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At least 883 records · Page 49

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DOE OSTI2020

Comparison of Eulerian Bin and Lagrangian Particle-Based Schemes in Simulations of Pi Chamber Dynamics and Microphysics

This paper presents a comparison of simulations applying either a traditional Eulerian bin microphysics or a novel particle-based Lagrangian approach to represent CCN activation and cloud droplet growth. The Eulerian microphysics solve the evolution equation for the spectral density function, whereas the Lagrangian approach follows computational particles referred to as superdroplets. Each superdroplet represents a multiplicity of natural droplets that makes the Lagrangian approach computationally feasible. The two schemes apply identical representation of CCN activation and use the same droplet growth equation; these make direct comparison between the two schemes practical. The comparison, the first of its kind, applies an idealized simulation setup motivated by laboratory experiments with the Pi Chamber and previous model simulations of the Pi Chamber dynamics and microphysics. The Pi Chamber laboratory apparatus considers interactions between turbulence, CCN activation, and cloud droplet growth in moist Rayleigh–Bénard convection. Simulated steady-state droplet spectra averaged over the entire chamber are similar, with the mean droplet concentration, mean radius, and spectral width close in Eulerian and Lagrangian simulations. Small differences that do exist are explained by the inherent differences between the two schemes and their numerical implementation. The local droplet spectra differ substantially, again in agreement with the inherent limitations of the theoretical foundation behind each approach. There is a general agreement between simulations and Pi Chamber observations, with simplifications of the CCN activation and droplet growth equation used in the simulations likely explaining specific differences.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1972

The earth's atmosphere.

Topics discussed include the effects of solar radiation on the heat balance of the earth and its atmosphere, the physicomathematical models of the atmosphere and the computational schemes used in numerical investigations of the general circulation of the atmosphere, the effects of atmospheric turbulence on aeronautical systems, te chemistry of different regions of the atmosphere, the use of hot-filament and cold-cathode vacuum gauges to measure upper-atmosphere densities, methods of determining the air density at heights near a satellite's perigee by analyzing changes in its orbit, and an evaluation of various atmospheric models in the 100- to 1000-km altitude range.

Vaughan, W. W.↗

NASA NTRS1972

Effects of circular geometry in simulation of convection in rotating spacecraft tanks

For computational simulation of the convection and mixing of stratified fluid in a rotating tank (such as used in Apollo flights) with time-dependent rotation, the Navier-Stokes convection problem was formulated for a circular tank configuration. The final equations results from a general approximate theory for combined forced and contained natural convection in a time-dependent rotating system. The equations are cast in terms of vorticity and stream function in a form convenient for computation, with a transformed coordinate system, and appropriate boundary conditions are derived. Accurate representations for the cryogenic supercritical oxygen thermodynamic properties are used in the computations, and an efficient numerical finite difference scheme and computational method are employed.

Martin, E. D.↗

NASA NTRS1976

Arrival time of satellite-broadened laser pulses

A method for measuring the time of arrival of very narrow laser pulses which have been reflected and randomly broadened by a target is examined. It is known that these return pulses from the target have very small rise times. A threshold detection algorithm that detects the rising edge of the pulse is used for obtaining the pulse arrival times. The errors of the scheme are evaluated numerically for different pulse shapes, and a loose bound on the errors of detecting a typical pulse is obtained. A gamma-density model is used to characterize the random gain processes of the optical receiver, and the effect of such random gains on the errors of threshold detection is analyzed.

Iyer, R. S.↗

NASA NTRS1980

A rapid implicit-explicit solution to the two-dimensional time dependent incompressible Navier-Stokes equations

A second-order time-accurate and spatially factored algorithm was used in a finite difference scheme for the numerical solution of the time-dependent, incompressible, two dimensional Navier-Stokes equations in conservation-law form using vorticity and stream function variables. The systems of equations are solved at each time step by an iterative technique. Numerical results were obtained for a circular cylinder at a Reynolds number of 15, and an NACA 0012 airfoil at zero angle of attack at Reynolds numbers of 10 to the third and 10 to the fourth powers. The results are in agreement with another numerical technique, and the computing time required to obtain the steady state solution at the Reynolds number of 10 to the 4th power was 49.7 sec on CDC 7600 computer using a 65 x 84 computational grind.

Davis, J. E.↗

NASA NTRS1980

On time discretizations for spectral methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

Gottlieb, D.↗

NASA NTRS1981

Transonic flow computations in cascades using finite element method

Analysis of transonic flow through a cascade of airfoils is investigated using the finite element method. Development of a computational grid suitable for complex flow structures and different types of boundary conditions is presented. An efficient pseudo-time integration scheme is developed for the solution of equations. Modeling of the shock and the convergence characteristics of the developed scheme are discussed. Numerical results include a 45 deg staggered cascade of NACA 0012 airfoils with inlet flow Mach number of 0.8 and angles of attack 1, 0, and 1 deg.

Akay, H. U.↗

NASA NTRS1981

A simple atmospheric model on the sphere with 100% parallelism

A simple shallow water equations model used to test numerical weather prediction schemes is presented. The spherical geometry is transformed into a formally doubly periodic configuration which can be implemented on a massively parallel computer at 100% parallelism. A nonstaggered grid with all variables defined at the grid points (circles) is used. The parallel structure was simulated by performing step 1 in a FORTRAN array, on an Amdahl serial machine, changing the signs of the winds on the dark side.

Kalnay, E.↗

NASA NTRS1982

Flows over wings with leading-edge vortex separation

The unsteady cross flow analogy reduces the steady three dimensional separation flow problem into an unsteady two dimensional flow problem in which the section shape changes with time. The two dimensional VORSEP code is extended to the case of arbitrary body growth rates in order to generate the initial vortex structures for the three dimensional free vortex sheet (FVS) code. Automatic procedures to reduce the wing geometry definition to a set of cross flow plane sections corresponding to the locations of the time step solutions and to generate the effective source distribution on each cross flow section to represent the section normal growth across the following steps are incorporated in the VORSEP code. Also, the wake shedding model is improved by adopting a redistribution scheme which improves the stability of the free sheet development with time. The improved wake shedding model combined with the redistribution scheme alleviated the numerical instabilities associated with the vortex rollup.

Rao, B. M.↗

NASA NTRS1982

Numerical experimentation on spherically symmetric one-dimensional magnetohydrodynamic /MHD/ wave propagation

Radial propagation of one-dimensional magnetohydrodynamic (MHD) waves are analyzed numerically on the basis of the Implicit-Continuous-Fluid-Eulerian (ICE) scheme. Accuracy of the numerical method and other properties are tested through the study of MHD wave propagation. The three different modes of MHD waves (i.e., fast-, slow- and Alfven (transverse) mode) are generated by applying physically consistent boundary perturbations derived from MHD compatibility relations. It is shown that the resulting flow following these waves depend upon the relative configurations of the initial magnetic field and boundary perturbations.

Han, S. M.↗

NASA NTRS1980

Numeric and fluid dynamic representation of tornadic double vortex thunderstorms

Current understanding of a double vortex thunderstorm involves a pair of contra-rotating vortices that exists in the dynamic updraft. The pair is believed to be a result of a blocking effect which occurs when a cylindrical thermal updraft of a thunderstorm protrudes into the upper level air and there is a large amount of vertical wind shear between the low level and upper level air layers. A numerical tornado prediction scheme based on the double vortex thunderstorm was developed. The Energy-Shear Index (ESI) is part of the scheme and is calculated from radiosonde measurements. The ESI incorporates parameters representative of thermal instability and blocking effect, and indicates appropriate environments for which the development of double vortex thunderstorms is likely.

Connell, J. R.↗

NASA NTRS1983

Interstellar ice

The 3250/cm 'ice' band observed in absorption and polarization in interstellar spectra is studied in the laboratory in low-temperature solid mixtures of H2O and other molecules. General empirical rules are derived which relate the shape and relative intensity of the H2O infrared absorptions to the degree of H2O dilution and hydrogen-bonding capacity of the dilutant. The chemical composition of mantles accreting on interstellar grains inside dense (1000-100,000/cu cm) molecular clouds has been calculated numerically. The reaction scheme comprises gas-phase as well as grain surface reactions. The results show that in most circumstances grain mantles consist of the molecules H2O, H2CO, NH3, N2, O2, CO, and CO2. The expected infrared characteristics of the calculated grain mantles are discussed with an emphasis on the observed 3250/cm 'ice' band. Grain mantles accreted at a density of about 10,000/cu cm contain large concentrations of H2O (about 60 percent) and produce a broad 3250/cm 'ice' band.

Tielens, A. G. G. M.↗

NASA NTRS1985

Generation of three-dimensional body-fitted coordinates using hyperbolic partial differential equations

An efficient numerical mesh generation scheme capable of creating orthogonal or nearly orthogonal grids about moderately complex three dimensional configurations is described. The mesh is obtained by marching outward from a user specified grid on the body surface. Using spherical grid topology, grids have been generated about full span rectangular wings and a simplified space shuttle orbiter.

Steger, J. L.↗

NASA NTRS1985

Nonlinear transient responses of initially stressed composite plates

The nonlinear transient response of initially stressed composite plates is investigated using the finite element method. A nine-node isoparametric quadrilateral element is developed to model laminated plates under initial deformation and initial stress according to the Mindlin plate theory and von Karman large deflection assumptions. In the time integration, the Newmark constant acceleration method in conjunction with an efficient and accurate iteration scheme is used. Numerical results for deflections and bending moments for isotropic and laminated plates are obtained.

Chen, J. K.↗

NASA NTRS1986

Initiation of breakdown in slender compressible vortices

The onset of vortex breakdown in compressible flows is investigated analytically for the case in which the flow is axially symmetric, the vortex is isolated, its axis is parallel to the main flow, and the vortex radius is small compared to the breakdown length. The conservation equations for mass, momentum, and energy are formulated and solved numerically using a finite-difference scheme, as described by Krause (1985); numerical results are presented in graphs and briefly characterized.

Krause, E.↗

NASA NTRS1988

General linear codes for fault-tolerant matrix operations on processor arrays

Various checksum codes have been suggested for fault-tolerant matrix computations on processor arrays. Use of these codes is limited due to potential roundoff and overflow errors. Numerical errors may also be misconstrued as errors due to physical faults in the system. In this a set of linear codes is identified which can be used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU-decomposition, with minimum numerical error. Encoding schemes are given for some of the example codes which fall under the general set of codes. With the help of experiments, a rule of thumb for the selection of a particular code for a given application is derived.

Nair, V. S. S.↗

NASA NTRS1990

An approximation theory for the identification of linear thermoelastic systems

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Rosen, I. G.↗

NASA NTRS1990

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Chakravarthy, Sukumar R.↗