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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2013

Autonomous Vision-Based Tethered-Assisted Rover Docking

Many intriguing science discoveries on planetary surfaces, such as the seasonal flows on crater walls and skylight entrances to lava tubes, are at sites that are currently inaccessible to state-of-the-art rovers. The in situ exploration of such sites is likely to require a tethered platform both for mechanical support and for providing power and communication. Mother/daughter architectures have been investigated where a mother deploys a tethered daughter into extreme terrains. Deploying and retracting a tethered daughter requires undocking and re-docking of the daughter to the mother, with the latter being the challenging part. In this paper, we describe a vision-based tether-assisted algorithm for the autonomous re-docking of a daughter to its mother following an extreme terrain excursion. The algorithm uses fiducials mounted on the mother to improve the reliability and accuracy of estimating the pose of the mother relative to the daughter. The tether that is anchored by the mother helps the docking process and increases the system's tolerance to pose uncertainties by mechanically aligning the mating parts in the final docking phase. A preliminary version of the algorithm was developed and field-tested on the Axel rover in the JPL Mars Yard. The algorithm achieved an 80% success rate in 40 experiments in both firm and loose soils and starting from up to 6 m away at up to 40 deg radial angle and 20 deg relative heading. The algorithm does not rely on an initial estimate of the relative pose. The preliminary results are promising and help retire the risk associated with the autonomous docking process enabling consideration in future martian and lunar missions.

Axel docking↗
NASA NTRS2014

An Improved Cryosat-2 Sea Ice Freeboard Retrieval Algorithm Through the Use of Waveform Fitting

We develop an empirical model capable of simulating the mean echo power cross product of CryoSat-2 SAR and SAR In mode waveforms over sea ice covered regions. The model simulations are used to show the importance of variations in the radar backscatter coefficient with incidence angle and surface roughness for the retrieval of surfaceelevation of both sea ice floes and leads. The numerical model is used to fit CryoSat-2 waveforms to enable retrieval of surface elevation through the use of look-up tables and a bounded trust region Newton least squares fitting approach. The use of a model to fit returns from sea ice regions offers advantages over currently used threshold retrackingmethods which are here shown to be sensitive to the combined effect of bandwidth limited range resolution and surface roughness variations. Laxon et al. (2013) have compared ice thickness results from CryoSat-2 and IceBridge, and found good agreement, however consistent assumptions about the snow depth and density of sea ice werenot used in the comparisons. To address this issue, we directly compare ice freeboard and thickness retrievals from the waveform fitting and threshold tracker methods of CryoSat-2 to Operation IceBridge data using a consistent set of parameterizations. For three IceBridge campaign periods from March 20112013, mean differences (CryoSat-2 IceBridge) of 0.144m and 1.351m are respectively found between the freeboard and thickness retrievals using a 50 sea ice floe threshold retracker, while mean differences of 0.019m and 0.182m are found when using the waveform fitting method. This suggests the waveform fitting technique is capable of better reconciling the seaice thickness data record from laser and radar altimetry data sets through the usage of consistent physical assumptions.

CryoSat-2↗
DOE OSTI2018

Communication-efficient Distributed Solutions to a System of Linear Equations with Laplacian Sparse Structure

Two communication-efficient distributed algorithms are proposed to solve a system of linear equations Ax = b with Laplacian sparse A. A system of linear equations with Laplacian sparse A can be found in many applications, e.g., the power flow problems and other network flow problems. The first algorithm is based on the gradient descent method in optimization and the agents only share two parts of the system state instead of that of the whole system state, which saves significant communication. The two parts shared by every agent through a communication link are the state information of its own and its neighbors connected by the communication link. The second method is obtained from an approximation of the Newton method, which converges faster. It requires twice as much communication as the first one but is still communicationefficient due to the low dimension of each part shared between agents. The convergence at a linear rate of both methods is proved. A comprehensive comparison of the convergence rate, communication burden, and computation costs between the methods is made. Finally, a simulation is conducted to show the effectiveness of both methods.

Wang, Peng↗
NASA NTRS2020

Intelligent Contingency Management for Urban Air Mobility

The third aviation revolution is seeking to enable transportation where users have access to immediate and flexible air travel; the users dictate trip origin, destination and timing. One of the major components of this vision is urban air mobility (UAM) for the masses. UAM means a safe and efficient system for vehicles to move passengers and cargo within a city. In order to reach UAM’s full market potential the vehicle will have to be autonomous. One of the primary challenges of autonomous flight is dealing with off-nominal events, both common and unforeseen; thus, intelligent contingency management (ICM) is one of the enabling technologies. In this context, the vehicle has to be aware of its internal state and external environment at all times, ascertain its capability and make decisions about mission completion or modification. All of these functions require data to model and assess the environment and then take actions based on these models. Necessarily, there is uncertainty associated with the data and the models generated from it. Since we are dealing with safety-critical systems, one of the main challenges of ICM is to generate sufficient data and to minimize its uncertainty to enable practical and safe decision making. We propose an overall architecture that incorporates deterministic and learning algorithms together to assess vehicle capabilities, project these into the future and make decisions on mission management level. A layered approach allows for mature parts and technologies to be integrated into early highly automated vehicles before the final state of autonomy is reached.

data-driven systems↗
DOE OSTI2016

Implementation of Material and Geometry Criticality Search in RMC Code

RMC is a continuous-energy Reactor Monte Carlo neutron and photon transport code being developed by Department of Engineering Physics at Tsinghua University, Beijing. For the use of simulation of reactor control or design of reactor with unknown material and geometry parameters, an accurate and efficient method of eigenvalue search is implemented in RMC code. The eigenvalue search focuses on two types of parameters. One is nuclide atom density, called material search, which includes the fuel density, enrichment or boron concentration. Perturbation theory of Monte Carlo Code, like differential operator method and adjoint-weighted perturbation method has been widely researched in sensitivity and uncertainty study. For material search, the perturbation algorithm needs to coupled with flexible material control block and optimized strategy. The other type of parameter is surface position, called geometry search, which includes fuel rod diameter, pitch and control rod position. MC21 iterated on surface position based on bisection method or regula-falsi method, and directly recalculated k-eff until it converged to target error interval. In this paper, the differential operator method, improved Newton-Raphson method is introduced. Based on these methods, the global material search is implemented. Then based on material search and finite method, global geometry search is implement. Finally, fuel enrichment, boron concentration and control rod position in normal PWR assembly are searched. The results show that RMC can search material and geometry parameters accurately and efficiently. In this paper, global eigenvalue search of material and geometry parameters have been implemented in RMC code. They are based on the differential operator method in Monte Carlo perturbation theory. The differential operator method samples δk/δρ{sub r}, δ{sup 2}k/δρ{sub r}{sup 2} along with k-eff estimator. Therefore it won't take up too much additional computational resource. For homogeneous material search, fission source effect has little effect of accuracy and can be ignored. The results of fuel enrichment and boron concentration searches in assembly show that improved Newton-Raphson method can iterate efficiently until k-eff is in the error interval. Based on material search and finite difference formula, the geometry parameter, like control rod axial position, can iterate until k-eff is in the error interval. However, the tiny perturbed region may not contain enough tracks to simulate. Besides, the large number density's relative change up to -1 may cause underestimation of Δk-eff, and then slope of k-x curve. This will cause non-convergence for Newton- Raphson method. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. In this work, we address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2011

Normalization of Gravitational Acceleration Models

Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Eckman, Randy A.↗
DOE OSTI2016

Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model

This work presents phase field fracture modeling in heterogeneous porous media. We develop robust and efficient numerical algorithms for pressure-driven and fluid-driven settings in which the focus relies on mesh adaptivity in order to save computational cost for large-scale 3D applications. In the fluid-driven framework, we solve for three unknowns pressure, displacements and phase field that are treated with a fixed-stress iteration in which the pressure and the displacement–phase-field system are decoupled. The latter subsystem is solved with a combined Newton approach employing a primal–dual active set method in order to account for crack irreversibility. Numerical examples for pressurized fractures and fluid filled fracture propagation in heterogeneous porous media demonstrate our developments. Finally in particular, mesh refinement allows us to perform systematic studies with respect to the spatial discretization parameter.

42 ENGINEERING↗
NASA NTRS2012

Ring Image Analyzer

Ring Image Analyzer software analyzes images to recognize elliptical patterns. It determines the ellipse parameters (axes ratio, centroid coordinate, tilt angle). The program attempts to recognize elliptical fringes (e.g., Newton Rings) on a photograph and determine their centroid position, the short-to-long-axis ratio, and the angle of rotation of the long axis relative to the horizontal direction on the photograph. These capabilities are important in interferometric imaging and control of surfaces. In particular, this program has been developed and applied for determining the rim shape of precision-machined optical whispering gallery mode resonators. The program relies on a unique image recognition algorithm aimed at recognizing elliptical shapes, but can be easily adapted to other geometric shapes. It is robust against non-elliptical details of the image and against noise. Interferometric analysis of precision-machined surfaces remains an important technological instrument in hardware development and quality analysis. This software automates and increases the accuracy of this technique. The software has been developed for the needs of an R&TD-funded project and has become an important asset for the future research proposal to NASA as well as other agencies.

Strekalov, Dmitry V.↗
NASA NTRS1992

Accelerated complete-linearization method for calculating NLTE model stellar atmospheres

Two approaches to accelerating the method of complete linearization for calculating NLTE model stellar atmospheres are suggested. The first one, the so-called Kantorovich variant of the Newton-Raphson method, consists of keeping the Jacobi matrix of the system fixed, which allows us to calculate the costly matrix inversions only a few times and then keep them fixed during the subsequent computations. The second method is an application of the Ng acceleration. Both methods are extremely easy to implement with any model atmosphere code based on complete linearization. It is demonstrated that both methods, and especially their combination, yield a rapidly and globally convergent algorithm, which takes 2 to 5 times less computer time, depending on the model at hand and the required accuracy, than the ordinary complete linearization. Generally, the time gain is more significant for more complicated models. The methods were tested for a broad range of atmospheric parameters, and in all cases they exhibited similar behavior. Ng acceleration applied on the Kantorovich variant thus offers a significant improvement of the standard complete-linearization method, and may now be used for calculating relatively involved NLTE model stellar atmospheres.

Hubeny, I.↗
DOE OSTI2018

Tool employing homotopy-based approaches in finding the controlling unstable equilibrium point in the electric power grid

The analysis tool employs a computer-implemented algorithm that uses homotopy-based approaches to map the solution from the exit point to the controlling unstable equilibrium point (UEP). The computational time is reduced significantly by using an approximate exit point rather than computing an accurate exit point as it is required in finding the controlling UEPs using traditional transient stability direct methods. In addition, this method eliminates the necessity of computing the minimum gradient point (MGP) which is a key element in using Newton methods. These properties provide an advantage to homotopy-based approaches over traditional iterative methods in terms of both speed of computation and reliability of finding solutions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Adjoint methods for aerodynamic wing design

A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.

Grossman, Bernard↗
DOE OSTI2017

On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.

42 ENGINEERING↗
NASA NTRS2016

Normalization and Implementation of Three Gravitational Acceleration Models

Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Eckman, Randy A.↗
NASA NTRS1993

An efficient nonlinear relaxation technique for the three-dimensional, Reynolds-averaged Navier-Stokes equations

An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.

Edwards, Jack R.↗
DOE OSTI2025

Efficient proximal subproblem solvers for a nonsmooth trust-region method

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

The equation of state for stellar envelopes. II - Algorithm and selected results

A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions.

Mihalas, Dimitri↗