Search NASA⌕ Search

SEARCH · Search NASA

Results for “RELAXATION METHOD”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Accelerated solution of the steady Euler equations

The present paper is concerned with two methods for the accelerated solution of the steady Euler equations. One method makes use of a second-order embedding to facilitate the derivation of the relaxation solution of the steady equations of motion, while the other method employs a multile-gridding concept to accelerate the convergence of a simple, explicit, time-marching scheme applied to the unsteady equations. It is pointed out that the surrogate equation technique provides a means for formulating problems involving the full steady Euler equations in such a way as to allow the use of relaxation solution procedures. It is, therefore, possible to solve either irrotational or rotational flow problems spanning the entire spectrum of subsonic, transonic, and supersonic conditions. The solutions can be obtained without an employement of either derived dependent variables, semidirect methods, or an unsteady formulation.

Johnson, G. M.↗
NASA NTRS1989

Application of multi-grid methods for solving the Navier-Stokes equations

This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Demuren, A. O.↗
NASA NTRS1989

Application of multi-grid methods for solving the Navier-Stokes equations

The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Demuren, A. O.↗
NASA NTRS1972

Energy distribution among reaction products. VI - F + H2, D2.

Study of the F + H2 reaction, which is of special theoretical interest since it is one of the simplest examples of an exothermic chemical reaction. The FH2 system involves only 11 electrons, and the computation of a potential-energy hypersurface to chemical accuracy may now be within the reach of ab initio calculations. The 'arrested relaxation' variant of the infrared chemiluminescence method is used to obtain the initial vibrational, rotational and translational energy distributions in the products of exothermic reactions.

Polanyi, J. C.↗
NASA NTRS1984

Development of a simplified procedure for cyclic structural analysis

Development was extended of a simplified inelastic analysis computer program (ANSYMP) for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects can be calculated on the basis of stress relaxation at constant strain, creep at constant stress, or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials, and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite-element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite-element analysis.

Kaufman, A.↗
NASA NTRS1985

A survey of unified constitutive theories

The state of the art of time temperature dependent elastic viscoplastic constitutive theories which are based on the unified approach werre assessed. This class of constitutive theories is characterized by the use of kinetic equations and internal variables with appropriate evolutionary equations for treating all aspects of inelastic deformation including plasticity, creep, and stress relaxation. More than 10 such unified theories which are shown to satisfy the uniqueness and stability criteria imposed by Drucker's postulate and Ponter's inequalities are identified. The theories are compared for the types of flow law, kinetic equation, evolutionary equation of the internal variables, and treatment of temperature dependence. The similarities and differences of these theories are outlined in terms of mathematical formulations and illustrated by comparisons of theoretical calculations with experimental results which include monotonic stress-strain curves, cyclic hysteresis loops, creep and stress relaxation rates, and thermomechanical loops. Numerical methods used for integrating these stiff time temperature dependent constitutive equations are reviewed.

Chan, K. S.↗
NASA NTRS1985

Mantle viscosity, J2 and the nontidal acceleration of Earth rotation

Recent interpretations of laser ranging for the LAGEOS satellite have rather conclusively established that the observed acceleration in the node of its orbit is just that expected to exist as a residual effect of the last deglaciation event which ended about 6000 years ago. The nontidal acceleration of rotation would be rather different than that observed if there were any significant melting of high latitude continental ice masses currently ongoing. The sensitivity of the expected nontidal acceleration to variations of several elements of the radial viscoelastic structure of the planet is explored using a new normal mode method for the computation of viscoelastic relaxation spectra. These calculations establish that the most important sensitivity is to variations in the mantle viscosity profile. Although the predicted nontidal acceleration does depend upon lithospheric thickness and on the elastic component of the radial structure, the dependence on these components of the structure is much weaker than it is upon mantle viscosity. The observed J sub 2 is therefore a particularly useful determinant of radial variations in the latter parameter.

Peltier, W. R.↗
NASA NTRS1988

Numerical simulation of the vortical flow over a round-edged double-delta wing

Simulations of three-dimensional vortical flows over a thin double-delta wing with an aspect ratio of 2.05 have been performed. Steady-state solutions to the unsteady incompressible Navier-Stokes equations are obtained using a new implicit upwind-relaxation finite-difference scheme. The method is second-order accurate spatially and naturally dissipative. Numerical results indicate that key features of both vortical interaction and vortex breakdown are successfully simulated. The computed lift coefficients and lateral trajectories of the vortical cores are in good agreement with the experimental data.

Hsu, C.-H.↗
NASA NTRS1990

Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows

A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.

Hsu, C.-H.↗
NASA NTRS1990

Numerical study of vortical flow over a sideslipping delta wing

The three-dimensional vortical viscous flow past a sideslipping delta wing at a high angle of attack is numerically investigated. A computational method for calculating low-speed viscous flowfields is developed. The time-iterative method uses an implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. An algebraic turbulence model is implemented to account for the eddy viscosity. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. Computed results are compared with experimental data.

Hsu, C.-H.↗
NASA NTRS1990

A user guide for the EMTAC-MZ CFD code

The computer code (EMTAC-MZ) was applied to investigate the flow field over a variety of very complex three-dimensional (3-D) configurations across the Mach number range (subsonic, transonic, supersonic, and hypersonic flow). In the code, a finite volume, multizone implementation of high accuracy, total variation diminishing (TVD) formulation (based on Roe's scheme) is used to solve the unsteady Euler equations. In the supersonic regions of the flow, an infinitely large time step and a space-marching scheme is employed. A finite time step and a relaxation or 3-D approximate factorization method is used in subsonic flow regions. The multizone technique allows very complicated configurations to be modeled without geometry modifications, and can easily handle combined internal and external flow problems. An elliptic grid generation package is built into the EMTAC-MZ code. To generate the computational grid, only the surface geometry data are required. Results obtained for a variety of configurations, such as fighter-like configurations (F-14, AVSTOL), flow through inlet, multi-bodies (shuttle with external tank and SRBs), are reported and shown to be in good agreement with available experimental data.

Szema, Kuo-Yen↗
NASA NTRS1994

Progress in modeling atmospheric propagation of sonic booms

The improved simulation of sonic boom propagation through the real atmosphere requires greater understanding of how the transient acoustic pulses popularly termed sonic booms are affected by humidity and turbulence. A realistic atmosphere is invariably somewhat turbulent, and may be characterized by an ambient fluid velocity v and sound speed c that vary from point to point. The absolute humidity will also vary from point to point, although possibly not as irregularly. What is ideally desired is a relatively simple scheme for predicting the probable spreads in key sonic boom signature parameters. Such parameters could be peak amplitudes, rise times, or gross quantities obtainable by signal processing that correlate well with annoyance or damage potential. The practical desire for the prediction scheme is that it require a relatively small amount of knowledge, possibly of a statistical nature, concerning the atmosphere along, the propagation path from the aircraft to the ground. The impact of such a scheme, if developed, implemented, and verified, would be that it would give the persons who make planning decisions a tool for assessing the magnitude of environmental problems that might result from any given overflight or sequence of overflights. The technical approach that has been followed by the author and some of his colleagues is to formulate a hierarchy of simple approximate models based on fundamental physical principles and then to test these models against existing data. For propagation of sonic booms and of other types of acoustic pulses in nonturbulent model atmospheres, there exists a basic overall theoretical model that has evolved as an outgrowth of geometrical acoustics. This theoretical model depicts the sound as propagating within ray tubes in a manner analogous to sound in a waveguide of slowly varying cross-section. Propagation along the ray tube is quasi-one-dimensional, and a wave equation for unidirectional wave propagation is used. A nonlinear term is added to this equation to account for nonlinear steepening, and the formulation has been carried through to allow for spatially varying sound speed, ambient density, and ambient wind velocities. The model intrinsically neglects diffraction, so it cannot take into account what has previously been mentioned in the literature as possibly important mechanisms for turbulence-related distortion. The model as originally developed could predict an idealized N-waveform which often agrees with data in terms of peak amplitude and overall positive phase duration. It is possible, moreover, to develop simple methods based on the physics of relaxation processes for incorporating molecular relaxation into the quasi-one-dimensional model of nonlinear propagation along ray tubes.

Pierce, Allan D.↗
NASA NTRS1996

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Zheng, Xiaoqing↗
NASA NTRS1998

Structure of Boron Nitride Nanotubes: Tube Closing Vs. Chirality

The structure of boron nitride nanotubes is investigated using a generalized tight-binding molecular dynamics method. It is shown that dynamic relaxation results in a wavelike or "rippled" surface in which the B atoms rotate inward and the N atoms move outward, reminiscent of the surface relaxation of the III-V semiconductors. More importantly, the three different morphologies of the tube closing with flat, conical and amorphous ends, as observed in experiments, are shown to be directly related to the tube chiralities. The abundance of flat end tubes observed in experiments is, thus, shown to be an indication of the greater stability of "zig-zag" BN tubes over the "arm-chair" tubes under experimental conditions.

Srivastava, Deepak↗
NASA NTRS2010

Robust Mosaicking of Stereo Digital Elevation Models from the Ames Stereo Pipeline

Robust estimation method is proposed to combine multiple observations and create consistent, accurate, dense Digital Elevation Models (DEMs) from lunar orbital imagery. The NASA Ames Intelligent Robotics Group (IRG) aims to produce higher-quality terrain reconstructions of the Moon from Apollo Metric Camera (AMC) data than is currently possible. In particular, IRG makes use of a stereo vision process, the Ames Stereo Pipeline (ASP), to automatically generate DEMs from consecutive AMC image pairs. However, the DEMs currently produced by the ASP often contain errors and inconsistencies due to image noise, shadows, etc. The proposed method addresses this problem by making use of multiple observations and by considering their goodness of fit to improve both the accuracy and robustness of the estimate. The stepwise regression method is applied to estimate the relaxed weight of each observation.

Kim, Tae Min↗
NASA NTRS2012

A Linear Programming Approach to the Development of Contrail Reduction Strategies Satisfying Operationally Feasible Constraints

A class of strategies has been proposed to reduce contrail formation in the United States airspace. A 3D grid based on weather data and the cruising altitude level of aircraft is adjusted to avoid the persistent contrail potential area with the consideration to fuel-efficiency. In this paper, the authors introduce a contrail avoidance strategy on 3D grid by considering additional operationally feasible constraints from an air traffic controller's aspect. First, shifting too many aircraft to the same cruising level will make the miles-in-trail at this level smaller than the safety separation threshold. Furthermore, the high density of aircraft at one cruising level may exceed the workload for the traffic controller. Therefore, in our new model we restrict the number of total aircraft at each level. Second, the aircraft count variation for successive intervals cannot be too drastic since the workload to manage climbing/descending aircraft is much larger than managing cruising aircraft. The contrail reduction is formulated as an integer-programming problem and the problem is shown to have the property of total unimodularity. Solving the corresponding relaxed linear programming with the simplex method provides an optimal and integral solution to the problem. Simulation results are provided to illustrate the methodology.

Wei, Peng↗