Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “convergence rate”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗
NASA NTRS2010

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗
NASA NTRS2013

Efficient Creation of Overset Grid Hole Boundaries and Effects of Their Locations on Aerodynamic Loads

Recent developments on the automation of the X-rays approach to hole-cutting in over- set grids is further improved. A fast method to compute an auxiliary wall-distance function used in providing a rst estimate of the hole boundary location is introduced. Subsequent iterations lead to automatically-created hole boundaries with a spatially-variable o set from the minimum hole. For each hole boundary location, an averaged cell attribute measure over all fringe points is used to quantify the compatibility between the fringe points and their respective donor cells. The sensitivity of aerodynamic loads to di erent hole boundary locations and cell attribute compatibilities is investigated using four test cases: an isolated re-entry capsule, a two-rocket con guration, the AIAA 4th Drag Prediction Workshop Common Research Model (CRM), and the D8 \Double Bubble" subsonic aircraft. When best practices in hole boundary treatment are followed, only small variations in integrated loads and convergence rates are observed for different hole boundary locations.

Overset↗
NASA NTRS2013

Numerical Modeling of Ablation Heat Transfer

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Ewing, Mark E.↗
NASA NTRS2015

The Development of a Deflectometer for Accurate Surface Figure Metrology

Marshall Space Flight Center is developing the method of direct fabrication for high resolution full-shell x-ray optics. In this technique the x-ray optics axial profiles are figured and polished using a computer-controlled ZeekoIRP600X polishing machine. Based on the Chandra optics fabrication history about one third of the manufacturing time is spent on moving a mirror between fabrication and metrology sites, reinstallation and alignment with either the metrology or fabrication instruments. Also, the accuracy of the alignment significantly affects the ultimate accuracy of the resulting mirrors. In order to achieve higher convergence rate it is highly desirable to have a metrology technique capable of in situ surface figure measurements of the optics under fabrication, so the overall fabrication costs would be greatly reduced while removing the surface errors due to the re-alignment necessary after each metrology cycle during the fabrication. The goal of this feasibility study is to demonstrate if the Phase Measuring Deflectometry can be applied for in situ metrology of full shell x-ray optics. Examples of the full-shell mirror substrates suitable for the direct fabrication

X-ray optics metrology↗
NASA NTRS2016

Attitude Control System Design for CubeSats Configured with Exo-Brake Parachute

This paper develops a novel attitude control strategy for an Earth orbiting CubeSat spacecraft by utilizing the exo-brake parachute to modulate the atmospheric drag forces as a source of attitude control authority, enabling orbital exo-sail maneuvers. In particular, the spacecraft attitude controls can be realized through the two dimensional exo-sail maneuvers in pitch and yaw directions. The uncertain atmospheric drag induced disturbance torque is estimated through an adaptive parameter estimation process which makes use of the adaptive least-squares minimization techniques. The covariance updating law with a variable forgetting factor is adopted and it can be shown that the convergent rate for the estimation errors can be chosen at the same level as the forgetting factor, in order to meet the design needs. The proposed approach is best suited for Earth orbiting micronano-satellite applications, which are configured with exo-brake parachute. With integration of exo-sail actuation mechanism and disturbance estimation, we demonstrate through simulations that exo-sail induced control torque for CubeSat attitude maneuver is feasible.

Disturbance estimation↗
NASA NTRS2019

An Initial Exploration of Improved Numerics within the Guidelines of the Negative Spalart-Allmaras Turbulence Model

A simple modification to the negative Spalart-Allmaras turbulence model is suggested so that when the turbulence working variable, ~v, is negative, diagonal dominance is increased, as is the tendency for the time-advancement scheme to push e toward positive values. Owing to the fact that the modification is only active when ~v is less than zero, the physical model is left unchanged. Using the proposed modification with a strong implicit solver based on Newton's method, convergence rates can be somewhat improved, with typical reductions in iterations and computer time on the order of 15-50%. The benefits are realized primarily when second- or higher-order accuracy is used for discretizing the convective terms in the turbulence model because of large overshoots that can occur with these schemes at the edges of boundary layers and wakes. For flowfields with few regions of negative ~v, or on very fine meshes where ~v is always greater than zero, little or no benefits should be expected.

Anderson, William K.↗
NASA NTRS2019

Streamlined Convergence Acceleration for CFD Codes

Enigma, a simplified interface to the PETSc library, is shown to enable the rapid solution of discrete partial differential equations. Two CFD codes, LAURA and HyperSolve, use Enigma to compute steady solutions of the Navier-Stokes equations. Using PETSc, Enigma is shown to provide a Jacobian-Free Newton-Krylov method (JFNK), globalized with pseudotransient continuation, that improves efficiency over the point-implicit relaxation method traditionally used by LAURA. It is shown that iterative error has a large impact on surface heat transfer predicted by LAURA on an axisymmetric sphere-cone geometry. Also, the convergence rate of HyperSolve simulating subsonic flow over a delta wing geometry with the JFNK method is shown to be more efficient than employing a defect correction method as the nonlinear solver.

Thompson, Kyle B.↗
NASA NTRSDate not supplied

Recent Progress in OVERFLOW Convergence Improvements

Improvements have been made to the implicit symmetric successive overrelaxation algorithm in the OVERFLOW 2.3 structured, overset grid, computational fluid dynamics flow solver. These improvements, consisting of implicit boundary conditions, improved flux Jacobian linearizations, and CFL number ramping, are a series of evolutionary changes to the linear solver that have resulted in increased nonlinear convergence rates and faster time to solution. A series of test cases are presented that demonstrate the effect of the changes through comparison with the original SSOR path and other linear solver implementations within OVERFLOW.

Joseph M Derlaga↗
NASA NTRS2022

Impact of 3D Structure on Magnetic Reconnection

Results from 2.5D and 3D studies of the onset and development of the tearing instability are presented, using high fidelity resistive MHD simulations. A limited parameter study of the strength of the reconnecting field (or shear angle) was performed. An initially simple 1D equilibrium was used, consisting of a modified force-free current sheet, with periodic boundary conditions in all directions. In all cases, the linear and nonlinear evolution led to a primary current sheet between two large flux ropes. The global reconnection rate during this later stage was analyzed in all simulations. It was found that in 2.5D the primary current sheet fragmented owing to plasmoids, and as expected, the global reconnection rate, calculated using multiple methods, increases with the strength of the reconnecting field owing to a stronger Alfvén speed. In 3D, the presence of interacting oblique modes of the tearing instability complicates the simple 2.5D picture, entangling the magnetic field of the inflow and introducing a negative effect on the reconnection rate. The two competing effects of stronger Alfvén speed and entangling, which both increase with the strength of the reconnecting field, resulted in a decrease in the reconnection rate with increasing reconnecting field. For all simulations, the 3D rates were less than in 2.5D but suggest that as one goes to weak reconnecting field (or strong guide field) the system becomes more 2.5D-like and the 2.5D and 3D rates converge. These results have relevance to situations like nanoflare heating and flare current sheets in the corona.

Lars K S Daldorff↗
DOE OSTI2021

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗
DOE OSTI2023

A Privacy Preserving Distributed Model Identification Algorithm for Power Distribution Systems: Preprint

Distributed control/optimization is a promising approach for network systems due to its advantages over centralized schemes, such as robustness, cost-effectiveness, and improved privacy. However, distributed methods can have drawbacks, such as slower convergence rates due to limited knowledge of the overall network model. Additionally, ensuring privacy in the communication of sensitive information can pose implementation challenges. To address this issue, we propose a distributed model identification algorithm that enables each agent to identify the sub-model that characterizes the relationship between its local control and the overall system outputs. The proposed algorithm maintains the privacy of local agents by only communicating through dummy variables. We demonstrate the efficacy of our algorithm in the context of power distribution systems by applying it to the voltage regulation of a modified IEEE distribution system. The proposed algorithm is well-suited to the needs of power distribution controls and offers an effective solution to the challenges of distributed model identification in network systems.

data-driven modeling↗
DOE OSTI2022

First-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions

Deterministic transport codes play a fundamental role in the modelling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the S method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solving them using non-traditional techniques such as ray tracing. One such code capable of doing this is Lawrence Livermore National Laboratory's deterministic transport code ARDRA. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low order of convergence and not being conservative. Therefore, a new method has been developed that traces instead to a set of points on each of a zone's surfaces and computing the currents, before using these to obtain the flux. A comparison between these two ray tracing methods showed significant advantages to the new surface method, including inherent conservation, a higher convergence rate, and an increase in calculable information like leakage. This work performed under the auspices of the U.S. Department of Energy by Lawrence Liver- more National Laboratory under Contract DE-AC52-07NA27344. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

The MP{sub N} method: a new angular discretization method based on piecewise polynomial interfaces fluxes

In transport calculations, it is well known how S{sub N} method is extremely inefficient in problems where the particle physics is dominated by streaming. The ray-effect eventually produced by the insufficient angular discretization, appears to be extremely persistent with respect to the refinement of the angular quadrature. The MP{sub N} method, that relies on continuous angular representation, offers a robust remedy to such an issue. MP{sub N} is based on the decomposition of the unit sphere into solid angles and on a piecewise continuous definition of interface fluxes, which are expanded in polynomials in each solid angle. This allows propagating more than one angular degree of freedom simultaneously while maintaining unaltered the block-diagonal pattern of the displacement plus removal operator. The method is therefore well suited for the flux resolution by means of a conventional sweep algorithm. Furthermore, unlike the S{sub N} method, MP{sub N} does not rely on discrete directions and, thus, on an angular quadrature formula, but rather constructs a set of linear equations solving for the angular moments of the flux for all discrete solid angles within the sweep. MP{sub N} shows an error convergence rate higher than S{sub N} at the expense of an increased size of the coefficient matrices, so of the computational cost. Although MP{sub N} is not free from ray-effect, the latter is effectively mitigated and less persistent with respect to the increase of the angular refinement order. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

FedOSAA: Improving Federated Learning with One-Step Anderson Acceleration

Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly those incorporating variance reduction techniques, are the most widely used FL algorithms due to their simple implementation and stable performance. However, these methods tend to be slow and require a large number of communication rounds to reach the global minimizer. We propose FedOSAA, a novel approach that preserves the simplicity of first-order methods while achieving the rapid convergence typically associated with second-order methods. Our approach applies one Anderson acceleration (AA) step following classical local updates based on first-order methods with variance reduction, such as FedSVRG and SCAFFOLD, during local training. This AA step is able to leverage curvature information from the history points and gives a new update that approximates the Newton-GMRES direction, thereby significantly improving the convergence. We establish a local linear convergence rate to the global minimizer of FedOSAA for smooth and strongly convex loss functions. Numerical comparisons show that FedOSAA substantially improves the communication and computation efficiency of the original first-order methods, achieving performance comparable to second-order methods like GIANT.

Feng, Xue [University of California, Davis]↗
NASA NTRS1988

Strain accumulation in the Santa Barbara Channel, 1971-1987

Geophysical evidence suggests a significant amount of north-south convergence occurs across the Santa Barbara Channel. Tectonic studies indicate a discrepancy between observed fault slip in California and the North American-Pacific plate motion. Newer plate motion models (NUVEL-1) yield a lower rate of convergence. Global Positioning System (GPS) data collected in the Santa Barbara Channel in 1987, when combined with 1971 trilateration measurements, should be sufficient to resolve the present-day convergence rate. In early 1987. from January 3 to 7, GPS data were collected at 14 sites in California and at 5 additional stations throughout North America. The data can be used to estimate the rate of crustal deformation (convergence) ocurring across the Santa Barbara Channel. The GPS baselines were computed with the Bernese 2nd generation software. A comparison was made between baseline lengths obtained with the Burnese and MIT softwares. Baseline changes from 1971 to January, 1987 (GPS-Bernese) across the Santa Barbara Channel were computed. A uniform strain model was calculated from the baseline changes. The present-day rate of convergence across the Santa Barbara Channel was determined to be 8 to 10 mm/yr. This conclusion is obtained from changes in the baseline length measured with a 1971 trilateration survey and a January, 1987, GPS survey. The rapid convergence rate, in addition to the history of large seismic events, suggests this region is a prime target for future geodetic and geophysical studies.

Larsen, Shawn↗
DOE OSTI2022

Code Verification and Solution Verification framework in pin-resolved neutron transport code MPACT

Program verification in scientific computing encompasses the application of formal and mathematical techniques to a scientific computing code for its credibility, accuracy, and validity. Code Verification identifies bugs and performance issues in the software development stage. Solution Verification assesses the applicability of the code and the accuracy of the solution to problems of interest. Both activities utilize application cases and quantify the error against prescribed acceptance criteria. However, simply executing more application cases does not guarantee stronger or more comprehensive credibility. Here, we establish a verification framework that involves Code Verification and Solution Verification, both of which work together such that the overarching goal of “converge to the correct answer for the intended application” can be reasonably inferred. The application of such a verification framework is demonstrated using the pin-resolved neutron transport code MPACT, where standard unit tests and regression tests are covered, and where the Method of Exact Solutions and the Method of Manufactured Solutions are successfully used. Additionally, the applicability of Method of Manufactured Solutions is extended to the OECD/NEA C5G7 benchmark problems of practical material and geometric configurations. Solution Verification activities are demonstrated on a practical hierarchy of application models of increasing complexity ranging from 2D pin cell problems to 3D assembly problems. The convergence behavior and rate of convergence with respect to each individual variable are studied and provided. This framework can be adapted broadly to other fields involving scientific computing codes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗