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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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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

The solution of non-linear hyperbolic equation systems by the finite element method

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Loehner, R.↗
NASA NTRS2001

Towards operational ocean state estimation

An assimilation effort is undertaken with the goal of understanding seasonal-to-interannual changes of the tropical Pacific Ocean from the late '80s to the present, encompassing the WOCE and TOPEX/POSEIDON (T/P) periods.

method↗
NASA NTRS2012

Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

Rallabhandi, Siriam K.↗
NASA NTRSDate not supplied

Anisotropic Goal-Based Mesh Adaptation Metric Clarification and Development

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows to control discretization error for reliable simulation results. Multiple independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics have matured. Goal-based metrics target estimated error in output functions, such as lift and drag, through the guidance of an adjoint solution. A unification of goal-based anisotropic metrics is presented for steady viscous flows, which is an active area of research. These goal-based metrics drive robust and efficient anisotropic mesh adaptation for the calculation of output functions. The super-convergent functional output error behavior of stabilized finite-element methods is exploited without a formal proof, and evidence of super-convergence is shown in numerical experiments. Mesh adapted drag and lift outputs for two simple bodies in compressible viscous flow show convergence of error to less than a single drag count. Asymptotic behavior established for relatively coarse meshes shows the efficiency of this goal-based metric when compared to solution interpolation error control and expert-guided meshing. Anisotropic mesh adaptation techniques are applied to a transport aircraft in a high-lift configuration where variation between approaches decreases with mesh refinement, but asymptotic behavior is not observed with available resources.

goal-based↗
NASA NTRS1975

A steepest descents method for reentry optimization

A steepest descents optimization program is applied to the problem of a lifting vehicle entering the earth's atmosphere. The program employs penalty functions representing terminal conditions and inflight inequality constraints. During each iteration, it reduces a single performance measure which is the sum of the performance index and the penalty functions. Therefore, only one set of adjoint equations must be integrated per iteration. Values of weight factors, multiplying the penalty functions, are automatically adjusted before each iteration in order that the penalty functions will approach acceptable values. This method is shown to be a form of the classical Lagrange multiplier methods.

Andrus, J. F.↗
DOE OSTI2013

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Monte Carlo Direct Simulation Method for Initiation Probability Problems

During the early period of a supercritical system, the growth of fission chains shows a significant stochastic feature. In multiplying medium, it is a probability issue of fail-pass type for a single neutron to sponsor a divergent fission chain, and the probability of success is named as single neutron initiation probability. Meanwhile, in the presence of a weak neutron source, the time at which fission burst occurs also exhibits a stochastic nature, which can be observed on experiments of pulsed reactors such as GODIVA I and GODIVA II. The initiation probability and burst waiting time reflect the dynamic feature of a supercritical system, which are very important for nuclear criticality safety concerns. It is desirable that a supercritical system has an initiation probability very close to zero and releases limited energy in case of criticality accidents. The stochastic process of neutron population evolution in early age in a multiplying system is governed by Bell's equation in the form of an adjoint neutron transport equation with a non-linear fission term. In order to solve this stochastic neutron transport equation, the deterministic method discretizing the phase space was proposed long ago and has been implemented in several SN codes such as Partisn, Ardra and PANDA. However, the deterministic method is of limited usage, due to its poor ability to precisely describe real-world 3D complex geometries and continuous energy neutron spectrum. Recently, Monte Carlo methods have gradually gained attention for solving Bell's equation. Greenman from LLNL proposed an analog Monte Carlo forward-transport method for calculating initiation probability in 2007. He implemented this method by introducing the maximum age parameter, the time sub-interval and the neutron progenitor tag into Mercury in time-dependent fixed-source simulation mode. This method is only suitable for initiation probability calculations, however not for analyzing the randomness of burst waiting time. Later, GANG in 2011 developed the GSMP (Generalized Semi-Markov Process method) Monte Carlo method according to Bell's equation. While the GSMP method, which can deal with both initiation probability and burst waiting time, is flexible and powerful for zero-dimensional problems, it is not favorable when extended to 3D and continuous energy problems due to severe lack of computational efficiency. In 2015, a direct Monte Carlo simulation method for stochastic systems problems was implemented in MCATK, yet this method has not been applied specifically to the burst waiting time. In this work, a new and efficient 3D Monte Carlo direct simulation method for calculating both the initiation probability and the burst waiting time is developed. By taking random factors during evolvement of fission chains into account in dynamic Monte Carlo simulation, this new method has the potential of simulating the whole process from source neutron injection to exponential growth of the neutron population, and finally to extinction of the neutron pulse. This capability is useful in criticality accidents evaluation and pulsed reactor experiments explanation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Variable-fidelity multipoint aerodynamic shape optimization with output-based adapted meshes

This work presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh.

42 ENGINEERING↗
DOE OSTI2016

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

15 GEOTHERMAL ENERGY↗
NASA NTRS2019

Using Graph Coloring to Compute Total Derivatives More Efficiently in OpenMDAO

When they are applicable, gradient based optimization algorithms are the most efficient way to solve design optimization problems. Although gradient based methods are generally efficient, they can be made significantly more so through the usage of analytic techniques to compute the necessary total derivatives. The traditional forward (direct) and reverse (adjoint) analytic techniques have computational costs that scale linearly with the number of design variables and the number of constraints, respectively. In this work, we present an application of a graph coloring algorithm to the analytic techniques for computing total derivative Jacobians in order to achieve much better computational scaling than the pure analytic methods can provide alone. A detailed theoretical explanation of how coloring algorithms interact with analytic derivative methods is presented that illustrates specific types of sparsity patterns that must be present in total derivative Jacobians in order for this coloring technique to be effective. The new technique has been implemented as a feature in the OpenMDAO framework and the implementation is demonstrated on two example problems. The performance on the example problems up to 50% reduction in compute cost for optimizations with bi-directional coloring compared to traditional constraint aggregation. Additionally, the results show how coloring technique alleviates some of the numerical difficulties that constraint aggregation can cause, leading to the ability to solve larger problems. It is expected that the new method will have wide applicability to multidisciplinary optimization problems, and that its availability in OpenMDAO will offer significant computational savings for users without the need for them to implement the coloring algorithm themselves.

Trajectory↗
DOE OSTI2010

Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model

We solve the operator ordering problem for the quantum continuous integrable su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum trace identities, and the spectrum for the higher-order local charges. We also show that this method, based on operator regularization and renormalization, which guarantees quantum integrability, as well as the construction of self-adjoint extensions, can be used as an alternative to the discretization procedure, and unlike the latter, is based only on integrable representations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Near the sill of the conformal window: Gauge theories with fermions in two-index representations

We apply Schroedinger functional methods to two gauge theories with fermions in two-index representations: the SU(3) theory with Nf=2 adjoint fermions, and the SU(4) theory with Nf=6 fermions in the two-index antisymmetric representation. Each theory is believed to lie near the bottom of the conformal window for its respective representation. In the SU(3) theory we find a small beta function in strong coupling but we cannot confirm or rule out an infrared fixed point. In the SU(4) theory we find a hint of walking - a beta function that approaches the axis and then turns away from it. In both theories the mass anomalous dimension remains small even at the strongest couplings, much like the theories with fermions in the two-index symmetric representation investigated earlier.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Hybrid nested sampling algorithm for Bayesian model selection applied to inverse subsurface flow problems

A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using Stochastic Ensemble Method (SEM). NS is an efficient sampling algorithm that can be used for Bayesian calibration and estimating the Bayesian evidence for prior model selection. Nested sampling has the advantage of computational feasibility. Within the nested sampling algorithm, a constrained sampling step is performed. For this step, we utilize HMC to reduce the correlation between successive sampled states. HMC relies on the gradient of the logarithm of the posterior distribution, which we estimate using a stochastic ensemble method based on an ensemble of directional derivatives. SEM only requires forward model runs and the simulator is then used as a black box and no adjoint code is needed. The developed HNS algorithm is successfully applied for Bayesian calibration and prior model selection of several nonlinear subsurface flow problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Large-Scale Optimization for Bayesian Inference in Complex Systems

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT₋Sandia component of the SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas₋Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A Parametric Study of the Adjoint Flux Calculation for TDKENO

TDKENO is a time-dependent transport code designed to simulate reactor transients. One application is to study experiments performed at the Transient Reactor Test Facility (TREAT) at the Idaho National Laboratory (INL). TDKENO solves the time-dependent, three-dimensional Boltzmann transport equation with explicit representation of delayed neutrons. Instead of directly integrating this equation, the Improved Quasi Static (IQS) method is employed. This involves factoring the neutron flux into two components - a rapidly varying (in time) amplitude equation and a slowly varying shape equation. These are solved separately on different time scales. The shape equation is solved using the Monte Carlo transport code KENO, from Oak Ridge National Laboratory's SCALE code package. Using the Monte Carlo method to solve the shape equation is computationally intensive, but the operation is only performed when needed - namely when the reactor system is undergoing a significant change. The amplitude equation is solved deterministically. This operation contains the time dependence and can be calculated relatively quickly, resulting in computational savings. TDKENO begins by solving the adjoint form of the transport equation for use as a weighting function. It uses this adjoint flux for multiple aspects of the simulation, including the calculation of all of the point kinetics parameters . The flux shape is found by solving a modified form of the transport equation in 'forward' mode. This paper examines the effect the adjoint weighting function has on the solution. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Response tailoring of elasto-plastic trusses

Abstract In this work we tailor the response of trusses loaded beyond their yield limit. The truss structures are modeled using finite strain theory and rate-independent elasto-plasticity. We design trusses with a tailored mechanical response that is between “elastic” and “elastic-ideal-plastic” subject to the volume constraint. The design updates are generated by the gradient-based Method of Moving Asymptotes (MMA) solver and the sensitivities of the response functions are computed using a path-dependent adjoint sensitivity analysis. The computations are performed in Matlab.

42 ENGINEERING↗
DOE OSTI2016

SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , and α Using PARTISN

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k eff , and α using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every isotope and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations. The tool can be used for one-dimensional spherical (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used for fixed-source and eigenvalue problems. The tool implements Generalized Perturbation Theory (GPT) as discussed by Williams and Stacey. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists all of the input files whose results are presented in Sec. VI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

A new least-squares transport equation compatible with voids

We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

97 MATHEMATICS AND COMPUTING↗