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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Multirate Exponential Rosenbrock Methods

In this paper we propose a novel class of methods for high-order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the action of matrix φ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called multirate ExpRB (MERB) methods. They consist of the solution to a sequence of modified “fast” initial-value problems, which may themselves be approximated through subcycling any desired initial-value problem solver. In addition to proving how to construct MERB methods from certain classes of ExpRB methods, we provide rigorous convergence analysis of these methods and derive efficient MERB schemes of orders 2 through 6 (the highest-order infinitesimal multirate methods to date). Lastly, we then present numerical simulations to confirm these theoretical convergence rates and to compare the efficiency of MERB methods against other recently introduced high-order multirate methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A comparison of eight optimization methods applied to a wind farm layout optimization problem

Abstract. Selecting a wind farm layout optimization method is difficult. Comparisons between optimization methods in different papers can be uncertain due to the difficulty of exactly reproducing the objective function. Comparisons by just a few authors in one paper can be uncertain if the authors do not have experience using each algorithm. In this work we provide an algorithm comparison for a wind farm layout optimization case study between eight optimization methods applied, or directed, by researchers who developed those algorithms or who had other experience using them. We provided the objective function to each researcher to avoid ambiguity about relative performance due to a difference in objective function. While these comparisons are not perfect, we try to treat each algorithm more fairly by having researchers with experience using each algorithm apply each algorithm and by having a common objective function provided for analysis. The case study is from the International Energy Association (IEA) Wind Task 37, based on the Borssele III and IV wind farms with 81 turbines. Of particular interest in this case study is the presence of disconnected boundary regions and concave boundary features. The optimization methods studied represent a wide range of approaches, including gradient-free, gradient-based, and hybrid methods; discrete and continuous problem formulations; single-run and multi-start approaches; and mathematical and heuristic algorithms. We provide descriptions and references (where applicable) for each optimization method, as well as lists of pros and cons, to help readers determine an appropriate method for their use case. All the optimization methods perform similarly, with optimized wake loss values between 15.48 % and 15.70 % as compared to 17.28 % for the unoptimized provided layout. Each of the layouts found were different, but all layouts exhibited similar characteristics. Strong similarities across all the layouts include tightly packing wind turbines along the outer borders, loosely spacing turbines in the internal regions, and allocating similar numbers of turbines to each discrete boundary region. The best layout by annual energy production (AEP) was found using a new sequential allocation method, discrete exploration-based optimization (DEBO). Based on the results in this study, it appears that using an optimization algorithm can significantly improve wind farm performance, but there are many optimization methods that can perform well on the wind farm layout optimization problem, given that they are applied correctly.

17 WIND ENERGY↗
DOE OSTI2018

Distributions of Functionals of Switching Diffusions

The paper deals with methods of computation of distributions of functionals of switching diffusions. The switching between two collections of diffusion coefficients occurs at the Poisson time moments which are independent of the initial diffusions. One can also consider more general diffusions when the choice is made from three or more collections of diffusion coefficients.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A general solution strategy of modified power method for higher mode solutions

A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the new strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Variance reduction for Fokker–Planck based particle Monte Carlo schemes

Recently, Fokker–Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1–3]. In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker–Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker–Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Sensitivity/Uncertainty Comparison Study: Oak Ridge National Laboratory Results [Slides]

Various methods and sensitivity/uncertainty tools have been developed over the years to assist in determining upper subcritical limits (USLs). The task is to compare calculated USLs from various methods on a small set of benchmark problems. The benchmark experiments selected are the following applications: HEU-MET-FAST-013-001, HEU-SOL-THERM-001-008, PU-MET-FAST-022-001, and PU-SOL-THERM-001-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. In this work, we introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7's finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7's FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from single- to specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7's FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Stochastic derivative-free optimization using a trust region framework

This study presents a trust region algorithm to minimize a function f when one has access only to noise-corrupted function values f¯. The model-based algorithm dynamically adjusts its step length, taking larger steps when the model and function agree and smaller steps when the model is less accurate. The method does not require the user to specify a fixed pattern of points used to build local models and does not repeatedly sample points. If f is sufficiently smooth and the noise is independent and identically distributed with mean zero and finite variance, we prove that our algorithm produces iterates such that the corresponding function gradients converge in probability to zero. As a result, we present a prototype of our algorithm that, while simplistic in its management of previously evaluated points, solves benchmark problems in fewer function evaluations than do existing stochastic approximation methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Users manual for Streamtube Curvature Analysis: Analytical method for predicting the pressure distribution about a nacelle at transonic speeds, volume 1

The computer program, Streamtube Curvature Analysis, is described for the engineering user and for the programmer. The user oriented documentation includes a description of the mathematical governing equations, their use in the solution, and the method of solution. The general logical flow of the program is outlined and detailed instructions for program usage and operation are explained. General procedures for program use and the program capabilities and limitations are described. From the standpoint of the grammar, the overlay structure of the program is described. The various storage tables are defined and their uses explained. The input and output are discussed in detail. The program listing includes numerous comments so that the logical flow within the program is easily followed. A test case showing input data and output format is included as well as an error printout description.

Keith, J. S.↗
DOE OSTI2018

Modeling Mesoscale Processes of Scalable Synthesis

Brown University is part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), led by PNNL. The Collaboratory focuses on developing rigorous mathematical foundations for understanding and controlling fundamental mechanisms in mesoscale processes to enable scalable synthesis of complex materials, through the design of efficient modeling methods and corresponding scalable algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

SU-F-T-656: Monte Carlo Study On Air Activation Around a Medical Electron Linac

Purpose: In high energy photon therapy, several radiation protection issues result from photonuclear reactions. The activation of air - directly by photonuclear reactions as well as indirectly by capture of photoneutrons generated inside the linac head - is a major point of concern for the medical staff. The purpose of this study was to estimate the annual effective dose to medical workers due to activated air around a medical high energy electron linac by means of Monte Carlo simulations. Methods: The treatment head of a Varian Clinac in 18 MV-X mode as well as the surrounding concrete bunker were modeled and the radiation transport was simulated using the Monte Carlo code FLUKA, starting from the primary electron striking the bremsstrahlung target. The activation yields in air from photo-disintegration of O-16 and N-14 nuclei as well as from neutron capture on Ar-40 nuclei were obtained from the simulations. The activation build-up, radioactive decay and air ventilation were studied using a mathematical model. The annual effective dose to workers was estimated by using published isotope specific conversion factors. Results: The oxygen and nitrogen activation yields were in contrast to the argon activation yield found to be field size dependent. The impact of the treatment room ventilation on the different air activation products was investigated and quantified. An estimate with very conservative assumptions gave an annual effective dose to workers of < 1 mSv/a. Conclusion: From the results of this study it can be concluded that the contribution of air activation to the radiation exposure to medical workers should be negligible in modern photon therapy, especially when it is compared to the dose due to prompt neutrons and the activation of heavy solid materials such as the jaws and the collimators inside the linac head.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2000

Scheduling and Estimating the Cost of Crew Time

In a previous paper, Theory and Application of the Equivalent System Mass Metric, Julie Levri, David Vaccari, and Alan Drysdale developed a method for computing the Equivalent System Mass (ESM) of crew time. ESM is an analog of cost. The suggested approach has been applied but seems to impose too high a cost for small additional requirements for crew time. The proposed method is based on the minimum average cost of crew time. In this work, the scheduling of crew time is examined in more detail, using suggested crew time allocations and daily work schedules. Crew tasks are typically assigned using priorities, which can also be used to construct a crew time demand curve mapping the value or cost per hour versus the total number of hours worked. The cost of additional crew time can be estimated by considering the intersection and shapes of the demand and supply curves. If e assume a mathematical form for the demand curve, a revised method can be developed for computing the cost or ESM of crew time. This method indicates a low cost per hour for small additional requirements for crew time and an increasing cost per hour for larger requirements.

Jones, Harry↗
NASA NTRS1982

Subsonic panel method for the efficient analysis of multiple geometry perturbations

An accurate and efficient method was developed for the aerodynamic analysis of a series of arbitrary small geometry perturbations to a given baseline configuration. The method is appropriate for wing-fuselage configurations in incompressible potential flow. Mathematical formulations are presented for three computer programs that are employed. The first program is a conventional surface panel method for calculating the baseline singularity distribution. The second program calculates a partial derivative matrix. Each element of the matrix is the rate of change of singularity strength at one point with respect to a surface coordinate of a different point. For each baseline configuration, the calculated quantities from the first two programs establish an input file for the third. The third program calculates the surface pressure distribution and forces and moments for a series of geometry perturbations.

Bristow, D. R.↗
DOE OSTI2021

Data-driven acceleration of thermal radiation transfer calculations with the dynamic mode decomposition and a sequential singular value decomposition

In this work, we present a method for accelerating discrete ordinates radiative transfer calculations for radiative transfer. Our method works with nonlinear positivity fixes, in contrast to most acceleration schemes. The method is based on the dynamic mode decomposition (DMD) and using a sequence of rank-one updates to compute the singular value decomposition needed for DMD. Using a sequential method allows us to automatically determine the number of solution vectors to include in the DMD acceleration. We present results for slab geometry discrete ordinates calculations with the standard temperature linearization. Compared with positive source iteration, our results demonstrate that our acceleration method reduces the number of transport sweeps required to solve the problem by a factor of about 3 on a standard diffusive Marshak wave problem, a factor of several thousand on a cooling problem where the effective scattering ratio approaches unity, and a factor of 20 improvement in a realistic, multimaterial radiating shock problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A Monte Carlo method for the simulation of coagulation and nucleation based on weighted particles and the concepts of stochastic resolution and merging

Monte Carlo simulations based on weighted simulation particles can solve a variety of population balance problems and allow thus to formulate a solution-framework for many chemical engineering processes. This study presents a novel concept for the calculation of coagulation rates of weighted Monte Carlo particles by introducing a family of transformations to non-weighted Monte Carlo particles. The tuning of the accuracy (named ‘stochastic resolution’ in this paper) of those transformations allows the construction of a constant-number coagulation scheme. Furthermore, a parallel algorithm for the inclusion of newly formed Monte Carlo particles due to nucleation is presented in the scope of a constant-number scheme: the low-weight merging. This technique is found to create significantly less statistical simulation noise than the conventional technique (named ‘random removal’ in this paper). Both concepts are combined into a single GPU-based simulation method which is validated by comparison with the discrete-sectional simulation technique. Two test models describing a constant-rate nucleation coupled to a simultaneous coagulation in 1) the free-molecular regime or 2) the continuum regime are simulated for this purpose.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2013

Final Report - Regulatory Considerations for Adaptive Systems

This report documents the findings of a preliminary research study into new approaches to the software design assurance of adaptive systems. We suggest a methodology to overcome the software validation and verification difficulties posed by the underlying assumption of non-adaptive software in the requirementsbased- testing verification methods in RTCA/DO-178B and C. An analysis of the relevant RTCA/DO-178B and C objectives is presented showing the reasons for the difficulties that arise in showing satisfaction of the objectives and suggested additional means by which they could be satisfied. We suggest that the software design assurance problem for adaptive systems is principally one of developing correct and complete high level requirements and system level constraints that define the necessary system functional and safety properties to assure the safe use of adaptive systems. We show how analytical techniques such as model based design, mathematical modeling and formal or formal-like methods can be used to both validate the high level functional and safety requirements, establish necessary constraints and provide the verification evidence for the satisfaction of requirements and constraints that supplements conventional testing. Finally the report identifies the follow-on research topics needed to implement this methodology.

Wilkinson, Chris↗