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At least 1,711 records · Page 95
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS2000

Kinetics of DSB rejoining and formation of simple chromosome exchange aberrations

PURPOSE: To investigate the role of kinetics in the processing of DNA double strand breaks (DSB), and the formation of simple chromosome exchange aberrations following X-ray exposures to mammalian cells based on an enzymatic approach. METHODS: Using computer simulations based on a biochemical approach, rate-equations that describe the processing of DSB through the formation of a DNA-enzyme complex were formulated. A second model that allows for competition between two processing pathways was also formulated. The formation of simple exchange aberrations was modelled as misrepair during the recombination of single DSB with undamaged DNA. Non-linear coupled differential equations corresponding to biochemical pathways were solved numerically by fitting to experimental data. RESULTS: When mediated by a DSB repair enzyme complex, the processing of single DSB showed a complex behaviour that gives the appearance of fast and slow components of rejoining. This is due to the time-delay caused by the action time of enzymes in biomolecular reactions. It is shown that the kinetic- and dose-responses of simple chromosome exchange aberrations are well described by a recombination model of DSB interacting with undamaged DNA when aberration formation increases with linear dose-dependence. Competition between two or more recombination processes is shown to lead to the formation of simple exchange aberrations with a dose-dependence similar to that of a linear quadratic model. CONCLUSIONS: Using a minimal number of assumptions, the kinetics and dose response observed experimentally for DSB rejoining and the formation of simple chromosome exchange aberrations are shown to be consistent with kinetic models based on enzymatic reaction approaches. A non-linear dose response for simple exchange aberrations is possible in a model of recombination of DNA containing a DSB with undamaged DNA when two or more pathways compete for DSB repair.

DNA Damage↗
NASA NTRS1977

Control logic to track the outputs of a command generator or randomly forced target

A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).

Trankle, T. L.↗
NASA NTRS1984

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

Ehlers, F. E.↗
NASA NTRS1976

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Bielawa, R. L.↗
NASA NTRS1986

Solvability condition for needle crystals at large undercooling in a nonlocal model of solidification

It is explicitly shown that, in a realistic model of diffusion-controlled dendritic solidification, Ivantsov's continuous family of steady-state needle crystals is destroyed by the addition of surface tension. The starting point is in the exact integro-differential equation for the one-sided model, in two dimensions, in a moving frame of reference. In the limit of large undercooling, where the range of the diffusion field is much smaller than the radius of curvature of the tip of the needle, this problem is reduced to a linear, inhomogeneous differential equation of infinite order. A solvability condition for this equation is derived and it is shown that solutions cease to exist for arbitrarily small but finite isotropic surface tension.

Caroli, B.↗
NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗
DOE OSTI2025

Coupling to rotational manifolds to improve gas-phase pump–probe spectroscopic models

The physical picture of gas-phase optical transitions is normally presented as an isolated two-level system balanced by upward and downward processes. Isolated models assume a phenomenological treatment of collisional dephasing but do not strictly account for collisional population exchange with the rotational baths. While this assumption is valid under low-intensity conditions, where excitation is rate-limiting, isolated models can deviate from Beer’s Law at sufficient pressures and monochromatic intensities when both collisional broadening and power broadening are comparable to (or greater than) lifetime broadening, which are not uncommon conditions for cavity enhanced spectroscopies in the mid-IR spectral range. Although this problem has been addressed by rate-equation models for linear absorption measurements, a general treatment for multi-level quantum mechanical models suitable for non-linear absorption measurements (two-photon/two-color/pump–probe) is lacking. Isolated models require physical parameter inputs that disagree with expected values by at least an order of magnitude. These non-physical models undermine the ability to predict non-linear signal strengths under untested conditions and thereby limit the potential to optimize the sensitivity of non-linear spectroscopies and to expand their analytical applications (e.g., new analytes and/or buffer gases, changes in cavity free-spectral-range, changes in intracavity powers or wavelengths, and accurate investigation of physical phenomena). In this study, we derive bath-coupled models for gaseous pump–probe spectroscopy by application of the quantum Lindblad equation and detailed balance. Bath-coupled models are shown to fit data consistently across variations in intensity and agree with all physically expected values.

Cavity ring-down spectroscopy↗
NASA NTRS1979

Eigenvalues and eigenvectors for hybrid coordinate equations of motion for flexible spacecraft

The eigenvalues and eigenvectors of a system of linear time-invariant equations describing the attitude motion of flexible spacecraft in terms of hybrid coordinates are characterized in terms of literal expressions by using peculiar properties of the system parameter matrices. For the undamped case the eigenvalues are localized in terms of inertial matrices and modal parameters. A procedure for calculating the eigenvectors is proposed whereby the eigenproblem associated with the original system of dimension (2N + 6) is reduced to that of a symmetric and positive definite matrix of dimension N with the zero-damping assumption. The eigenvectors for systems of large dimension are obtained explicitly in terms of a 3x1 matrix whose elements are available from a system of three algebraic equations, which is provided.

Ohkami, Y.↗
NASA NTRS1986

On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

Gunzburger, M. D.↗
NASA NTRS1989

Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.

Burkhart, G. R.↗
NASA NTRS1992

Mapping unstructured grid computations to massively parallel computers

Investigated here is this mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time two fold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases.

Hammond, Steven Warren↗
NASA NTRS1990

Cell averaging Chebyshev methods for hyperbolic problems

A cell averaging method for the Chebyshev approximations of first order hyperbolic equations in conservation form is described. Formulas are presented for transforming between pointwise data at the collocation points and cell averaged quantities, and vice-versa. This step, trivial for the finite difference and Fourier methods, is nontrivial for the global polynomials used in spectral methods. The cell averaging methods presented are proven stable for linear scalar hyperbolic equations and present numerical simulations of shock-density wave interaction using the new cell averaging Chebyshev methods.

Wei, Cai↗
NASA NTRS1990

Linear iterative solvers for implicit ODE methods

The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.

Saylor, Paul E.↗
NASA NTRS1971

A variable-step-size robust delta modulator.

Description of an analytically obtained optimum adaptive delta modulator-demodulator configuration. The device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov-Gaussian source. The optimum system is compared, using computer simulations, with a linear delta modulator and an enhanced Abate delta modulator. In addition, the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The highly nonlinear equations obtained for the optimum transmitter and receiver are approximated by piecewise-linear equations in order to obtain system equations which can be transformed into hardware. The derivation of the experimental system is presented.

Song, C. L.↗
NASA NTRS1986

Linearly polarized magnetic fluctuations at comet Giacobini-Zinner

The fully electromagnetic linear Vlasov dispersion equation for instabilities in a homogeneous, magnetized plasma is solved. Parameters appropriate to conditions observed during the ICE encounter with comet Giacobini-Zinner are used to study the polarization of electromagnetic instabilities driven by the relative streaming of two ion components. If the ion/ion relative drift is near the Alfven speed, the associated long-wavelength modes may be approximately linearly polarized at relatively small angles of propagation with respect to the magnetic field. The relatively inhomogeneous plasma background of the comet may impose such oblique propagation, so that this result provides an alternate explanation to the observations of linearly polarized waves near the comet.

Gary, S. Peter↗
NASA NTRS1992

Stability of a class of interconnected evolution systems

Stability conditions for a class of interconnected systems modeled by linear abstract evolution equations and a memoryless nonlinearity are derived. These conditions are stated in terms of the passivity of each of the subsystems and can be considered as a partial generalization of the hyperstability theorem. A Liapunov function approach is used in the proof without requiring the positive definiteness of the Liapunov function. Application to the robustness analysis of the infinite-dimensional linear quadratic regulator is also discussed.

Wen, John T.↗