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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Wall-Modeled Large Eddy Simulation Method for Unstructured-Grid Navier-Stokes Solvers

This paper reports on the implementation and assessment of a Wall-Modeled Large-Eddy Simulation (WMLES) methodology in an unstructured-grid, node-centered flow solver, FUN3D that is developed and supported at the NASA Langley Research Center. Finite-volume (FV) and finite-element (FE) discretization schemes considered in the study provide formal second-order spatial accuracy. Large-Eddy Simulations (LES) resolve large-scale turbulent-flow features and filter out small-scale effects using the Vreman subgrid-scale model. At solid-wall boundaries, a shear-stress model is employed to provide a proper boundary-flux closure. The nonlinear equations are integrated in time using either an optimized backward difference formula or an implicit multistage Runge-Kutta temporal scheme. The implicit equations at each time step are solved by strong nonlinear iteration schemes. WMLES demonstrations are shown for two high-lift configurations, namely, the McDonnell Douglas 30P30N multielement airfoil and a NASA High-Lift Common Research Model. Results show that the WMLES approaches implemented in the FV and FE discretization methods produce consistent solutions and are capable of capturing key aerodynamic characteristics and flow structures for high-lift configurations at a wide range of angles of attack including maximum-lift conditions. In the 30P30N example, correct trends in the variations of integrated aerodynamic forces and moments, surface pressure distributions, and boundary-layer profiles are captured as the Reynolds number is increased.

CFD; turbulence modeling; High-Lift flow simulatio↗
NASA NTRS1985

A Lagrange-D'Alembert formulation of the equations of motion of a helicopter carrying an externally suspended load

The exact nonlinear equations of motion are derived for a helicopter with an extenal load suspended by fore and aft, rigid-link cables. Lagrange's form of D'Alembert's principle is used. Ten degrees of freedom are necessary to represent the motion of this system in an inertial reference frame: six for the helicopter relative to inertial space and four for the load relative to the helicopter.

Weber, J. M.↗
NASA NTRS1990

Parallel homotopy curve tracking on a hypercube

An investigation is conducted to find good parallel algorithms for solving systems of nonlinear equations using probability-one homotopy methods. Particular attention is paid to algorithms for the hypercube. Methods for one of the most computationally expensive steps of the homotopy approach, the computation of the kernel of the Jacobian matrix of the homotopy map, are studied. General nonlinear systems of equations with small and dense Jacobian matrices are considered, however, polynomial systems are not, since their structure leads to different strategies for parallelism. The mathematics behind the homotopy algorithm is summarized and the use of orthogonal factorizations is discussed. Parallel algorithms for orthogonal factorizations and triangular system solving are described. Computational results are presented and discussed.

Chakraborty, A.↗
DOE OSTI2022

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Finally, several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

The barotropic normal modes in certain shear flows and the traveling waves in the atmosphere

It is shown analytically and numerically that in certain shear flows the linearized nondivergent barotropic vorticity equation has a limited number of neutral normal modes. The latitudinal structures of these shear flows can be expressed as polynomials of the sine of latitude. The first few such shear flows resemble the gross features of the zonal winds in the atmosphere of the earth at different times and altitudes. The spatial structures of the neutral normal modes in these shear flows are spherical harmonics, and, as a consequence, these modes are also the exact solutions of the fully nonlinear equation because the nonlinear interaction term vanishes identically. The spatial structures of the observed 5-, 4-, 2-, and 16-day free traveling waves in the atmosphere are often identified with the spherical harmonics with indices of (m, n) = ( 1, 2), (2, 3), (3, 3), and ( 1, 4), which are known previously as the neutral normal modes of the nondivergent barotropic vorticity equation in a motionless background state. Our results could explain why these free traveling waves can survive the shearing effects of zonal flows that are far different from rest because these spherical harmonics are also normal modes in certain shear flows that resemble the observations of the atmosphere.

Chen, Ping↗
NASA NTRS1978

Liquid jet impingement normal to a disk in zero gravity

An experimental and analytical investigation was conducted to determine the free surface shapes of circular jets impinging normal to sharp-edged disks in zero gravity. Experiments conducted in a zero gravity drop tower yielded three distinct flow patterns which were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted indicating regions where viscous forces were not significant when computing free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane. The resulting nonlinear equations were solved numerically and comparisons were made with the experimental data for the inertia dominated regime.

Labus, T. L.↗
NASA NTRS1974

The application of MINIQUASI to thermal program boundary and initial value problems

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Source record↗
NASA NTRS1992

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Hanson, R. J.↗
NASA NTRS2020

Application of Quasi-Static Modal Analysis to an Orion Multi-Purpose Crew Vehicle Test

Bolted structural joints often exhibit load-dependent stiffness and energy dissipation that leads to nonlinear, amplitude dependent frequency and damping in the structure. As an alternative to direct integration of the nonlinear equations of motion, quasi-static modal analysis (QSMA) determines the dependence of frequency and damping on response amplitude using loading behavior from nonlinear static analyses. QSMA has previously been demonstrated to substantially reduce computational cost and maintain accuracy relative to full nonlinear dynamic simulation. This work explores the applicability of QSMA to a complex, large-scale aerospace structure. QSMA is employed to analyze a nonlinear model of test hardware developed to support the Orion Multi-Purpose Crew Vehicle program, which exhibited nonlinear behavior during dynamic testing at flight-like load levels. In addition to the extraction of amplitude-dependent frequency and damping curves, a Bouc-Wen hysteresis model was used in conjunction with the quasi-static results to develop nonlinear, uncoupled, time-domain modal equations of motion for the structure. Excellent agreement was observed between the reduced and full-order nonlinear models, encouraging future employment of QSMA to support accurate and efficient model reduction of structures with bolted joint nonlinearities.

QSMA↗
NASA NTRS1988

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

Peterson, Lee D.↗
NASA NTRS1994

Multilevel algorithms for nonlinear optimization

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Alexandrov, Natalia↗
NASA NTRS1983

Estimation of delays and other parameters in nonlinear functional differential equations

A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

Banks, H. T.↗
NASA NTRS2010

Forces Associated with Nonlinear Nonholonomic Constraint Equations

A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the point of application. This result is a consequence of expressing constraint equations in terms of dot products of vectors rather than in the usual way, which is entirely in terms of scalars and matrices. The constraint forces in vector form are used together with two new analytical approaches for deriving equations governing motion of a system subject to such constraints. If constraint forces are of interest they can be brought into evidence in explicit dynamical equations by employing the well-known nonholonomic partial velocities associated with Kane's method; if they are not of interest, equations can be formed instead with the aid of vectors introduced here as nonholonomic partial accelerations. When the analyst requires only the latter, smaller set of equations, they can be formed directly; it is not necessary to expend the labor to form the former, larger set first and subsequently perform matrix multiplications.

Roithmayr, Carlos M.↗
DOE OSTI2022

Development and Analysis of Optimal Multilevel Solvers on Advanced Computers. Final Report

Constrained optimization in the context of time dependent, partial differential equations (PDE) leads to a symmetric, block-tridiagonal system of nonlinear equations that must be solved repeatedly in an iterative solution strategy. The blocks represent spatial discretization, while the connection between the blocks represents a forward and backward integration in time. The focus of this project is to apply a parallel-in-time (PiT) solution technique to the large block-triangular system.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Predicting Ecologically Important Vegetation Variables from Remotely Sensed Optical/Radar Data Using Neural Networks

A number of satellite sensor systems will collect large data sets of the Earth's surface during NASA's Earth Observing System (EOS) era. Efforts are being made to develop efficient algorithms that can incorporate a wide variety of spectral data and ancillary data in order to extract vegetation variables required for global and regional studies of ecosystem processes, biosphere-atmosphere interactions, and carbon dynamics. These variables are, for the most part, continuous (e.g. biomass, leaf area index, fraction of vegetation cover, vegetation height, vegetation age, spectral albedo, absorbed photosynthetic active radiation, photosynthetic efficiency, etc.) and estimates may be made using remotely sensed data (e.g. nadir and directional optical wavelengths, multifrequency radar backscatter) and any other readily available ancillary data (e.g., topography, sun angle, ground data, etc.). Using these types of data, neural networks can: 1) provide accurate initial models for extracting vegetation variables when an adequate amount of data is available; 2) provide a performance standard for evaluating existing physically-based models; 3) invert multivariate, physically based models; 4) in a variable selection process, identify those independent variables which best infer the vegetation variable(s) of interest; and 5) incorporate new data sources that would be difficult or impossible to use with conventional techniques. In addition, neural networks employ a more powerful and adaptive nonlinear equation form as compared to traditional linear, index transformations, and simple nonlinear analyses. These neural networks attributes are discussed in the context of the authors' investigations of extracting vegetation variables of ecological interest.

Kimes, Daniel S.↗