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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations

This paper is one of a series of papers describing the development of a new numerical approach for solving the steady Navier-Stokes equations. The key features in the current development are (1) the discrete representation of the dependent variables by way of high order polynomial expansions, (2) the retention of all derivatives in the expansions as unknowns to be explicitly solved for, (3) the automatic balancing of fluxes at cell interfaces, and (4) the discrete simulation of both the integral and differential forms of the governing equations. The main purpose of this paper is, first, to provide a systematic and rigorous derivation of the conditions that are used to simulate the differential form of the Navier-Stokes equations, and second, to extend our previously-presented internal flow scheme to external flows and nonuniform grids. Numerical results are presented for high Reynolds number flow (Re = 100,000) around a finite flat plate, and detailed comparisons are made with the Blasius flat plate solution and Goldstein wake solution. It is shown that the error in the streamwise velocity decreases like r(sup alpha)(Delta)y(exp 2), where alpha approx. 0.25 and r = delta(y)/delta(x) is the grid aspect ratio.

Scott, James R.↗
NASA NTRS1983

Necessary conditions for optimization in multiparameter discrete systems

A general first-order dynamic representation for discrete systems with several independent variables is proposed, based on the Dieudonne-Rashevsky form for partial differential equations. This representation does not restrict consideration to causal systems. A minimum principle for such systems is proved, thus extending results known for discrete-time systems to the case of several independent variables. The proof requires only the classical implicit function theorem.

Hegg, D. R.↗
NASA NTRS1975

Time domain modelling and stability analysis of an integral pulse frequency modulated dc to dc power converter

Using state variable representation a nonlinear, discrete-time system is derived that models the converter exactly. This system is linearized about its steady state solution, and converter stability, transient response and audio susceptibility are studied. The steady state solution of the converter is stable if and only if all the roots of the linearized system are absolutely less than unity. Excellent agreement with laboratory test data has been observed.

Iwens, R. P.↗
DOE OSTI2021

Mixture Model Framework for Traumatic Brain Injury Prognosis Using Heterogeneous Clinical and Outcome Data

Prognoses of Traumatic Brain Injury (TBI) outcomes are neither easily nor accurately determined from clinical indicators. This is due in part to the heterogeneity of damage inflicted to the brain, ultimately resulting in diverse and complex outcomes. Using a data-driven approach on many distinct data elements may be necessary to describe this large set of outcomes and thereby robustly depict the nuanced differences among TBI patients’ recovery. In this work, we develop a method for modeling large heterogeneous data types relevant to TBI. Our approach is geared toward the probabilistic representation of mixed continuous and discrete variables with missing values. The model is trained on a dataset encompassing a variety of data types, including demographics, blood-based biomarkers, and imaging findings. In addition, it includes a set of clinical outcome assessments at 3, 6, and 12 months post-injury. The model is used to stratify patients into distinct groups in an unsupervised learning setting. We use the model to infer outcomes using input data, and show that the collection of input data reduces uncertainty of outcomes over a baseline approach. In addition, we quantify the performance of a likelihood scoring technique that can be used to self-evaluate the extrapolation risk of prognosis on unseen patients.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

System Identification and POD Method Applied to Unsteady Aerodynamics

The representation of unsteady aerodynamic flow fields in terms of global aerodynamic modes has proven to be a useful method for reducing the size of the aerodynamic model over those representations that use local variables at discrete grid points in the flow field. Eigenmodes and Proper Orthogonal Decomposition (POD) modes have been used for this purpose with good effect. This suggests that system identification models may also be used to represent the aerodynamic flow field. Implicit in the use of a systems identification technique is the notion that a relative small state space model can be useful in describing a dynamical system. The POD model is first used to show that indeed a reduced order model can be obtained from a much larger numerical aerodynamical model (the vortex lattice method is used for illustrative purposes) and the results from the POD and the system identification methods are then compared. For the example considered, the two methods are shown to give comparable results in terms of accuracy and reduced model size. The advantages and limitations of each approach are briefly discussed. Both appear promising and complementary in their characteristics.

Tang, Deman↗
NASA NTRS1990

Shape design sensitivities using fully automatic 3-D mesh generation

Previous work in three dimensional shape optimization involved specifying design variables by associating parameters directly with mesh points. More recent work has shown the use of fully-automatic mesh generation based upon a parameterized geometric representation. Design variables have been associated with a mathematical model of the part rather than the discretized representation. The mesh generation procedure uses a nonuniform grid intersection technique to place nodal points directly on the surface geometry. Although there exists an associativity between the mesh and the geometrical/topological entities, there is no mathematical functional relationship. This poses a problem during certain steps in the optimization process in which geometry modification is required. For the large geometrical changes which occur at the beginning of each optimization step, a completely new mesh is created. However, for gradient calculations many small changes must be made and it would be too costly to regenerate the mesh for each design variable perturbation. For that reason, a local remeshing procedure has been implemented which operates only on the specific edges and faces associated with the design variable being perturbed. Two realistic design problems are presented which show the efficiency of this process and test the accuracy of the gradient computations.

Botkin, M. E.↗
DOE OSTI2025

Co-designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation

We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete- or continuous-variable (qubit or qumode) hardware. To illustrate the oracle’s representation-theoretic power and near-term experimental accessibility, we encode a Gaussian imaginary time-evolution spectral filter. As a result, we define a continuous linear combination of unitaries block encoding. Due to the ancillary qumode’s infinite-dimensional nature, continuous-variable qumodes constitute a powerful compilation tool for encoding continuous spectral functions without discretization errors while minimizing resource requirements. We then focus on the ubiquitous task of preparing eigenstates in quantum spin models. For completeness, we provide an end-to-end compilation which expresses high-level oracles in terms of an experimentally realizable instruction set architecture in both 1D and 2D. Finally, we examine the leading-order effects of physical errors and highlight open research directions. Our algorithms scale linearly with the spatial extent of the target system and are applicable to both near-term and large-scale quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Here, this paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate conformal meshes, this work uses an extended finite element method (XFEM) to discretize the governing equations on non-conforming, embedding meshes. A flexible approach to create truncated hierarchical B-splines discretizations is presented. This approach enables the refinement of each state variable field individually to meet field-specific accuracy requirements. To obtain an immersed geometry representation that is consistent across all hierarchically refined B-spline discretizations, the geometry is immersed into a single mesh, the XFEM background mesh, which is constructed from the union of all hierarchical B-spline meshes. An extraction operator is introduced to represent the truncated hierarchical B-spline bases in terms of Lagrange shape functions on the XFEM background mesh without loss of accuracy. The truncated hierarchical B-spline bases are enriched using a generalized Heaviside enrichment strategy to accommodate small geometric features and multi-material problems. The governing equations are augmented by a formulation of the face-oriented ghost stabilization enhanced for locally refined B-spline bases. We present examples for two- and three-dimensional linear elastic and thermo-elastic problems. The numerical results validate the accuracy of our framework. The results also demonstrate the applicability of the proposed framework to large, geometrically complex problems.

42 ENGINEERING↗
NASA NTRS1972

Design of non-interacting multivariable discrete time systems

The theory of decoupling a multivariable system with the help of state variable feedback is applied to discrete time systems. The system differential equations in the continuous time domain are converted to a discrete time representation. A discrete time controller is designed to control the overall input to the system such that a specified desired decoupled output response is obtained. The decoupled system behaves as a set of single-input, single-output systems and state variable techniques can be easily applied to control each output individually. Control is achieved by periodically sampling the inputs and all the states and feeding them back through a controller. For linear time invariant systems the control is time invariant. The basic theory of decoupling involves feeding back all the states twice, first to decouple the system and then to achieve a desired response. The states of the system are computed with the help of a state estimator which calculates all the present states of the system so that on-line control can be applied to real time systems. The theory is applied to a model of a nuclear rocket engine.

Agrawal, B. L.↗
NASA NTRS1976

The Relation of Finite Element and Finite Difference Methods

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Vinokur, M.↗
NASA NTRS1990

Discrete approximations to optimal trajectories using direct transcription and nonlinear programming

A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.

Enright, Paul J.↗
NASA NTRS1988

The discrete correlation function - A new method for analyzing unevenly sampled variability data

A method for measuring correlation functions without interpolating in the temporal domain is proposed which provides an assumption-free representation of the correlation measured in the data and allows meaningful error estimates. Physical interpretation of the cross-correlation function of two series believed to be related by a convolution is shown to require knowledge of the input function's fluctuation power spectrum. Application of the method to two systems reveals no correlation for the optical data of Akn 120, but a strong correlation for the UV data of NGC 4151, placing bounds of between 1.2 and 20 light days on the size of the line-emitting region.

Edelson, R. A.↗
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
NASA NTRS1988

The discrete correlation function: A new method for analyzing unevenly sampled variability data

A method of measuring correlation functions without interpolating in the temporal domain, the discrete correlation function, is introduced. It provides an assumption-free representation of the correlation measured in the data, and allows meaningful error estimates. This method does not produce spurious correlations at zero lag due to correlated errors. It is shown that physical interpretation of active galactic nuclei cross-correlation functions requires knowledge of the input function's fluctuation power spectrum, involves model-dependence in the form of symmetry assumptions, and must take into account intrinsic scale bias. This technique was used to find a correlation in published IUE data for NGC 4151, which indicates that the broad C IV feature emanates from a shell 15 to 75 light-days in radius, assuming spherical symmetry.

Edelson, R. A.↗
DOE OSTI2025

An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

Ideal State Reconstructor For Control System

Ideal state reconstructor is conceptual subsystem of deterministic digital control system estimating state of controlled plant periodically at discrete sampling intervals of duration T. Does not add new states, eigenvalues, or dynamics. Based on concepts described in "State-Variable Representations For Moving-Average Sampling" (MFS-28405).

Polites, Michael E.↗
NASA NTRS2003

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

Zeng, Xi-Ping↗
DOE OSTI2023

Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r -dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.

25 ENERGY STORAGE↗