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NASA NTRS1993

Semi-analytical static nonlinear structural sensitivity analysis

The paper discusses two uses of the semianalytical methods for nonlinear sensitivity analysis. First, the application to noncritical response is analyzed. It is shown that the semianalytical method is equivalent to a particular form of the overall finite difference approach. It is concluded that the difference between overall finite differences and the semianalytical approach is blurred for the case of nonlinear static response. Next, the application of the semianalytical method to calculating sensitivities of limit loads is discussed. A formulation that is easy to implement in general purpose finite element programs is derived. Three examples are used to demonstrate the application of the formulation and to explore its accuracy.

Haftka, Raphael T.↗

NASA NTRS1988

Hypercube matrix computation task

A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18).

Calalo, Ruel H.↗

NASA NTRS1988

An initial investigation into methods of computing transonic aerodynamics sensitivity coefficients

Based upon the program outlined in the modified proposal, the initial effort has concentrated on developing the quasi-analytical approach for determining aerodynamic influence coefficients. In addition, in order to keep these initial efforts computationally efficient and straightforward, it was decided to first consider only two-dimensional flow and to model the problem using the transonic small perturbation equation with surface boundary conditions applied along the slit. The small perturbation equation was selected instead of the full potential equation because it permits the capturing of important nonlinear physical phenomena while being by comparison easy to handle from a coding standpoint. Consequently, the initial objectives were: (1) investigate the feasibility of using the quasi-analytical approach for determining aerodynamic sensitivity coefficients in the transonic regime; (2) determine the accuracy of the quasi-analytical approach by comparing results to those computed using finite difference techniques; and (3) investigate efficient methods for solving the large set of equations associated with the quasi-analytical approach.

Carlson, Leland A.↗

NASA NTRS1993

An adaptive grid/Navier-Stokes methodology for the calculation of nozzle afterbody base flows with a supersonic freestream

This paper describes an adaptive grid method for base flows in a supersonic freestream. The method is based on the direct finite-difference statement of the equidistribution principle. The weighting factor is a combination of the Mach number, density, and velocity first-derivative gradients in the radial direction. Two key ideas of the method are to smooth the weighting factor by using a type of implicit smoothing and to allow boundary points to move in the grid adaptation process. An AGARD nozzle afterbody base flow configuration is used to demonstrate the performance of the adaptive grid methodology. Computed base pressures are compared to experimental data. The adapted grid solutions offer a dramatic improvement in base pressure prediction compared to solutions computed on a nonadapted grid. A total-variation-diminishing (TVD) Navier-Stokes scheme is used to solve the governing flow equations.

Williams, Morgan↗

NASA NTRS1993

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

Carpenter, Mark H.↗

NASA NTRS1994

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

Carpenter, Mark H.↗

NASA NTRS1992

Dispersion-relation-preserving schemes for computational aeroacoustics

Finite difference schemes that have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A method to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is presented. A sequence of numerical simulations is then performed.

Tam, Christopher K. W.↗

NASA NTRS1985

Investigation of chemically-reacting supersonic internal flows

This report covers work done on the research project Analysis and Computation of Internal Flow Field in a Scramjet Engine. The work is supported by the NASA Langley Research Center (Computational Methods Branch of the High-Speed Aerodynamics Division) through research grant NAG1-423. The governing equations of two-dimensional chemically-reacting flows are presented together with the global two-step chemistry model. The finite-difference algorithm used is illustrated and the method of circumventing the stiffness is discussed. The computer program developed is used to solve two model problems of a premixed chemically-reacting flow. The results obtained are physically reasonable.

Chitsomboon, T.↗

NASA NTRS1990

Algebraic grid generation with boundary orthogonality control

This paper presents a new approach in applying the blending function method to the generation of structured finite-difference meshes. It is shown that the surface equation developed by Coons (1967) can be easily adapted to generate two-dimensional meshes, and its extension to hyperspace allows the construction of three-dimensional meshes. The robust method in its basic form blends among the boundary curves/surfaces conforming to their intrinsic slopes. When parameter-controlled boundary-slope corrections are introduced, it is possible to establish varying degrees of orthogonality along the boundaries. Additional controls are made possible by moving points in the parameter space, which affects the movement of points in the physical space. The combination of these controls provides a simple and yet powerful means for exploiting the blending-function method to satisfy the needs of practical CFD applications. Results from a validation program for two-dimensions are shown for a variety of geometries.

Luh, Raymond Ching-Chung↗

NASA NTRS1991

Discretized Newton-relaxation solution of high resolution flux-difference split schemes

A method is presented for the implicit solution of high resolution flux-difference split schemes for which it is impractical to obtain the Jacobian matrix analytically. The method is used frequently in numerical schemes for solving nonlinear systems of equations, but apparently has not been used to date for approximating the Jacobian of the Roe numerical flux vectors. The method consists of obtaining a discretized Jacobian by using simple finite-differences of the flux vectors, and then using this discretized Jacobian in a Newton-relaxation solution method. The method is applied to both compressible and incompressible flows. Numerical results are presented that demonstrate the method works for both inviscid and viscous flows.

Whitfield, David L.↗

DOE OSTI2025

Material Fracturing and Failure Simulation Datasets

Fracturing is a fundamental physics phenomena with broad relevance across multiple domains, ranging from infrastructure integrity, aerospace durability, reservoir production, and seismic events. We present a diverse dataset of simulated fracture evolution and material failure generated from two numerical solvers: the phase-field method and the combined finite-discrete element method (FDEM). These solvers differ in formulation, physical fidelity, and computational efficiency. The dataset includes five materials: PBX, anisotropic shale, tungsten, aluminum, and steel. For each, phase-field simulations span 400,000 cases: 200,000 under uniaxial tension and 200,000 under biaxial tension. The computationally expensive FDEM simulations include 90,000 split evenly among PBX, shale, and tungsten under uniaxial loading. All simulations begin with randomized initial fracture patterns. Each entry includes temporal data capturing fracture propagation dynamics. This comprehensive dataset is designed to support the development of foundational or surrogate machine learning approaches for predicting material failure. While no such models are introduced here, the dataset lays a robust foundation for advancing future research and innovation in these areas.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Observing Profiles of Derived Kinematic Field Quantities Using a Network of Profiling Sites

Abstract Observations of thermodynamic and kinematic parameters associated with derivatives of the thermodynamics and wind fields, namely, advection, vorticity, divergence, and deformation, can be obtained by applying Green’s theorem to a network of observing sites. The five nodes that comprise the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) profiling network, spaced 50–80 km apart, are used to obtain measurements of these parameters over a finite region. To demonstrate the applicability of this technique at this location, it is first applied to gridded model output from the High-Resolution Rapid Refresh (HRRR) numerical weather prediction model, using profiles from the locations of ARM network sites, so that values calculated from this method can be directly compared to finite difference calculations. Good agreement is found between both approaches as well as between the model and values calculated from the observations. Uncertainties for the observations are obtained via a Monte Carlo process in which the profiles are randomly perturbed in accordance with their known error characteristics. The existing size of the ARM network is well suited to capturing these parameters, with strong correlations to model values and smaller uncertainties than a more closely spaced network, yet it is small enough that it avoids the tendency for advection to go to zero over a large area.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1973

An economical method of analyzing transient motion of gas-lubricated rotor-bearing systems.

A method of economically evaluating the hydrodynamic forces generated in a gas-lubricated tilting-pad bearing is presented. The numerical method consists of solving the case of the infinite width bearing and then converting this solution to the case of the finite bearing by accounting for end leakage. The approximate method is compared to the finite-difference solution of Reynolds equation and yields acceptable accuracy while running about one-hundred times faster. A mathematical model of a gas-lubricated tilting-pad vertical rotor systems is developed. The model is capable of analyzing a two-bearing-rotor system in which the rotor center of mass is not at midspan by accounting for gyroscopic moments. The numerical results from the model are compared to actual test data as well as analytical results of other investigators.

Falkenhagen, G. L.↗

NASA NTRS1975

Preliminary thermal-structural design and analysis of an airframe-integrated hydrogen-cooled scramjet

This paper presents the salient features of a preliminary thermal-structural design and analysis study of a hydrogen-fueled, regeneratively cooled, airframe-integrated scramjet. This three-dimensional fixed geometry scramjet concept which was developed at NASA Langley Research Center is designed to operate over a flight Mach number range from 4 to 10. The thermal-structural study was focused on a scramjet application to one concept for a hypersonic research vehicle and was based on technology developed under the NASA Hypersonic Research Engine Project. State-of-the-art analytical methods consisting of lumped system and finite difference steady-state thermal analyses and a finite element structural analysis were used. The results of the study indicated that this scramjet concept is viable from both a structural mass and cooling requirement standpoint. However, advances in material and fabrication technology for hydrogen-cooled structures appear necessary for acceptable engine life for commercial application.

Wieting, A. R.↗

NASA NTRS1977

Vector sweep

Program is numerical procedure for calculating radiation/geometrical configuration factors and/or space-environmental heat-flux histories. System can accomodate complex systems of diverse geometric shapes residing in unlimited variety of mutual shadow conditions. Basic analytical device is finite-difference employment of unit-sphere method of calculating configuration factors.

Moutrie, C. L.↗

NASA NTRS1978

Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions

A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

NASA NTRS1980

Navier-Stokes calculations with a coupled strongly implicit method. II Spline deferred-corrector solutions

The coupled strongly implicit (CSIP) method described previously is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equations. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered (equal to or less than 1000). In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

NASA NTRS1986

Steady flow past sudden expansions at large Reynolds number. I - Boundary layer solutions

A global Newton method is used to obtain accurate finite difference solutions for uniform inflows to several sudden expansion geometries, avoiding the instabilities encountered at large Reynolds numbers. Steady solutions for lambda values greater than those attained previously are obtained only if lambda is below a critical value. The presence of a singularity at this critical value renders invalid the assumptions of the boundary layer model. The results indicate that for uniform inflows and smaller values of the expansion ratio, the eddy length will no longer increase linearly with R when R becomes sufficiently large.

Milos, F. S.↗