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NASA NTRS1986

Grain processes in massive star formation

Observational evidence suggests that stars greater than 100 M(solar) exist in the Galaxy and Large Magellanic Cloud (LMC), however classical star formation theory predicts stellar mass limits of only approx. 60 M(solar). A protostellar accretion flow consists of inflowing gas and dust. Grains are destroyed as they are near the central protostar creating a dust shell or cocoon. Radiation pressure acting on the grain can halt the inflow of material thereby limiting the amount of mass accumulated by the protostar. We first consider rather general constraints on the initial grain to gas ratio and mass accretion rates that permit inflow. We further constrain these results by constructing a numerical model. Radiative deceleration of grains and grain destruction processes are explicitly accounted for in an iterative solution of the radiation-hydrodynamic equations. Findings seem to suggest that star formation by spherical accretion requires rather extreme preconditioning of the grain and gas environment.

Wolfire, M. G.↗

NASA NTRS1986

Iterative methods for elliptic finite element equations on general meshes

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

Nicolaides, R. A.↗

NASA NTRS1987

A strategy for automatically generating programs in the lucid programming language

A strategy for automatically generating and verifying simple computer programs is described. The programs are specified by a precondition and a postcondition in predicate calculus. The programs generated are in the Lucid programming language, a high-level, data-flow language known for its attractive mathematical properties and ease of program verification. The Lucid programming is described, and the automatic program generation strategy is described and applied to several example problems.

Johnson, Sally C.↗

NASA NTRS1986

Research on Computational Fluid Dynamics and Turbulence

Preconditioning matrices for Chebyshev derivative operators in several space dimensions; the Jacobi matrix technique in computational fluid dynamics; and Chebyshev techniques for periodic problems are discussed.

Source record↗

NASA NTRS1987

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

NASA NTRS1986

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Young, D. P.↗

NASA NTRS1987

TRANAIR - A computer code for transonic analyses of arbitrary configurations

Attention is given to a new approach to solving full potential equations about arbitrary configurations. Numerical algorithms from such fields as finite elements, preconditioned Krylov subspace methods, discrete Fourier analysis, and integral equations are combined to take advantage of the size and speed of current and emerging supercomputers. On the basis of this appraoch, a robust, efficient and easy to use computer code referred to as TRANAIR has been developed for transonic analysis of complex geometries.

Samant, S. S.↗

NASA NTRS1986

A new approach to the solution of boundary value problems involving complex configurations

A new approach for solving certain types of boundary value problems about complex configurations is presented. Numerical algorithms from such diverse fields as finite elements, preconditioned Krylov subspace methods, discrete Fourier analysis, and integral equations are combined to take advantage of the memory, speed and architecture of current and emerging supercomputers. Although the approach has application to many branches of computational physics, the present effort is concentrated in areas of Computational Fluid Dynamics (CFD) such as steady nonlinear aerodynamics, time harmonic unsteady aerodynamics, and aeroacoustics. The most significant attribute of the approach is that it can handle truly arbitrary boundary geometries and eliminates the difficult task of generating surface fitted grids.

Rubbert, P. E.↗

NASA NTRS1987

Upwelling at the ice edge - A mechanism for deep water formation?

This study sets forward a hypothesis which anticipates deep water formation due to ice edge upwelling. The upwelling can raise thermocline waters (the lower Arctic Intermediate Water) to the surface or near it, where the water is exposed to cooling, evaporation, mixing, and oxygenation. Thus, upwelling can act as a preconditioning mechanism for deep convection. The conjecture would also explain the salinity range of the Greenland Sea Deep Water if the upper and lower Arctic Intermediate Water masses are mixed so that the latter has at least an 80-percent contribution. It is also anticipated that the convection events induced by ice edge upwelling during winter season could give rise to a new deep water annual production rate consistent with observations.

Hakkinen, Sirpa↗

NASA NTRS1987

Relaxation schemes for spectral multigrid methods

The effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined. Iterative methods are an attractive alternative to direct methods because Fourier transform techniques enable the discrete matrix-vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations. Preconditioning is found to be essential for acceptable rates of convergence. Preconditioners based on second-order finite difference methods are used. A comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary. The investigations show that iterations based on incomplete LU decompositions provide the most efficient methods for solving these algebraic systems.

Phillips, Timothy N.↗

NASA NTRS1987

Conditions for the formation of massive stars

Upper limits on the masses of stars that can form are reexamined and models for the inflow of matter through cocoons around stars of 60, 100, and 200 solar masses are calculated. Consideration is given to the general conditions that must hold at the inner and outer boundaries of a protostellar cocoon; limits on the dust-to-gas ratios and mass inflow rates that will permit inflow onto very massive stars are determined. It is found that inflow can occur if intermediate-sized grains (0.05-0.25 micron) are missing from the initial gas/dust mixture. The existence of massive stars in certain locations in galaxies indicates that preconditioning of the interstellar medium by shocks or turbulence is necessary for massive star formation.

Wolfire, Mark G.↗

NASA NTRS1987

Non-linear analysis of symmetric structures with unsymmetric boundary conditions

Two computational techniques are developed analytically to generate global approximation vectors for use in the nonlinear large-deflection analysis of symmetric structures with asymmetric boundary conditions. One method is based on linear combinations of FEM-generated symmetric and antisymmetric vector components, while the other employs a preconditioned-conjugate-gradient technique. The derivation of the procedures is explained in detail, and their effectiveness is evaluated in sample computations for an elliptic toroid and a cylindrical panel; the results are presented in tables and graphs and characterized.

Noor, Ahmed K.↗

NASA NTRS1988

Effects of moisture, elevated temperature, and fatigue loading on the behavior of graphite/epoxy buffer strip panels with center cracks

The effects of fatigue loading combined with moisture and heat on the behavior of graphite epoxy panels with either Kevlar-49 or S-glass buffer strips were studied. Buffer strip panels, that had a slit in the center to represent damage, were moisture conditioned or heated, fatigue loaded, and then tested in tension to measure their residual strength. The buffer strips were parallel to the loading direction and were made by replacing narrow strips of the 0 deg graphite plies with Kevlar-49 epoxy or S-glass epoxy on a 1-for-1 basis. The panels were subjected to a fatigue loading spectrum. One group of panels was preconditioned by soaking in 60 C water to produce a 1 percent weight gain then tested at room temperature. One group was heated to 82 C during the fatigue loading. Another group was moisture conditioned and then tested at 82 C. The residual strengths of the buffer panels were not highly affected by the fatigue loading, the number of repetitions of the loading spectrum, or the maximum strain level. The moisture conditioning reduced the residual strengths of the S-glass buffer strip panel by 10 to 15 percent below the ambient results. The moisture conditioning did not have a large effect on the Kevlar-49 panels.

Bigelow, C. A.↗

NASA NTRS1987

Simultaneous stochastic inversion for geomagnetic main field and secular variation. I - A large-scale inverse problem

The method of stochastic inversion is extended to the simultaneous inversion of both main field and secular variation. In the present method, the time dependency is represented by an expansion in Legendre polynomials, resulting in a simple diagonal form for the a priori covariance matrix. The efficient preconditioned Broyden-Fletcher-Goldfarb-Shanno algorithm is used to solve the large system of equations resulting from expansion of the field spatially to spherical harmonic degree 14 and temporally to degree 8. Application of the method to observatory data spanning the 1900-1980 period results in a data fit of better than 30 nT, while providing temporally and spatially smoothly varying models of the magnetic field at the core-mantle boundary.

Bloxham, Jeremy↗

NASA NTRS1988

Climatology of the stratospheric polar vortex and planetary wave breaking

The distribution of Ertel's potential vorticity (PV) on the 850 K isentropic surface is used to establish a climatology for the transient evolution of the planetary scale circulation in the Northern Hemisphere winter midstratosphere. PV distributions are computed from gridded NMC daily temperature and height maps for the 10 and 30 mb levels, and show that a very good approximation for 850 K PV can be derived from 10 mb heights and temperatures alone. It is assumed that reversals of the latitudinal gradient of PV, localized in longitude and latitude may be regarded as signatures of planetary wave breaking. Wave breaking identified by such signatures tends to occur mainly in the vicinity of the Aleutian anticyclone, with a secondary maximum over Europe. The area of the polar vortex, defined as the area enclosed by PV contours greater than a certain critical value, is strongly influenced by wave breaking. Erosion of the polar vortex due to transport and mixing of PV leads to a preconditioned state, when defined in terms of vortex area, that always occurs prior to major stratospheric warmings. During winters with little PV transport or mixing, the vortex area evolves rather uniformly in response to radiative forcing. During winters with major sudden warmings, the wave breaking signature as defined here first appears at low values of PV, then rapidly moves toward higher values as the vortex area is reduced and the 'surf-zone' structure becomes well defined.

Baldwin, Mark P.↗

NASA NTRS1988

Error indicators and accuracy improvements of finite element solutions

Practical and reliable estimators of the discretization errors in engineering problems are developed. Error indicators for identifying the regions or elements of the solution domain which are likely to have the largest discretization errors are presented, and a simple computational procedure for improving the accuracy of the finite element solutions for shell problems is given. The similarities between the proposed procedure and a preconditioned conjugate gradient (PCG) technique are identified and exploited to generate pointwise error indicators from the PCG technique. Numerical examples in the linear static analysis of shells are presented.

Noor, Ahmed K.↗

NASA NTRS1987

Solving finite element equations on concurrent computers

This paper discusses the development of a concurrent algorithm for the solution of systems of equations arising in finite element applications. The approach is based on a hybrid of direct elimination method and preconditioned conjugate iteration. Two different preconditioners are used; diagonal scaling and a concurrent implementation of incomplete LU factorization. First, an automatic procedure is used to partition the finite element mesh into sub-structures. The particular mesh partition is chosen to minimize an estimate of the cost for evaluating the solution using this algorithm on a concurrent computer. These procedures are implemented in a finite element program on the JPL/CalTech MARK III hypercube computer. An overview of the structure of this program is presented. The performance of the solution method is demonstrated with the aid of a number of numerical test runs, and its advantages for concurrent implementations are discussed. Efficiency and speed-up factors over sequential machines for the numerical examples are highlighted.

Nour-Omid, B.↗

NASA NTRS1988

Reanalysis procedure for large structural systems

Global-basis-vector approximate reanalysis techniques for use in automated structural optimization schemes are developed and demonstrated. The vibrational response of a modified structure (MS) is estimated by lumping the design variables into a single tracing parameter, applying an operator splitting procedure to express the FEM equations of the MS in terms of the original-structure equations plus correction terms, and reducing the MS equations via a classical Bubnov-Galerkin scheme. The sensitivity of the vibrational response to structural modifications is evaluated, and the relationship between this method and the preconditioned conjugate-gradient method (Noor and Peters, 1988) is explored. Numerical results for linear static and free vibration problems involving beamlike lattices, double-layered hexahedral grids, and structural gridworks are presented in tables and graphs and briefly characterized.

Noor, Ahmed K.↗