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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 NTRS1991

Ocean tide models for satellite geodesy and Earth rotation

A theory is presented which predicts tides in turbulent, self-gravitating, and loading oceans possessing linearized bottom friction, realistic bathymetry, and continents (at coastal boundaries no-flow conditions are imposed). The theory is phrased in terms of spherical harmonics, which allows the tide equations to be reduced to linear matrix equations. This approach also allows an ocean-wide mass conservation constraint to be applied. Solutions were obtained for 32 long and short period luni-solar tidal constituents (and the pole tide), including the tidal velocities in addition to the tide height. Calibrating the intensity of bottom friction produces reasonable phase lags for all constituents; however, tidal amplitudes compare well with those from observation and other theories only for long-period constituents. In the most recent stage of grant research, traditional theory (Liouville equations) for determining the effects of angular momentum exchange on Earth's rotation were extended to encompass high-frequency excitations (such as short-period tides).

Dickman, Steven R.↗
NASA NTRS1973

Quantum theory of an optical maser. VI - Transient behavior.

The transient behavior of a laser is discussed using the quantum theory as did Scully and Lamb. The formal solution of the density-matrix equation is expressed in terms of exponentially decaying eigenmodes. Some of the lower decay constants are obtained numerically. The equations for the moments of the density matrix are then derived and solved by a truncation method. The equations of motion are integrated numerically for the case where the average number of photons in a laser cavity has the realistically large value 1.3 x 100,000. An alternative Fokker-Planck-equation approach is discussed.

Wang, Y. K.↗
NASA NTRS1981

Numerical solution of compressible viscous flows at high Reynolds numbers

A new numerical method which was used to reduce the computation time required in fluid dynamics to solve the Navier-Stokes equations at flight Reynolds numbers is described. The method is the implicit analogue of the explicit finite different method. It uses this as its first stage, while the second stage removes the restrictive stability condition by recasting the difference equations in an implicit form. The resulting matrix equations to be solved are either upper or lower block bidiagonal equations. The new method makes it possible and practical to calculate many important three dimensional, high Reynolds number flow fields on computers.

Maccormack, R. W.↗
NASA NTRS1959

Modified Matrix Method for Calculating Steady-State Span Loading on Flexible Wings in Subsonic Flight

A method is presented for shortening the computations required to determine the steady-state span loading on flexible wings in subsonic flight. The method makes use of tables of downwash factors to find the necessary aerodynamic-influence coefficients for the application of lifting-line theory. Explicit matrix equations of equilibrium are converted into a matrix power series with a finite number of terms by utilizing certain characteristic properties of matrices. The number of terms in the series is determined by a trial-and-error process dependent upon the required accuracy of the solution. Spanwise distributions of angle of attack, airload, shear, bending moment, and pitching moment are readily obtained as functions of qm(sub R) where q denotes the dynamic pressure and mR denotes the lift-curve slope of a rigid wing. This method is intended primarily to make it practical to solve steady-state aeroelastic problems on the ordinary manually operated desk calculators, but the method is also readily adaptable to automatic computing equipment.

Gainer, Patrick A.↗
NASA NTRS1988

The dynamic behaviour of postbuckled composite plates under acoustic excitation

The Rayleigh-Ritz method was used to find the postbuckling static displacement pattern of a composite plane (CFRP) under uniaxial in-plane compression of uniform edge-shortening. The resonance frequencies and mode shapes at various postbuckled states are then evaluated by eigenvalue analysis of the dynamical matrix equation consisting of up-dated tangential stiffness matrix at corresponding static configuration. The theoretical results are compared with experimental results obtained in 16-layered CFRP laminate of aspect ratio 1.5. The resonance frequencies and mode shapes obtained are used to interpret the multimodal and nonlinear strain responses to high level of acoustic excitation. The dominance of second-mode contribution and softening-spring behavior are found in the strain response of postbuckled plates.

Ng, C. F.↗
NASA NTRS1992

A finite element method for the thermochemical decomposition of polymeric materials. I - Theory

The governing differential equations are developed to model the thermomechanical behavior of chemically decomposing, polymeric materials. These equations account for thermal and gaseous diffusion through a poroelastic, transversely isotropic solid. The Bubnov-Galerkin finite element method is applied to the governing equations to cast the coupled set into a single matrix equation. A method for solving these equations simultaneously at each time step is discussed.

Sullivan, R. M.↗
NASA NTRS2001

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Watson, W. R.↗
NASA NTRS1985

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Barth, T. J.↗
NASA NTRS1978

Conservative implicit schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) were investigated for the solution of matrix equations resulting from finite difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, was introduced by an upwind bias of the density. Two implicit AF procedures are presented and their convergence performance is compared with that of the standard transonic solution procedure, successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. The results indicate that the AF schemes are substantially faster than SLOR.

Holst, T. L.↗
NASA NTRS1979

Fast, conservative schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) are investigated for the solution of matrix equations resulting from finite-difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, is introduced by an upwind bias of the density. Two implicit AF procedures are presented, and their convergence performance is compared with that of the standard transonic solution procedure: successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. Results indicate a substantial improvement in convergence rate for AF schemes relative to SLOR.

Holst, T. L.↗
NASA NTRS1976

An iterative decoupling solution method for large scale Lyapunov equations

A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.

Athay, T. M.↗
NASA NTRS1981

Design for active and passive flutter suppression and gust alleviation

Analytical design techniques for active and passive control of aeroelastic systems are based on a rational approximation of the unsteady aerodynamic loads in the entire Laplace domain, which yields matrix equations of motion with constant coefficients. Some existing schemes are reviewed, the matrix Pade approximant is modified, and a technique which yields a minimal number of augmented states for a desired accuracy is presented. The state-space aeroelastic model is used to design an active control system for simultaneous flutter suppression and gust alleviation. The design target is for a continuous controller which transfers some measurements taken on the vehicle to a control command applied to a control surface. Structural modifications are formulated in a way which enables the treatment of passive flutter suppression system with the same procedures by which active control systems are designed.

Karpel, M.↗
NASA NTRS1982

On redistribution and the equations for radiative transfer

The derivation of the equations of statistical equilibrium are outlined, starting from the quantum density-matrix equations, drawing particular attention to the approximations and assumptions used in the development of tractable expressions. Then, using the quantum-fluctuation-regression theorem, emission and absorption coefficients are obtained for multilevel atomic systems which are nondegenerate except for m-substates. These coefficients are valid to first order in the incident intensity. Possible extensions to higher intensity broadband incoherent fields are suggested.

Cooper, J.↗
NASA NTRS1993

Incompressible spectral-element method: Derivation of equations

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Deanna, Russell G.↗