphics program. RESULTS The CAD model of the US Lab module of the International Space Station, inclusive of all the racks and components, was simplified to remove holes and volume overlaps. Problematic features within the drawing were also removed or repaired to prevent runtime issues. The cleaned drawing was then run through the DAGMC workflow to prepare for analysis. Pilot tests modeling transport of 1GeV proton and 800MeV/A oxygen sources show that reasonable results are converged upon in an acceptable amount of overall computation time from drawing preparation to data analysis. The FLUKA radiation transport code will next be used to model both a GCR and a trapped radiation source. These results will then be compared with measurements that have been made by the radiation instrumentation deployed inside the US Lab module. DISCUSSION Early analyses have indicated that the DAGMC workflow is a promising toolkit for running vehicle geometries of interest to NASA through multiple radiation transport codes. In addition, recent work has shown that a realistic human phantom, provided via a subcontract with the University of Florida, can be placed inside any vehicle geometry for a combinatorial analysis. This added functionality gives the user the ability to score various parameters at the organ level, and the results can then be used as input for cancer risk models.

Barzilla, J. E.↗