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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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A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.
Three dimensional elastostatics problems solution method using singular integral equations solvable numerically for surface tractions and displacements of fully mixed boundary value problem
A finite difference numerical technique for solving the differential equations which describe thermal convection of compressible fluids in low gravity are reported. Results of one-dimensional calculations are presented, and comparisons are made to previous solutions. The primary result presented is a one-dimensional radial model of the Apollo 14 heat flow and convection demonstration flight experiment. The numerical calculations show that thermally induced convective motion in a confined fluid can have significant effects on heat transfer in a low gravity environment.
A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.
Numerical integration of meson-nucleon cascade equations for accelerator shielding calculations
Systematic numerical analysis of two dimensional and axisymmetric laminar jet of incompressible fluid with and without free stream
A numerical procedure is proposed for solving optimal control problems governed by linear retarded functional differential equations. The procedure is based on the idea of 'averaging approximations', due to Banks and Burns (1975). For illustration, numerical results generated on an IBM 370/158 computer, which demonstrate the rapid convergence of the method are presented.
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.
An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.
We construct steady, axisymmetric, numerical models of the sub-Alfvenic regions of cool winds driven by the X-celerator mechanism. We find that smooth acceleration to speeds of the order of the escape speed accompanied by substantial collimation of the flow can be achieved within the Alfven surface, located characteristically at several stellar radii. We apply the nondimensional results to winds which emerge from the equator of magnetized YSOs rotating at breakup and from circumstellar disks interacting with the magnetospheres of slowly rotating T Tauri stars. Stellar magnetic fields of kilogauss strength can drive wind mass-loss rates of 10(exp -6) solar mass/year from rapidly accreting YSOs and 10(exp -8) solar mass/year from slowly accreting T Tauri stars. The X-celerator mechanism can accelerate winds from these systems to velocities of hundreds of km/sec within a few stellar radii in the case of embedded YSOs and approximately 10 stellar radii in the case of T Tauri stars.
The albedo of plant canopies is treated as a problem in radiative transfer. Albedos calcualted from an iterative multistream numerical model are compared with those calculated with an analytic two-stream solution. With the assumption of a randomly homogeneous distribution of leaf positions and orientations and isotropic scattering by individual leaves, the single-scattering albedo of the canopy can be found analytically. This single-scattering solution is incorporated into the two-stream solution and used to benchmark the multistream numerical model in the single-scattering limit. Relative errors so established in the multistream model are O(0.3 percent) or less. The two-stream model is also found to be remarkably accurate, with the error in multiply scattered radiation O(5 percent) or less, corresponding to absolute errors in visible albedo of less than 0.001 and near-infrared albedo of less than or equal to 0.01. Thus the two-stream model should be adequate for many purposes, such as climate modeling, provided the assumptions of homogeneous canopy and isotropic scattering are not too unrealistic.
An effort is made to develop a satisfactory numerical method for the calculation of steady solutions of the Euler equations for inviscid compressible gas flows. The intended application is the prediction of the aerodynamic properties of aircraft flying at transonic speeds. Particular consideration is given to the modification of the equations to improve convergence to a steady state; finite volume formulation; adaptive dissipation; schemes designed to improve the resolution of shock waves; hybrid multistage time stepping schemes; residual averaging; a multigrid scheme; and trials with Burgers' equation. Results clearly demonstrate that the convergence of a time-dependent hyperbolic system to a steady state can be substantially accelerated by the introduction of multiple grids.
Numerical analysis of aerodynamic forces on thin airfoil operating in unsteady potential flow
A numerical scheme for predicting complex two-dimensional viscous flow fields is presented. The algorithm uses Roe's method for defining the inviscid fluxes and a line relaxation scheme to solve the resulting discrete approximation. The effects of turbulence are modelled using an algebraic eddy viscosity model. An adaptive grid scheme is employed to improve the resolution of complex flow field phenomena. The algorithm is applied to the solution of a sonic jet in a supersonic crossflow. Numerical results are compared with experimental data to validate the numerical approach.
A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.
Incompressible viscous flow fields induced by initial vorticity distributions with bounded support or exponential decay in the far field are investigated. A numerical scheme for the solution of the vorticity distribution and the velocity field is presented with special emphasis on the treatment of the boundary data. The efficiency of the scheme is demonstrated. The present method has been applied to the study of the merging and collision of vortex rings.
The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.
The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.