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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Efficient and Robust Weighted Least-Squares Cell-Average Gradient Construction Methods for the Simulation of Scramjet Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches designed to minimize the number of cells used to augment/stabilize the least-squares stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cellaverage gradients is described. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet engine flowpath is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the preferred gradient method for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗
NASA NTRS1986

Transformation of two and three-dimensional regions by elliptic systems

Grid smoothing and orthogonalization procedures were developed and implemented in the construction of two and three dimensional grids. The procedures are based on the variational methods of grid generation. The two-dimensional examples were computed using the MSU IRIS Graphics Workstation. It was demonstrated that the elliptic grid generation equations, with arbitrary forcing functions, can be solved, in their variational formulation, using a gradient method. Since gradient methods have a global convergence property, the divergence problems often encountered when using SOR iterative methods can be avoided. It is not to be concluded, however, that SOR methods should be abandoned, since gradient methods tend to converge very slowly. In fact, slow convergence was the major problem encountered in the three-dimensional grids. Further progress was made on the continuing effort to develop conservative interpolation formulas for overlapping grids.

Mastin, C. Wayne↗
NASA NTRS1972

A modified secant method for unconstrained minimization

A gradient-secant algorithm for unconstrained optimization problems is presented. The algorithm uses Armijo gradient method iterations until it reaches a region where the Newton method is more efficient, and then switches over to a secant form of operation. It is concluded that an efficient method for unconstrained minimization has been developed, and that any convergent minimization method can be substituted for the Armijo gradient method.

Polak, E.↗
NASA NTRS1986

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

Christodoulou, C. G.↗
NASA NTRS1988

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Freund, Roland↗
NASA NTRS2014

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties

Meshes↗
NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗
NASA NTRS1988

Optimization with artificial neural network systems - A mapping principle and a comparison to gradient based methods

General formulae for mapping optimization problems into systems of ordinary differential equations associated with artificial neural networks are presented. A comparison is made to optimization using gradient-search methods. The performance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient-search. Settling time was investigated for a more complicated optimization problem using computer simulations. The problem was a simplified version of a problem in medical imaging: determining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.

Leong, Harrison Monfook↗
NASA NTRS1983

A robust Feasible Directions algorithm for design synthesis

A nonlinear optimization algorithm is developed which combines the best features of the Method of Feasible Directions and the Generalized Reduced Gradient Method. This algorithm utilizes the direction-finding sub-problem from the Method of Feasible Directions to find a search direction which is equivalent to that of the Generalized Reduced Gradient Method, but does not require the addition of a large number of slack variables associated with inequality constraints. This method provides a core-efficient algorithm for the solution of optimization problems with a large number of inequality constraints. Further optimization efficiency is derived by introducing the concept of infrequent gradient calculations. In addition, it is found that the sensitivity of the optimum design to changes in the problem parameters can be obtained using this method without the need for second derivatives or Lagrange multipliers. A numerical example is given in order to demonstrate the efficiency of the algorithm and the sensitivity analysis.

Vanderplaats, G. N.↗
NASA NTRS1991

Applications of the conjugate gradient FFT method in scattering and radiation including simulations with impedance boundary conditions

The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. The boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. A general full wave analysis of 2-D and 3-D rectangular grooves and cavities is presented which will also serve as a reference for future work.

Barkeshli, Kasra↗
NASA NTRS1999

A Single-Lap Joint Adhesive Bonding Optimization Method Using Gradient and Genetic Algorithms

A natural process for any engineer, scientist, educator, etc. is to seek the most efficient method for accomplishing a given task. In the case of structural design, an area that has a significant impact on the structural efficiency is joint design. Unless the structure is machined from a solid block of material, the individual components which compose the overall structure must be joined together. The method for joining a structure varies depending on the applied loads, material, assembly and disassembly requirements, service life, environment, etc. Using both metallic and fiber reinforced plastic materials limits the user to two methods or a combination of these methods for joining the components into one structure. The first is mechanical fastening and the second is adhesive bonding. Mechanical fastening is by far the most popular joining technique; however, in terms of structural efficiency, adhesive bonding provides a superior joint since the load is distributed uniformly across the joint. The purpose of this paper is to develop a method for optimizing single-lap joint adhesive bonded structures using both gradient and genetic algorithms and comparing the solution process for each method. The goal of the single-lap joint optimization is to find the most efficient structure that meets the imposed requirements while still remaining as lightweight, economical, and reliable as possible. For the single-lap joint, an optimum joint is determined by minimizing the weight of the overall joint based on constraints from adhesive strengths as well as empirically derived rules. The analytical solution of the sin-le-lap joint is determined using the classical Goland-Reissner technique for case 2 type adhesive joints. Joint weight minimization is achieved using a commercially available routine, Design Optimization Tool (DOT), for the gradient solution while an author developed method is used for the genetic algorithm solution. Results illustrate the critical design variables as a function of adhesive properties and convergences of different joints based on the two optimization methods.

Smeltzer, Stanley S., III↗
NASA NTRS1987

Experience in grid optimization

Two optimization methods for solving a variational problem in grid generation are described and evaluated. The smoothness, cell volumes, and orthogonality of the variational integrals are examined. The Jacobi-Newton iterative method is compared to the Fletcher-Reeves conjugate gradient method. It is observed that a combination of the Jacobi-Newton iteration and the direct solution of the variational problem produces an algorithm which is easy to program and requires less storage and computer time/iteration than the conjugate gradient method.

Mastin, C. W.↗
NASA NTRS1973

Optimal control of a variable spin speed CMG system for space vehicles

Many future NASA programs require very high accurate pointing stability. These pointing requirements are well beyond anything attempted to date. This paper suggests a control system which has the capability of meeting these requirements. An optimal control law for the suggested system is specified. However, since no direct method of solution is known for this complicated system, a computation technique using successive approximations is used to develop the required solution. The method of calculus of variations is applied for estimating the changes of index of performance as well as those constraints of inequality of state variables and terminal conditions. Thus, an algorithm is obtained by the steepest descent method and/or conjugate gradient method. Numerical examples are given to show the optimal controls.

Liu, T. C.↗
NASA NTRS2004

Putting Priors in Mixture Density Mercer Kernels

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Srivastava, Ashok N.↗
NASA NTRS2005

An Ensemble Approach to Building Mercer Kernels with Prior Information

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Srivastava, Ashok N.↗
NASA NTRS1999

A Novel Method Of Gradient Forming and Fluid Manipulation in Reduced Gravity Environments

The use of magnetic fields to control the motion and position of non-conducting liquids has received growing interest in recent times. The possibility of using the forces exerted by a nonuniform magnetic field on a ferrofluid to not only achieve fluid manipulation but also to actively control fluid motion makes it an attractive candidate for applications such as heat transfer in space systems. Terrestrial heat transfer equipment often relies on the normal gravitational force to hold liquid in a desired position or to provide a buoyant force to enhance the heat transfer rate. The residual gravitational force present in a space environment may no longer serve these useful functions and other forces, such as surface tension, can play a significant role in determining heat transfer rates. Although typically overwhelmed by gravitational forces in terrestrial applications, the body force induced in a ferrofluid by a nonuniform magnetic field can help to achieve these objectives in a microgravity environment. This paper will address the fluid manipulation aspect and will comprise of results from model fluid experiments and numerical modeling of the problem. Results from a novel method of forming concentration gradients that are applicable to low gravity applications will be presented. The ground based experiments are specifically tailored to demonstrate the magnetic manipulation capability of a ferrofluid and show that gravitational effects can be countered in carefully designed systems. The development of governing equations for the system will be presented along with a sampling of numerical results.

Ramachandran N.↗