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At least 109 records · Page 6

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DOE OSTI2022

An efficient high-order numerical solver for diffusion equations with strong anisotropy

In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. Additionally, we demonstrate the accuracy produced by the high-order scheme and develop an efficient preconditioning technique to solve the corresponding linear system, which is robust to the mesh size and anisotropy of the problem. Several numerical tests are provided to validate the accuracy and efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations

The derivation of storage explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, 16 ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been assessed using the differential equation testing code DETEST, and with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be pearl), matched while still saving two to three registers of memory.

Kennedy, Chistopher A.↗

NASA NTRS1972

Synthesis of stiffened conical shells.

The development of a method to effect the automated minimum weight design of ring and stringer stiffened shells is presented. Membrane theory is used for the shell prebuckling analysis. The buckling analysis is based upon an arbitrary shell of revolution computer program. The structural analysis includes both buckling and yielding modes of failure. The synthesis involves the coupling of an exterior penalty function with a method for the unconstrained minimization of a function comprised of a sum of squares. Results of the application of the method to the design of the Viking Aeroshell cone are presented. The least weight Viking Aeroshell appears to be an all magnesium shell with ring stiffeners of hollow circular cross section. Because the method incorporates a general shell of revolution buckling analysis, it can be readily modified and applied to the design of any axisymmetrically loaded uniformly stiffened shell of revolution for which a membrane prebuckling solution exists.

Thornton, W. A.↗

NASA NTRS1986

Impact of mismodeled idle engine performance on calculation and tracking of optimal 4-D descent trajectories

Advanced flight management systems are being developed which are capable of calculating optimal 3-D and 4-D flight trajectories for arbitrary fuel and time costs. These systems require mathematical models of airplane performance in order to compute the optimal profiles. Mismodeled idle engine characteristics can result in descent trajectories requiring excessive throttle and/or speedbrake activity in order to achieve the desired end conditions. This paper evaluates the cost and fuel penalties, trajectory variations, and flight control requirements associated with typical idle engine modeling errors for a twin-jet transport airplane. Variations in idle power setting, thrust, fuel flow, and surge bleed operation were evaluated for a cruise/descent flight segment. The results of this analysis provide insight into the penalties associated with uncertainties in idle engine performance and suggest methods of modeling which minimize these penalties.

Williams, D. H.↗

NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗

NASA NTRS1990

A balloon borne 19-GHz radiometer

The design and performance of a 19-GHz one-horn maser radiometer is discussed. The antenna is a lensed, conical horn with 3-deg angular resolution. The radiometer is stabilized by chopping against an internal cold load. A novel chopping scheme allows continual calibration of maser gain fluatuations with only a modest penalty in noise. The method of calibrating this instrument is described. The instrument has been used to map the sky with an equivalent blackbody temperature sensitivity of 1 mK per 3 x 3 deg resolution element.

Boughn, S. P.↗

NASA NTRS1991

Airfoil optimization with efficient gradient calculations

The viscous airfoil design analysis code XFOIL was extended to allow optimization using conformal mapping coefficients as design variables. The optimization technique used was the Steepest Descent method applied to a Penalty Function. The gradients of the aerodynamic variables with respect to the design variables were cheaply calculated as by-products of XFOIL's integral boundary layer Newton solver. The speed of the optimization process further increased by updating the Newton system boundary layer variables after each optimization step using the available gradient information. Two examples are presented.

Sorensen, Thomas↗

DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2004

Penalty-Based Interface Technology for Prediction of Delamination Growth in Laminated Structures

An effective interface element technology has been developed for connecting and simulating crack growth between independently modeled finite element subdomains (e.g., composite plies). This method has been developed using penalty constraints and allows coupling of finite element models whose nodes do not necessarily coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. The present interface element has been implemented in the commercial finite element code ABAQUS as a User Element Subroutine (UEL), making it easy to test the approach for a wide range of problems. The interface element technology has been formulated to simulate delamination growth in composite laminates. Thanks to its special features, the interface element approach makes it possible to release portions of the interface surface whose length is smaller than that of the finite elements. In addition, the penalty parameter can vary within the interface element, allowing the damage model to be applied to a desired fraction of the interface between the two meshes. Results for double cantilever beam DCB, end-loaded split (ELS) and fixed-ratio mixed mode (FRMM) specimens are presented. These results are compared to measured data to assess the ability of the present damage model to simulate crack growth.

Averill, Ronald C.↗

NASA NTRS1976

Evaluation of a cost-effective loads approach

A shock spectra/impedance method for loads prediction is used to estimate member loads for the Viking Orbiter, a 7800-lb interplanetary spacecraft that has been designed using transient loads analysis techniques. The transient loads analysis approach leads to a lightweight structure but requires complex and costly analyses. To reduce complexity and cost a shock spectra/impedance method is currently being used to design the Mariner Jupiter Saturn spacecraft. This method has the advantage of using low-cost in-house loads analysis techniques and typically results in more conservative structural loads. The method is evaluated by comparing the increase in Viking member loads to the loads obtained by the transient loads analysis approach. An estimate of the weight penalty incurred by using this method is presented. The paper also compares the calculated flight loads from the transient loads analyses and the shock spectra/impedance method to measured flight data.

Garba, J. A.↗

NASA NTRS1976

Evaluation of a cost-effective loads approach

A shock spectra/impedance method for loads predictions is used to estimate member loads for the Viking Orbiter, a 7800-lb interplanetary spacecraft that has been designed using transient loads analysis techniques. The transient loads analysis approach leads to a lightweight structure but requires complex and costly analyses. To reduce complexity and cost, a shock spectra/impedance method is currently being used to design the Mariner Jupiter Saturn spacecraft. This method has the advantage of using low-cost in-house loads analysis techniques and typically results in more conservative structural loads. The method is evaluated by comparing the increase in Viking member loads to the loads obtained by the transient loads analysis approach. An estimate of the weight penalty incurred by using this method is presented. The paper also compares the calculated flight loads from the transient loads analyses and the shock spectra/impedance method to measured flight data.

Garba, J. A.↗

DOE OSTI2022

An IIPG-based finite element framework in MOOSE for modeling fiber reinforced composite failure governed by extrinsic cohesive laws

Fiber reinforced composites (FRC) are widely applied to many important engineering structures such as silicon carbide ceramic matrix composite (SiC CMC) of nuclear fuel claddings. Many material and structure failures are initiated at the interface between two distinctive materials, such as the debonding of interfaces of matrix/fiber of composites or bulk matrix/inclusion in metals at micro-scales. Accurate and robust modeling of these interface failures is critical to the development of novel material and structure with improved functionality. This paper presents a discontinuous Galerkin (DG) finite element method based on the Incomplete Interior Penalty scheme and its implementation in MOOSE for modeling material interface behaviors. The proposed method naturally accommodates important extrinsic cohesive zone material models and is capable of modeling the failures of material interfaces across which material properties are highly distinctive. We demonstrate a good performance of the proposed method using single fiber and multiple fiber debonding problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1986

New methodology for shaft design based on life expectancy

The design of power transmission shafting for reliability has not historically received a great deal of attention. However, weight sensitive aerospace and vehicle applications and those where the penalties of shaft failure are great, require greater confidence in shaft design than earlier methods provided. This report summarizes a fatigue strength-based, design method for sizing shafts under variable amplitude loading histories for limited or nonlimited service life. Moreover, applications factors such as press-fitted collars, shaft size, residual stresses from shot peening or plating, corrosive environments can be readily accommodated into the framework of the analysis. Examples are given which illustrate the use of the method, pointing out the large life penalties due to occasional cyclic overloads.

Loewenthal, S. H.↗

NASA NTRS1979

A cubic extended interior penalty function for structural optimization

This paper describes an optimization procedure for the minimum weight design of complex structures. The procedure is based on a new cubic extended interior penalty function (CEIPF) used with the sequence of unconstrained minimization technique (SUMT) and Newton's method. The Hessian matrix of the penalty function is approximated using only constraints and their derivatives. The CEIPF is designed to minimize the error in the approximation of the Hessian matrix, and as a result the number of structural analyses required is small and independent of the number of design variables. Three example problems are reported. The number of structural analyses is reduced by as much as 50 per cent below previously reported results.

Prasad, B.↗

NASA NTRS1988

Stabilization of computational procedures for constrained dynamical systems

A new stabilization method of treating constraints in multibody dynamical systems is presented. By tailoring a penalty form of the constraint equations, the method achieves stabilization without artificial damping and yields a companion matrix differential equation for the constraint forces; hence, the constraint forces are obtained by integrating the companion differential equation for the constraint forces in time. A principal feature of the method is that the errors committed in each constraint condition decay with its corresponding characteristic time scale associated with its constraint force. Numerical experiments indicate that the method yields a marked improvement over existing techniques.

Park, K. C.↗

NASA NTRS1978

A new formulation for the epsilon method applied to the minimum-time-to-climb problem

Balakrishnan's epsilon technique is used to compute minimum-time profiles for the F-104 airplane. This technique differs from the classical gradient method in that a quadratic penalty on the error in satisfying the equation of motion is included in the cost function to be minimized as a means of eliminating the requirement of satisfying the equations of motion. Although the number of unknown independent functions is increased to include the state variables, the evaluation of the gradient of the cost function is simplified, resulting in considerable computational savings, thereby making it appear feasible to use the epsilon method for real-time application.

Taylor, L. W., Jr.↗

NASA NTRS1979

A multi-disciplinary approach to structural design for stochastic loads

The development of aircraft gust design techniques is reviewed with emphasis on those techniques applicable to large scale multidisciplinary closed-loop optimization methods. An overall view is presented of the optimization methodology utilized. An analysis is presented wherein the bivariate normal distribution function for a particular loading condition is considered. By use of maximization techniques, functions are derived for stress components along equal probability contours which allow for directionality and auto-correlation effects to be considered. These functions are then applied to the problem being considered and the effects on the structural sizing and weight penalties evaluated against more conventional methods.

Gross, D. W.↗

NASA NTRS1984

Penalty function finite element analysis of steady viscous incompressible flow in rotating coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuile flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimenal measurements.

Rosen, M. C.↗