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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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Numerical methods for high-dimensional probability density function equations

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Three dimensions, two microscopes, one code: Automatic differentiation for x-ray nanotomography beyond the depth of focus limit

Conventional tomographic reconstruction algorithms assume that one has obtained pure projection images, involving no within-specimen diffraction effects nor multiple scattering. Advances in x-ray nanotomography are leading toward the violation of these assumptions, by combining the high penetration power of x-rays, which enables thick specimens to be imaged, with improved spatial resolution that decreases the depth of focus of the imaging system. We describe a reconstruction method where multiple scattering and diffraction effects in thick samples are modeled by multislice propagation and the 3D object function is retrieved through iterative optimization. We show that the same proposed method works for both full-field microscopy and for coherent scanning techniques like ptychography. Our implementation uses the optimization toolbox and the automatic differentiation capability of the open-source deep learning package TensorFlow, demonstrating a straightforward way to solve optimization problems in computational imaging with flexibility and portability.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials

An improved version of a recently developed stochastic cluster dynamics (SCD) method (Marian and Bulatov, 2012) [6] is introduced as an alternative to rate theory (RT) methods for solving coupled ordinary differential equation (ODE) systems for irradiation damage simulations. SCD circumvents by design the curse of dimensionality of the variable space that renders traditional ODE-based RT approaches inefficient when handling complex defect population comprised of multiple (more than two) defect species. Several improvements introduced here enable efficient and accurate simulations of irradiated materials up to realistic (high) damage doses characteristic of next-generation nuclear systems. The first improvement is a procedure for efficiently updating the defect reaction-network and event selection in the context of a dynamically expanding reaction-network. Next is a novel implementation of the τ-leaping method that speeds up SCD simulations by advancing the state of the reaction network in large time increments when appropriate. Lastly, a volume rescaling procedure is introduced to control the computational complexity of the expanding reaction-network through occasional reductions of the defect population while maintaining accurate statistics. The enhanced SCD method is then applied to model defect cluster accumulation in iron thin films subjected to triple ion-beam (Fe{sup 3+}, He{sup +} and H{sup +}) irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo simulations are prohibitively expensive.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Algorithms and Abstractions for Assembly in PDE Codes: Workshop Report

The emergence of high-concurrency architectures offering unprecedented performance has brought many high-performance partial differential equation (PDE) discretization codes to the precipice of a major refactor. To help address this challenge a workshop titled "Algorithms and Abstractions for Assembly in PDE Codes" was held in the Computer Science Research Institute at Sandia National Laboratories on May 12th-14th, 2014. This document summarizes the goals of the workshop and the results of the presentations and subsequent discussions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Electromagnetic Transient (EMT) Simulation Algorithm for Evaluation of Photovoltaic (PV) Generation Systems

Use of inverter-based resources facilitating renewable energy resources such as photovoltaic (PV) generation is increasing rapidly with decreasing costs and reduced emissions associated. To accommodate such rapid growth of inverter-based resources like PV systems, electromagnetic transient (EMT) simulation models of both PV systems and grids are required to analyze the interaction of PVs in the grid (like the post-event analysis). In addition, the EMT simulation would help with the planning of future power grid with a large number of PVs as well as other inverter-based distributed generation systems. In this paper, the EMT simulation models of PV systems and grids are developed based on the differential algebraic equations (DAEs) representing their EMT dynamics. Furthermore, advanced simulation algorithms including numerical stiffness-based hybrid discretization, DAE clustering and aggregation, multi-order integration, and matrix splitting approaches are applied to accelerate the EMT simulation. The proposed algorithm was applied to 125 PV inverters within 52-bus medium-voltage (MV) distribution grid.

Choi, Jongchan↗
NASA NTRS1983

Optimal trajectories for aeroassisted orbital transfer

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Miele, A.↗
DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Dynamic grid refinement for partial differential equations on parallel computers

The fast adaptive composite grid method (FAC) is an algorithm that uses various levels of uniform grids to provide adaptive resolution and fast solution of PDEs. An asynchronous version of FAC, called AFAC, that completely eliminates the bottleneck to parallelism is presented. This paper describes the advantage that this algorithm has in adaptive refinement for moving singularities on multiprocessor computers. This work is applicable to the parallel solution of two- and three-dimensional shock tracking problems.

Mccormick, S.↗
DOE OSTI2021

Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

42 ENGINEERING↗
NASA NTRS2001

Application of multivariate statistics to vestibular testing: discriminating between Meniere's disease and migraine associated dizziness

Meniere's disease (MD) and migraine associated dizziness (MAD) are two disorders that can have similar symptomatologies, but differ vastly in treatment. Vestibular testing is sometimes used to help differentiate between these disorders, but the inefficiency of a human interpreter analyzing a multitude of variables independently decreases its utility. Our hypothesis was that we could objectively discriminate between patients with MD and those with MAD using select variables from the vestibular test battery. Sinusoidal harmonic acceleration test variables were reduced to three vestibulo-ocular reflex physiologic parameters: gain, time constant, and asymmetry. A combination of these parameters plus a measurement of reduced vestibular response from caloric testing allowed us to achieve a joint classification rate of 91%, independent quadratic classification algorithm. Data from posturography were not useful for this type of differentiation. Overall, our classification function can be used as an unbiased assistant to discriminate between MD and MAD and gave us insight into the pathophysiologic differences between the two disorders.

NASA Discipline Neuroscience↗
NASA NTRS1990

An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Gutierrez, William E.↗
DOE OSTI2021

Deliberate Motion Analytics Fused Radar and Video Test Results Deployed Beyond the Perimeter Fence in a High Noise Environment

Security systems that protect the nation’s critical facilities must be capable of detecting physical intrusions in all weather conditions. Intrusion detection sensors in a perimeter with a high nuisance alarm rate (NAR) significantly undermine detection performance and degrade security system effectiveness. This research demonstrated a fused sensor system that can differentiate foliage and weather-induced nuisance alarms from those caused by intruders, providing reliable detection within a two-fence perimeter or beyond the fence. A key element of this work is the creation and application of a “deliberate motion algorithm” that fuses alarm data from radar and video analytics to create video motion detection fused radar system. The two-layer architecture of the algorithm uses machine learning, multi-hypothesis tracking, and Dynamic Bayes Nets to differentiate intruder alarms from weather induced alarms.

47 OTHER INSTRUMENTATION↗
DOE OSTI2013

PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise

A partitioned implicit–explicit orthogonal Runge–Kutta method (PIROCK) is proposed for the time integration of diffusion–advection–reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise terms (solved explicitly) are integrated in the algorithm as finishing procedures. It is shown that the various coupling (between diffusion, reaction, advection and noise) can be stabilized in the PIROCK method. The method, implemented in a single black-box code that is fully adaptive, provides error estimators for the various terms present in the problem, and requires from the user solely the right-hand side of the differential equation. Numerical experiments and comparisons with existing Chebyshev methods, IMEX methods and partitioned methods show the efficiency and flexibility of our new algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2019

Real-Time Modeling of Thermal Interactions in Cryogenic Ball Bearings

Based on the integration of classical differential equations of motion of bearing elements, a real-time dynamic simulation of ball bearing performance is coupled with simultaneous modeling of thermal interactions between the bearing elements. The transient heat generations are time averaged over a significantly larger time step before they are used to compute the changes in bearing temperature fields. Such an averaging algorithm eliminates the numerical difficulties associated with simultaneous integration of mechanical thermal differential equations with vastly different time scales. Under stable operation, the step change in temperatures at each thermal time step converges to a steady-state solution. Following is a list of accomplishments in the present investigation: (1) A real-time dynamic performance of both 440C and hybrid ball bearings in a LOX environment is modeled in both transient and steady-state time domains, as the inner race accelerates to a prescribed operating speed. (2) The frictional interactions at the ball to race contacts are modeled by experimentally measured traction coefficients as a function of slide-to-roll ratios. (3) Bearing heat generation, as defined by the heat transferred to circulating LOX, is validated against experimental values determined by measured LOX temperatures under prescribed pressures and flow rates. The predicted heat generation is in good agreement with the experimental values. (4) The steady-state solutions are shown to be independent of initial conditions. This establishes convergence of the numerical integration of a differential equation of motion of the bearing elements. (5) Churning and drag losses in the circulating LOX constitutes the majority of bearing heat generation under the experimental test conditions. (6) The heat dissipated in frictional interactions in hybrid bearings is significantly lower in hybrid bearings in comparison to that simulated in all-steel bearings, while the churning and drag losses are relatively unchanged.

Gupta, P. K.↗
DOE OSTI2014

Comparative genomic and proteomic analyses of Clostridium acetobutylicum Rh8 and its parent strain DSM 1731 revealed new understandings on butanol tolerance

Highlights: • Genomes of a butanol tolerant strain and its parent strain were deciphered. • Comparative genomic and proteomic was applied to understand butanol tolerance. • None differentially expressed proteins have mutations in its corresponding genes. • Mutations in ribosome might be responsible for the global difference of proteomics. - Abstract: Clostridium acetobutylicum strain Rh8 is a butanol-tolerant mutant which can tolerate up to 19 g/L butanol, 46% higher than that of its parent strain DSM 1731. We previously performed comparative cytoplasm- and membrane-proteomic analyses to understand the mechanism underlying the improved butanol tolerance of strain Rh8. In this work, we further extended this comparison to the genomic level. Compared with the genome of the parent strain DSM 1731, two insertion sites, four deletion sites, and 67 single nucleotide variations (SNVs) are distributed throughout the genome of strain Rh8. Among the 67 SNVs, 16 SNVs are located in the predicted promoters and intergenic regions; while 29 SNVs are located in the coding sequence, affecting a total of 21 proteins involved in transport, cell structure, DNA replication, and protein translation. The remaining 22 SNVs are located in the ribosomal genes, affecting a total of 12 rRNA genes in different operons. Analysis of previous comparative proteomic data indicated that none of the differentially expressed proteins have mutations in its corresponding genes. Rchange Algorithms analysis indicated that the mutations occurred in the ribosomal genes might change the ribosome RNA thermodynamic characteristics, thus affect the translation strength of these proteins. Take together, the improved butanol tolerance of C. acetobutylicum strain Rh8 might be acquired through regulating the translational process to achieve different expression strength of genes involved in butanol tolerance.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

On domain symmetry and its use in homogenization

The present study focuses on solving partial differential equations in domains exhibiting symmetries and periodic boundary conditions for the purpose of homogenization. We show in a systematic manner how the symmetry can be exploited to significantly reduce the complexity of the problem and the computational burden. This is especially relevant in inverse problems, when one needs to solve the partial differential equation (the primal problem) many times in an optimization algorithm. The main motivation of our study is inverse homogenization used to design architected composite materials with novel properties which are being fabricated at ever increasing rates thanks to recent advances in additive manufacturing. For example, one may optimize the morphology of a two-phase composite unit cell to achieve isotropic homogenized properties with maximal bulk modulus and minimal Poisson ratio. Typically, the isotropy is enforced by applying constraints to the optimization problem. However, in two dimensions, one can alternatively optimize the morphology of an equilateral triangle and then rotate and reflect the triangle to form a space filling D 3 symmetric hexagonal unit cell that necessarily exhibits isotropic homogenized properties. One can further use this D 3 symmetry to reduce the computational expense by performing the “unit strain” periodic boundary condition simulations on the single triangle symmetry sector rather than the six fold larger hexagon. In this paper we use group representation theory to derive the necessary periodic boundary conditions on the symmetry sectors of unit cells. The developments are done in a general setting, and specialized to the two-dimensional dihedral symmetries of the abelian D 2 , i.e. orthotropic, square unit cell and nonabelian D 3 , i.e. trigonal, hexagon unit cell. We then demonstrate how this theory can be applied by evaluating the homogenized properties of a two-phase planar composite over the triangle symmetry sector of a D 3 symmetric hexagonal unit cell.

36 MATERIALS SCIENCE↗
DOE OSTI2011

A hybrid method for hydrodynamic-kinetic flow Part I: A particle-grid method for reducing stochastic noise in kinetic regimes

In this work we present a hybrid particle-grid Monte Carlo method for the Boltzmann equation, which is characterized by a significant reduction of the stochastic noise in the kinetic regime. The hybrid method is based on a first order splitting in time to separate the transport from the relaxation step. The transport step is solved by a deterministic scheme, while a hybrid DSMC-based method is used to solve the collision step. Such a hybrid scheme is based on splitting the solution in a collisional and a non-collisional part at the beginning of the collision step, and the DSMC method is used to solve the relaxation step for the collisional part of the solution only. This is accomplished by sampling only the fraction of particles candidate for collisions from the collisional part of the solution, performing collisions as in a standard DSMC method, and then projecting the particles back onto a velocity grid to compute a piecewise constant reconstruction for the collisional part of the solution. The latter is added to a piecewise constant reconstruction of the non-collisional part of the solution, which in fact remains unchanged during the relaxation step. Numerical results show that the stochastic noise is significantly reduced at large Knudsen numbers with respect to the standard DSMC method. Indeed in this algorithm, the particle scheme is applied only on the collisional part of the solution, so only this fraction of the solution is affected by stochastic fluctuations. But since the collisional part of the solution reduces as the Knudsen number increases, stochastic noise reduces as well at large Knudsen numbers.

97 MATHEMATICS AND COMPUTING↗