Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAF2, developed to calculate high Reynolds number internal/external flows is described. The program solves the two dimensional, time dependent Navier-Stokes equations. Turbulence is modeled with either a mixing length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, external, and internal/external flow calculations are presented.

Multivariant function model generation

NASA Technical Reports Server (NTRS)

1974-01-01

The development of computer programs applicable to space vehicle guidance was conducted. The subjects discussed are as follows: (1) determination of optimum reentry trajectories, (2) development of equations for performance of trajectory computation, (3) vehicle control for fuel optimization, (4) development of equations for performance trajectory computations, (5) applications and solution of Hamilton-Jacobi equation, and (6) stresses in dome shaped shells with discontinuities at the apex.

Dynamics of flexible bodies in tree topology - A computer oriented approach

NASA Technical Reports Server (NTRS)

Singh, R. P.; Vandervoort, R. J.; Likins, P. W.

1984-01-01

An approach suited for automatic generation of the equations of motion for large mechanical systems (i.e., large space structures, mechanisms, robots, etc.) is presented. The system topology is restricted to a tree configuration. The tree is defined as an arbitrary set of rigid and flexible bodies connected by hinges characterizing relative translations and rotations of two adjoining bodies. The equations of motion are derived via Kane's method. The resulting equation set is of minimum dimension. Dynamical equations are imbedded in a computer program called TREETOPS. Extensive control simulation capability is built in the TREETOPS program. The simulation is driven by an interactive set-up program resulting in an easy to use analysis tool.

Computer programs for optical dendrometer measurements of standing tree profiles

Treesearch

Jacob R. Beard; Thomas G. Matney; Emily B. Schultz

2015-01-01

Tree profile equations are effective volume predictors. Diameter data for building these equations are collected from felled trees using diameter tapes and calipers or from standing trees using optical dendrometers. Developing and implementing a profile function from the collected data is a tedious and error prone task. This study created a computer program, Profile...

Modeling the missile-launch tube problem in DYSCO

NASA Technical Reports Server (NTRS)

Berman, Alex; Gustavson, Bruce A.

1989-01-01

DYSCO is a versatile, general purpose dynamic analysis program which assembles equations and solves dynamics problems. The executive manages a library of technology modules which contain routines that compute the matrix coefficients of the second order ordinary differential equations of the components. The executive performs the coupling of the equations of the components and manages the solution of the coupled equations. Any new component representation may be added to the library if, given the state vector, a FORTRAN program can be written to compute M, C, K, and F. The problem described demonstrates the generality of this statement.

A computer program for fitting smooth surfaces to an aircraft configuration and other three dimensional geometries

NASA Technical Reports Server (NTRS)

Craidon, C. B.

1975-01-01

A computer program that uses a three-dimensional geometric technique for fitting a smooth surface to the component parts of an aircraft configuration is presented. The resulting surface equations are useful in performing various kinds of calculations in which a three-dimensional mathematical description is necessary. Programs options may be used to compute information for three-view and orthographic projections of the configuration as well as cross-section plots at any orientation through the configuration. The aircraft geometry input section of the program may be easily replaced with a surface point description in a different form so that the program could be of use for any three-dimensional surface equations.

Bifilar analysis users manual, volume 2

NASA Technical Reports Server (NTRS)

Cassarino, S. J.

1980-01-01

The digital computer program developed to study the vibration response of a coupled rotor/bifilar/airframe coupled system is described. The theoretical development of the rotor/airframe system equations of motion is provided. The fuselage and bifilar absorber equations of motion are discussed. The modular block approach used in the make-up of this computer program is described. The input data needed to run the rotor and bifilar absorber analyses is described. Sample output formats are presented and discussed. The results for four test cases, which use the major logic paths of the computer program, are presented. The overall program structure is discussed in detail. The FORTRAN subroutines are described in detail.

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

PAN AIR: A Computer Program for Predicting Subsonic or Supersonic Linear Potential Flows About Arbitrary Configurations Using a Higher Order Panel Method. Volume 1; Theory Document (Version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, Alfred E.; Epton, Michael A.

1981-01-01

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the PAN AIR (Panel Aerodynamics) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformations, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments.

Computer-Generated Phase Diagrams for Binary Mixtures.

ERIC Educational Resources Information Center

Jolls, Kenneth R.; And Others

1983-01-01

Computer programs that generate projections of thermodynamic phase surfaces through computer graphics were used to produce diagrams representing properties of water and steam and the pressure-volume-temperature behavior of most of the common equations of state. The program, program options emphasizing thermodynamic features of interest, and…

Automation of reliability evaluation procedures through CARE - The computer-aided reliability estimation program.

NASA Technical Reports Server (NTRS)

Mathur, F. P.

1972-01-01

Description of an on-line interactive computer program called CARE (Computer-Aided Reliability Estimation) which can model self-repair and fault-tolerant organizations and perform certain other functions. Essentially CARE consists of a repository of mathematical equations defining the various basic redundancy schemes. These equations, under program control, are then interrelated to generate the desired mathematical model to fit the architecture of the system under evaluation. The mathematical model is then supplied with ground instances of its variables and is then evaluated to generate values for the reliability-theoretic functions applied to the model.

A 4-cylinder Stirling engine computer program with dynamic energy equations

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1983-01-01

A computer program for simulating the steady state and transient performance of a four cylinder Stirling engine is presented. The thermodynamic model includes both continuity and energy equations and linear momentum terms (flow resistance). Each working space between the pistons is broken into seven control volumes. Drive dynamics and vehicle load effects are included. The model contains 70 state variables. Also included in the model are piston rod seal leakage effects. The computer program includes a model of a hydrogen supply system, from which hydrogen may be added to the system to accelerate the engine. Flow charts are provided.

Combustion of hydrogen-air jets in local chemical equilibrium: A guide to the CHARNAL computer program

NASA Technical Reports Server (NTRS)

Spalding, D. B.; Launder, B. E.; Morse, A. P.; Maples, G.

1974-01-01

A guide to a computer program, written in FORTRAN 4, for predicting the flow properties of turbulent mixing with combustion of a circular jet of hydrogen into a co-flowing stream of air is presented. The program, which is based upon the Imperial College group's PASSA series, solves differential equations for diffusion and dissipation of turbulent kinetic energy and also of the R.M.S. fluctuation of hydrogen concentration. The effective turbulent viscosity for use in the shear stress equation is computed. Chemical equilibrium is assumed throughout the flow.

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.

1986-01-01

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

VNAP2: A Computer Program for Computation of Two-dimensional, Time-dependent, Compressible, Turbulent Flow

NASA Technical Reports Server (NTRS)

Cline, M. C.

1981-01-01

A computer program, VNAP2, for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow is presented. It solves the two dimensional, time dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing length model, a one equation model, or the Jones-Launder two equation model. The geometry may be a single or a dual flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference plane characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet powered afterbodies, airfoils, and free jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

NASA Astrophysics Data System (ADS)

Muruganandam, P.; Adhikari, S. K.

2009-10-01

Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 122 907 No. of bytes in distributed program, including test data, etc.: 609 662 Distribution format: tar.gz Programming language: FORTRAN 77 and Fortran 90/95 Computer: PC Operating system: Linux, Unix RAM: 1 GByte (i, iv, v), 2 GByte (ii, vi, vii, x, xi), 4 GByte (iii, viii, xii), 8 GByte (ix) Classification: 2.9, 4.3, 4.12 Nature of problem: These programs are designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-, two- or three-space dimensions with a harmonic, circularly-symmetric, spherically-symmetric, axially-symmetric or anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Solution method: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation, in either imaginary or real time, over small time steps. The method yields the solution of stationary and/or non-stationary problems. Additional comments: This package consists of 12 programs, see "Program title", above. FORTRAN77 versions are provided for each of the 12 and, in addition, Fortran 90/95 versions are included for ii, iii, vi, viii, ix, xii. For the particular purpose of each program please see the below. Running time: Minutes on a medium PC (i, iv, v, vii, x, xi), a few hours on a medium PC (ii, vi, viii, xii), days on a medium PC (iii, ix). Program summary (1)Title of program: imagtime1d.F Title of electronic file: imagtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (2)Title of program: imagtimecir.F Title of electronic file: imagtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (3)Title of program: imagtimesph.F Title of electronic file: imagtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (4)Title of program: realtime1d.F Title of electronic file: realtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (5)Title of program: realtimecir.F Title of electronic file: realtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (6)Title of program: realtimesph.F Title of electronic file: realtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (7)Title of programs: imagtimeaxial.F and imagtimeaxial.f90 Title of electronic file: imagtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (8)Title of program: imagtime2d.F and imagtime2d.f90 Title of electronic file: imagtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (9)Title of program: realtimeaxial.F and realtimeaxial.f90 Title of electronic file: realtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (10)Title of program: realtime2d.F and realtime2d.f90 Title of electronic file: realtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (11)Title of program: imagtime3d.F and imagtime3d.f90 Title of electronic file: imagtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (12)Title of program: realtime3d.F and realtime3d.f90 Title of electronic file: realtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum Ram Memory: 8 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems.

Digital computer simulation of inductor-energy-storage dc-to-dc converters with closed-loop regulators

NASA Technical Reports Server (NTRS)

Ohri, A. K.; Owen, H. A.; Wilson, T. G.; Rodriguez, G. E.

1974-01-01

The simulation of converter-controller combinations by means of a flexible digital computer program which produces output to a graphic display is discussed. The procedure is an alternative to mathematical analysis of converter systems. The types of computer programming involved in the simulation are described. Schematic diagrams, state equations, and output equations are displayed for four basic forms of inductor-energy-storage dc to dc converters. Mathematical models are developed to show the relationship of the parameters.

An integral equation formulation for predicting radiation patterns of a space shuttle annular slot antenna

NASA Technical Reports Server (NTRS)

Jones, J. E.; Richmond, J. H.

1974-01-01

An integral equation formulation is applied to predict pitch- and roll-plane radiation patterns of a thin VHF/UHF (very high frequency/ultra high frequency) annular slot communications antenna operating at several locations in the nose region of the space shuttle orbiter. Digital computer programs used to compute radiation patterns are given and the use of the programs is illustrated. Experimental verification of computed patterns is given from measurements made on 1/35-scale models of the orbiter.

A computer program to generate equations of motion matrices, L217 (EOM). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Kroll, R. I.; Clemmons, R. E.

1979-01-01

The equations of motion program L217 formulates the matrix coefficients for a set of second order linear differential equations that describe the motion of an airplane relative to its level equilibrium flight condition. Aerodynamic data from FLEXSTAB or Doublet Lattice (L216) programs can be used to derive the equations for quasi-steady or full unsteady aerodynamics. The data manipulation and the matrix coefficient formulation are described.

Nationwide summary of US Geological Survey regional regression equations for estimating magnitude and frequency of floods for ungaged sites, 1993

USGS Publications Warehouse

Jennings, M.E.; Thomas, W.O.; Riggs, H.C.

1994-01-01

For many years, the U.S. Geological Survey (USGS) has been involved in the development of regional regression equations for estimating flood magnitude and frequency at ungaged sites. These regression equations are used to transfer flood characteristics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally these equations have been developed on a statewide or metropolitan area basis as part of cooperative study programs with specific State Departments of Transportation or specific cities. The USGS, in cooperation with the Federal Highway Administration and the Federal Emergency Management Agency, has compiled all the current (as of September 1993) statewide and metropolitan area regression equations into a micro-computer program titled the National Flood Frequency Program.This program includes regression equations for estimating flood-peak discharges and techniques for estimating a typical flood hydrograph for a given recurrence interval peak discharge for unregulated rural and urban watersheds. These techniques should be useful to engineers and hydrologists for planning and design applications. This report summarizes the statewide regression equations for rural watersheds in each State, summarizes the applicable metropolitan area or statewide regression equations for urban watersheds, describes the National Flood Frequency Program for making these computations, and provides much of the reference information on the extrapolation variables needed to run the program.

Supplement to the ICRPG turbulent boundary layer nozzle analysis computer program

NASA Technical Reports Server (NTRS)

Omori, S.; Gross, K. W.

1972-01-01

A supplement is presented for a turbulent boundary layer nozzle analysis computer program. It describes the program calculation sequence and presents a detailed documentation of each subroutine. Important equations are derived explicitly, and improvements to the program are discussed.

ISPATOM: A Generic Real-Time Data Processing Tool Without Programming

NASA Technical Reports Server (NTRS)

Dershowitz, Adam

2007-01-01

Information Sharing Protocol Advanced Tool of Math (ISPATOM) is an application program allowing for the streamlined generation of comps, which subscribe to streams of incoming telemetry data, perform any necessary computations on the data, then send the data to other programs for display and/or further processing in NASA mission control centers. Heretofore, the development of comps was difficult, expensive, and time-consuming: Each comp was custom written manually, in a low-level computing language, by a programmer attempting to follow requirements of flight controllers. ISPATOM enables a flight controller who is not a programmer to write a comp by simply typing in one or more equation( s) at a command line or retrieving the equation(s) from a text file. ISPATOM then subscribes to the necessary input data, performs all of necessary computations, and sends out the results. It sends out new results whenever the input data change. The use of equations in ISPATOM is no more difficult than is entering equations in a spreadsheet. The time involved in developing a comp is thus limited to the time taken to decide on the necessary equations. Thus, ISPATOM is a real-time dynamic calculator.

A Computer Program for the Calculation of Three-Dimensional Transonic Nacelle/Inlet Flowfields

NASA Technical Reports Server (NTRS)

Vadyak, J.; Atta, E. H.

1983-01-01

A highly efficient computer analysis was developed for predicting transonic nacelle/inlet flowfields. This algorithm can compute the three dimensional transonic flowfield about axisymmetric (or asymmetric) nacelle/inlet configurations at zero or nonzero incidence. The flowfield is determined by solving the full-potential equation in conservative form on a body-fitted curvilinear computational mesh. The difference equations are solved using the AF2 approximate factorization scheme. This report presents a discussion of the computational methods used to both generate the body-fitted curvilinear mesh and to obtain the inviscid flow solution. Computed results and correlations with existing methods and experiment are presented. Also presented are discussions on the organization of the grid generation (NGRIDA) computer program and the flow solution (NACELLE) computer program, descriptions of the respective subroutines, definitions of the required input parameters for both algorithms, a brief discussion on interpretation of the output, and sample cases to illustrate application of the analysis.

A computer program for calculating laminar and turbulent boundary layers for two-dimensional time-dependent flows

NASA Technical Reports Server (NTRS)

Cebeci, T.; Carr, L. W.

1978-01-01

A computer program is described which provides solutions of two dimensional equations appropriate to laminar and turbulent boundary layers for boundary conditions with an external flow which fluctuates in magnitude. The program is based on the numerical solution of the governing boundary layer equations by an efficient two point finite difference method. An eddy viscosity formulation was used to model the Reynolds shear stress term. The main features of the method are briefly described and instructions for the computer program with a listing are provided. Sample calculations to demonstrate its usage and capabilities for laminar and turbulent unsteady boundary layers with an external flow which fluctuated in magnitude are presented.

Program helps quickly calculate deviated well path

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gardner, M.P.

1993-11-22

A BASIC computer program quickly calculates the angle and measured depth of a simple directional well given only the true vertical depth and total displacement of the target. Many petroleum engineers and geologists need a quick, easy method to calculate the angle and measured depth necessary to reach a target in a proposed deviated well bore. Too many of the existing programs are large and require much input data. The drilling literature is full of equations and methods to calculate the course of well paths from surveys taken after a well is drilled. Very little information, however, covers how tomore » calculate well bore trajectories for proposed wells from limited data. Furthermore, many of the equations are quite complex and difficult to use. A figure lists a computer program with the equations to calculate the well bore trajectory necessary to reach a given displacement and true vertical depth (TVD) for a simple build plant. It can be run on an IBM compatible computer with MS-DOS version 5 or higher, QBasic, or any BASIC that does no require line numbers. QBasic 4.5 compiler will also run the program. The equations are based on conventional geometry and trigonometry.« less

Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics

NASA Astrophysics Data System (ADS)

Halkos, George E.; Tsilika, Kyriaki D.

2011-09-01

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.

Ray Modeling Methods for Range Dependent Ocean Environments

DTIC Science & Technology

1983-12-01

the eikonal equation, gives rise to equations for ray paths which are perpendicular to the wave fronts. Equation II.4, the transport equation, leads... databases for use by MEDUSA. The author has assisted in the installation of MEDUSA at computer facilities which possess databases containing archives of...sound velocity profiles, bathymetry, and bottom loss data. At each computer site, programs convert the archival data retrieved by the database system

Particle trajectory computer program for icing analysis of axisymmetric bodies

NASA Technical Reports Server (NTRS)

Frost, Walter; Chang, Ho-Pen; Kimble, Kenneth R.

1982-01-01

General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.

EnviroLand: A Simple Computer Program for Quantitative Stream Assessment.

ERIC Educational Resources Information Center

Dunnivant, Frank; Danowski, Dan; Timmens-Haroldson, Alice; Newman, Meredith

2002-01-01

Introduces the Enviroland computer program which features lab simulations of theoretical calculations for quantitative analysis and environmental chemistry, and fate and transport models. Uses the program to demonstrate the nature of linear and nonlinear equations. (Author/YDS)

Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations

NASA Astrophysics Data System (ADS)

Husa, Sascha; Hinder, Ian; Lechner, Christiane

2006-06-01

We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert certain (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code for solving initial boundary value problems. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations. Program summaryTitle of program: Kranc Catalogue identifier: ADXS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXS_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computer for which the program is designed and others on which it has been tested: General computers which run Mathematica (for code generation) and Cactus (for numerical simulations), tested under Linux Programming language used: Mathematica, C, Fortran 90 Memory required to execute with typical data: This depends on the number of variables and gridsize, the included ADM example requires 4308 KB Has the code been vectorized or parallelized: The code is parallelized based on the Cactus framework. Number of bytes in distributed program, including test data, etc.: 1 578 142 Number of lines in distributed program, including test data, etc.: 11 711 Nature of physical problem: Solution of partial differential equations in three space dimensions, which are formulated as an initial value problem. In particular, the program is geared towards handling very complex tensorial equations as they appear, e.g., in numerical relativity. The worked out examples comprise the Klein-Gordon equations, the Maxwell equations, and the ADM formulation of the Einstein equations. Method of solution: The method of numerical solution is finite differencing and method of lines time integration, the numerical code is generated through a high level Mathematica interface. Restrictions on the complexity of the program: Typical numerical relativity applications will contain up to several dozen evolution variables and thousands of source terms, Cactus applications have shown scaling up to several thousand processors and grid sizes exceeding 500 3. Typical running time: This depends on the number of variables and the grid size: the included ADM example takes approximately 100 seconds on a 1600 MHz Intel Pentium M processor. Unusual features of the program: based on Mathematica and Cactus

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 3: Computer program manual

NASA Technical Reports Server (NTRS)

Schneider, J.; Boccio, J.

1972-01-01

A computer program is described capable of determining the properties of a compressible turbulent boundary layer with pressure gradient and heat transfer. The program treats the two-dimensional problem assuming perfect gas and Crocco integral energy solution. A compressibility transformation is applied to the equation for the conservation of mass and momentum, which relates this flow to a low speed constant property flow with simultaneous mass transfer and pressure gradient. The resulting system of describing equations consists of eight ordinary differential equations which are solved numerically. For Part 1, see N72-12226; for Part 2, see N72-15264.

A calculation procedure for viscous flow in turbomachines, volume 3. [computer programs

NASA Technical Reports Server (NTRS)

Khalil, I.; Sheoran, Y.; Tabakoff, W.

1980-01-01

A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.

Residue Management: A Computer Program About Conservation Tillage Decisions.

ERIC Educational Resources Information Center

Thien, Steve J.

1986-01-01

Describes a computer program, Residue Management, which is designed to supplement discussions on the Universal Soil Loss Equation and the impact of tillage on soil properties for introductory soil courses. The program advances the user through three stages of residue management. Information on obtaining the program is also included. (ML)

Probabilistic lifetime strength of aerospace materials via computational simulation

NASA Technical Reports Server (NTRS)

Boyce, Lola; Keating, Jerome P.; Lovelace, Thomas B.; Bast, Callie C.

1991-01-01

The results of a second year effort of a research program are presented. The research included development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic phenomenological constitutive relationship, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects of primitive variables. These primitive variables often originate in the environment and may include stress from loading, temperature, chemical, or radiation attack. This multifactor interaction constitutive equation is included in the computer program, PROMISS. Also included in the research is the development of methodology to calibrate the constitutive equation using actual experimental materials data together with the multiple linear regression of that data.

Parallel scheduling of recursively defined arrays

NASA Technical Reports Server (NTRS)

Myers, T. J.; Gokhale, M. B.

1986-01-01

A new method of automatic generation of concurrent programs which constructs arrays defined by sets of recursive equations is described. It is assumed that the time of computation of an array element is a linear combination of its indices, and integer programming is used to seek a succession of hyperplanes along which array elements can be computed concurrently. The method can be used to schedule equations involving variable length dependency vectors and mutually recursive arrays. Portions of the work reported here have been implemented in the PS automatic program generation system.

The pEst version 2.1 user's manual

NASA Technical Reports Server (NTRS)

Murray, James E.; Maine, Richard E.

1987-01-01

This report is a user's manual for version 2.1 of pEst, a FORTRAN 77 computer program for interactive parameter estimation in nonlinear dynamic systems. The pEst program allows the user complete generality in definig the nonlinear equations of motion used in the analysis. The equations of motion are specified by a set of FORTRAN subroutines; a set of routines for a general aircraft model is supplied with the program and is described in the report. The report also briefly discusses the scope of the parameter estimation problem the program addresses. The report gives detailed explanations of the purpose and usage of all available program commands and a description of the computational algorithms used in the program.

Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

ERIC Educational Resources Information Center

Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

2015-01-01

The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

A Special Topic From Nuclear Reactor Dynamics for the Undergraduate Physics Curriculum

ERIC Educational Resources Information Center

Sevenich, R. A.

1977-01-01

Presents an intuitive derivation of the point reactor equations followed by formulation of equations for inverse and direct kinetics which are readily programmed on a digital computer. Suggests several computer simulations involving the effect of control rod motion on reactor power. (MLH)

A computer program for estimating instream travel times and concentrations of a potential contaminant in the Yellowstone River, Montana

USGS Publications Warehouse

McCarthy, Peter M.

2006-01-01

The Yellowstone River is very important in a variety of ways to the residents of southeastern Montana; however, it is especially vulnerable to spilled contaminants. In 2004, the U.S. Geological Survey, in cooperation with Montana Department of Environmental Quality, initiated a study to develop a computer program to rapidly estimate instream travel times and concentrations of a potential contaminant in the Yellowstone River using regression equations developed in 1999 by the U.S. Geological Survey. The purpose of this report is to describe these equations and their limitations, describe the development of a computer program to apply the equations to the Yellowstone River, and provide detailed instructions on how to use the program. This program is available online at [http://pubs.water.usgs.gov/sir2006-5057/includes/ytot.xls]. The regression equations provide estimates of instream travel times and concentrations in rivers where little or no contaminant-transport data are available. Equations were developed and presented for the most probable flow velocity and the maximum probable flow velocity. These velocity estimates can then be used to calculate instream travel times and concentrations of a potential contaminant. The computer program was developed so estimation equations for instream travel times and concentrations can be solved quickly for sites along the Yellowstone River between Corwin Springs and Sidney, Montana. The basic types of data needed to run the program are spill data, streamflow data, and data for locations of interest along the Yellowstone River. Data output from the program includes spill location, river mileage at specified locations, instantaneous discharge, mean-annual discharge, drainage area, and channel slope. Travel times and concentrations are provided for estimates of the most probable velocity of the peak concentration and the maximum probable velocity of the peak concentration. Verification of estimates of instream travel times and concentrations for the Yellowstone River requires information about the flow velocity throughout the 520 mi of river in the study area. Dye-tracer studies would provide the best data about flow velocities and would provide the best verification of instream travel times and concentrations estimated from this computer program; however, data from such studies does not currently (2006) exist and new studies would be expensive and time-consuming. An alternative approach used in this study for verification of instream travel times is based on the use of flood-wave velocities determined from recorded streamflow hydrographs at selected mainstem streamflow-gaging stations along the Yellowstone River. The ratios of flood-wave velocity to the most probable velocity for the base flow estimated from the computer program are within the accepted range of 2.5 to 4.0 and indicate that flow velocities estimated from the computer program are reasonable for the Yellowstone River. The ratios of flood-wave velocity to the maximum probable velocity are within a range of 1.9 to 2.8 and indicate that the maximum probable flow velocities estimated from the computer program, which corresponds to the shortest travel times and maximum probable concentrations, are conservative and reasonable for the Yellowstone River.

Computer simulation of space station computer steered high gain antenna

NASA Technical Reports Server (NTRS)

Beach, S. W.

1973-01-01

The mathematical modeling and programming of a complete simulation program for a space station computer-steered high gain antenna are described. The program provides for reading input data cards, numerically integrating up to 50 first order differential equations, and monitoring up to 48 variables on printed output and on plots. The program system consists of a high gain antenna, an antenna gimbal control system, an on board computer, and the environment in which all are to operate.

Numerical solutions of 3-dimensional Navier-Stokes equations for closed bluff-bodies

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

NASA Technical Reports Server (NTRS)

Mitchell, C. E.; Eckert, K.

1979-01-01

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

A Symbolic and Graphical Computer Representation of Dynamical Systems

NASA Astrophysics Data System (ADS)

Gould, Laurence I.

2005-04-01

AUTONO is a Macsyma/Maxima program, designed at the University of Hartford, for solving autonomous systems of differential equations as well as for relating Lagrangians and Hamiltonians to their associated dynamical equations. AUTONO can be used in a number of fields to decipher a variety of complex dynamical systems with ease, producing their Lagrangian and Hamiltonian equations in seconds. These equations can then be incorporated into VisSim, a modeling and simulation program, which yields graphical representations of motion in a given system through easily chosen input parameters. The program, along with the VisSim differential-equations graphical package, allows for resolution and easy understanding of complex problems in a relatively short time; thus enabling quicker and more advanced computing of dynamical systems on any number of platforms---from a network of sensors on a space probe, to the behavior of neural networks, to the effects of an electromagnetic field on components in a dynamical system. A flowchart of AUTONO, along with some simple applications and VisSim output, will be shown.

Two-dimensional computer simulation of EMVJ and grating solar cells under AMO illumination

NASA Technical Reports Server (NTRS)

Gray, J. L.; Schwartz, R. J.

1984-01-01

A computer program, SCAP2D (Solar Cell Analysis Program in 2-Dimensions), is used to evaluate the Etched Multiple Vertical Junction (EMVJ) and grating solar cells. The aim is to demonstrate how SCAP2D can be used to evaluate cell designs. The cell designs studied are by no means optimal designs. The SCAP2D program solves the three coupled, nonlinear partial differential equations, Poisson's Equation and the hole and electron continuity equations, simultaneously in two-dimensions using finite differences to discretize the equations and Newton's Method to linearize them. The variables solved for are the electrostatic potential and the hole and electron concentrations. Each linear system of equations is solved directly by Gaussian Elimination. Convergence of the Newton Iteration is assumed when the largest correction to the electrostatic potential or hole or electron quasi-potential is less than some predetermined error. A typical problem involves 2000 nodes with a Jacobi matrix of order 6000 and a bandwidth of 243.

Computer Applications in Balancing Chemical Equations.

ERIC Educational Resources Information Center

Kumar, David D.

2001-01-01

Discusses computer-based approaches to balancing chemical equations. Surveys 13 methods, 6 based on matrix, 2 interactive programs, 1 stand-alone system, 1 developed in algorithm in Basic, 1 based on design engineering, 1 written in HyperCard, and 1 prepared for the World Wide Web. (Contains 17 references.) (Author/YDS)

Using Computer Symbolic Algebra to Solve Differential Equations.

ERIC Educational Resources Information Center

Mathews, John H.

1989-01-01

This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)

Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

NASA Technical Reports Server (NTRS)

Sitchin, A.

1972-01-01

Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

Analysis and testing of numerical formulas for the initial value problem

NASA Technical Reports Server (NTRS)

Brown, R. L.; Kovach, K. R.; Popyack, J. L.

1980-01-01

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions.

Computationally efficient multibody simulations

NASA Technical Reports Server (NTRS)

Ramakrishnan, Jayant; Kumar, Manoj

1994-01-01

Computationally efficient approaches to the solution of the dynamics of multibody systems are presented in this work. The computational efficiency is derived from both the algorithmic and implementational standpoint. Order(n) approaches provide a new formulation of the equations of motion eliminating the assembly and numerical inversion of a system mass matrix as required by conventional algorithms. Computational efficiency is also gained in the implementation phase by the symbolic processing and parallel implementation of these equations. Comparison of this algorithm with existing multibody simulation programs illustrates the increased computational efficiency.

A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach

NASA Astrophysics Data System (ADS)

Wu, Dongmei; Wang, Zhongcheng

2006-03-01

According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as y˜(x)=∑n=1m acos[(2n-1)ωx]. How to calculate the coefficients of the Fourier series efficiently with a computer program is still an open problem. For HB method, by substituting approximation y˜(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation y˜(x) [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563]. But for nonlinear differential equations such as Duffing equation, it is very difficult to construct higher-order analytical approximations, because the HB method requires solving a set of algebraic equations for a large number of unknowns with very complex nonlinearities. To overcome the difficulty, forty years ago, Urabe derived a computational method for Duffing equation based on Galerkin procedure [M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin's procedure, J. Math. Anal. Appl. 14 (1966) 107-140]. Dooren obtained an approximate solution of the Duffing oscillator with a special set of parameters by using Urabe's method [R. van Dooren, Stabilization of Cowell's classic finite difference method for numerical integration, J. Comput. Phys. 16 (1974) 186-192]. In this paper, in the frame of the general HB method, we present a new iteration algorithm to calculate the coefficients of the Fourier series. By using this new method, the iteration procedure starts with a(x)cos(ωx)+b(x)sin(ωx), and the accuracy may be improved gradually by determining new coefficients a,a,… will be produced automatically in an one-by-one manner. In all the stage of calculation, we need only to solve a cubic equation. Using this new algorithm, we develop a Mathematica program, which demonstrates following main advantages over the previous HB method: (1) it avoids solving a set of associate nonlinear equations; (2) it is easier to be implemented into a computer program, and produces a highly accurate solution with analytical expression efficiently. It is interesting to find that, generally, for a given set of parameters, a nonlinear Duffing equation can have three independent oscillation modes. For some sets of the parameters, it can have two modes with complex displacement and one with real displacement. But in some cases, it can have three modes, all of them having real displacement. Therefore, we can divide the parameters into two classes, according to the solution property: there is only one mode with real displacement and there are three modes with real displacement. This program should be useful to study the dynamically periodic behavior of a Duffing oscillator and can provide an approximate analytical solution with high-accuracy for testing the error behavior of newly developed numerical methods with a wide range of parameters. Program summaryTitle of program:AnalyDuffing.nb Catalogue identifier:ADWR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed and others on which it has been tested:the program has been designed for a microcomputer and been tested on the microcomputer. Computers:IBM PC Installations:the address(es) of your computer(s) Operating systems under which the program has been tested:Windows XP Programming language used:Software Mathematica 4.2, 5.0 and 5.1 No. of lines in distributed program, including test data, etc.:23 663 No. of bytes in distributed program, including test data, etc.:152 321 Distribution format:tar.gz Memory required to execute with typical data:51 712 Bytes No. of bits in a word: No. of processors used:1 Has the code been vectorized?:no Peripherals used:no Program Library subprograms used:no Nature of physical problem:To find an approximate solution with analytical expressions for the undamped nonlinear Duffing equation with periodic driving force when the fundamental frequency is identical to the driving force. Method of solution:In the frame of the general HB method, by using a new iteration algorithm to calculate the coefficients of the Fourier series, we can obtain an approximate analytical solution with high-accuracy efficiently. Restrictions on the complexity of the problem:For problems, which have a large driving frequency, the convergence may be a little slow, because more iterative times are needed. Typical running time:several seconds Unusual features of the program:For an undamped Duffing equation, it can provide all the solutions or the oscillation modes with real displacement for any interesting parameters, for the required accuracy, efficiently. The program can be used to study the dynamically periodic behavior of a nonlinear oscillator, and can provide a high-accurate approximate analytical solution for developing high-accurate numerical method.

The National Streamflow Statistics Program: A Computer Program for Estimating Streamflow Statistics for Ungaged Sites

USGS Publications Warehouse

Ries(compiler), Kernell G.; With sections by Atkins, J. B.; Hummel, P.R.; Gray, Matthew J.; Dusenbury, R.; Jennings, M.E.; Kirby, W.H.; Riggs, H.C.; Sauer, V.B.; Thomas, W.O.

2007-01-01

The National Streamflow Statistics (NSS) Program is a computer program that should be useful to engineers, hydrologists, and others for planning, management, and design applications. NSS compiles all current U.S. Geological Survey (USGS) regional regression equations for estimating streamflow statistics at ungaged sites in an easy-to-use interface that operates on computers with Microsoft Windows operating systems. NSS expands on the functionality of the USGS National Flood Frequency Program, and replaces it. The regression equations included in NSS are used to transfer streamflow statistics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally, the equations were developed on a statewide or metropolitan-area basis as part of cooperative study programs. Equations are available for estimating rural and urban flood-frequency statistics, such as the 1 00-year flood, for every state, for Puerto Rico, and for the island of Tutuila, American Samoa. Equations are available for estimating other statistics, such as the mean annual flow, monthly mean flows, flow-duration percentiles, and low-flow frequencies (such as the 7-day, 0-year low flow) for less than half of the states. All equations available for estimating streamflow statistics other than flood-frequency statistics assume rural (non-regulated, non-urbanized) conditions. The NSS output provides indicators of the accuracy of the estimated streamflow statistics. The indicators may include any combination of the standard error of estimate, the standard error of prediction, the equivalent years of record, or 90 percent prediction intervals, depending on what was provided by the authors of the equations. The program includes several other features that can be used only for flood-frequency estimation. These include the ability to generate flood-frequency plots, and plots of typical flood hydrographs for selected recurrence intervals, estimates of the probable maximum flood, extrapolation of the 500-year flood when an equation for estimating it is not available, and weighting techniques to improve flood-frequency estimates for gaging stations and ungaged sites on gaged streams. This report describes the regionalization techniques used to develop the equations in NSS and provides guidance on the applicability and limitations of the techniques. The report also includes a users manual and a summary of equations available for estimating basin lagtime, which is needed by the program to generate flood hydrographs. The NSS software and accompanying database, and the documentation for the regression equations included in NSS, are available on the Web at http://water.usgs.gov/software/.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, A. E.; Epton, M. A.

1981-01-01

Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.

Wind Factor Simulation Model: User’s Manual.

DTIC Science & Technology

1980-04-01

computer program documentation; com- puterized simulation; equivalent headwind technique; great circle; great circle distance; great circle equation ; great... equation of a great circle. Program listing and flow chart are included. iv UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(WIh.n Date EnItrd) USER’S...THE EQUATOR . 336 C 337 NTRIFG = 0 338 C 339 C END OF FUNCTION ICONV I 1. RETURN TO MAIN PROGRAM . 340 C 42 341 RETURN 34? C 343 C 344 C 345 C * PART II

Space-Plane Spreadsheet Program

NASA Technical Reports Server (NTRS)

Mackall, Dale

1993-01-01

Basic Hypersonic Data and Equations (HYPERDATA) spreadsheet computer program provides data gained from three analyses of performance of space plane. Equations used to perform analyses derived from Newton's second law of physics, derivation included. First analysis is parametric study of some basic factors affecting ability of space plane to reach orbit. Second includes calculation of thickness of spherical fuel tank. Third produces ratio between volume of fuel and total mass for each of various aircraft. HYPERDATA intended for use on Macintosh(R) series computers running Microsoft Excel 3.0.

Implications of a quadratic stream definition in radiative transfer theory.

NASA Technical Reports Server (NTRS)

Whitney, C.

1972-01-01

An explicit definition of the radiation-stream concept is stated and applied to approximate the integro-differential equation of radiative transfer with a set of twelve coupled differential equations. Computational efficiency is enhanced by distributing the corresponding streams in three-dimensional space in a totally symmetric way. Polarization is then incorporated in this model. A computer program based on the model is briefly compared with a Monte Carlo program for simulation of horizon scans of the earth's atmosphere. It is found to be considerably faster.

Computer program for investigating effects of nonlinear suspension-system elastic properties on parachute inflation loads and motions

NASA Technical Reports Server (NTRS)

Poole, L. R.

1972-01-01

A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.

Modeling and Analysis of Power Processing Systems (MAPPS). Volume 2: Appendices

NASA Technical Reports Server (NTRS)

Lee, F. C.; Radman, S.; Carter, R. A.; Wu, C. H.; Yu, Y.; Chang, R.

1980-01-01

The computer programs and derivations generated in support of the modeling and design optimization program are presented. Programs for the buck regulator, boost regulator, and buck-boost regulator are described. The computer program for the design optimization calculations is presented. Constraints for the boost and buck-boost converter were derived. Derivations of state-space equations and transfer functions are presented. Computer lists for the converters are presented, and the input parameters justified.

Viscous wing theory development. Volume 2: GRUMWING computer program user's manual

NASA Technical Reports Server (NTRS)

Chow, R. R.; Ogilvie, P. L.

1986-01-01

This report is a user's manual which describes the operation of the computer program, GRUMWING. The program computes the viscous transonic flow over three-dimensional wings using a boundary layer type viscid-inviscid interaction approach. The inviscid solution is obtained by an approximate factorization (AFZ)method for the full potential equation. The boundary layer solution is based on integral entrainment methods.

Kmonodium, a Program for the Numerical Solution of the One-Dimensional Schrodinger Equation

ERIC Educational Resources Information Center

Angeli, Celestino; Borini, Stefano; Cimiraglia, Renzo

2005-01-01

A very simple strategy for the solution of the Schrodinger equation of a particle moving in one dimension subjected to a generic potential is presented. This strategy is implemented in a computer program called Kmonodium, which is free and distributed under the General Public License (GPL).

Titration Calculations with Computer Algebra Software

ERIC Educational Resources Information Center

Lachance, Russ; Biaglow, Andrew

2012-01-01

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

Creating Printed Materials for Mathematics with a Macintosh Computer.

ERIC Educational Resources Information Center

Mahler, Philip

This document gives instructions on how to use a Macintosh computer to create printed materials for mathematics. A Macintosh computer, Microsoft Word, and objected-oriented (Draw-type) art program, and a function-graphing program are capable of producing high quality printed instructional materials for mathematics. Word 5.1 has an equation editor…

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

NASA Technical Reports Server (NTRS)

Morozov, S. K.; Krasitskiy, O. P.

1978-01-01

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

The prediction of satellite ephemeris errors as they result from surveillance system measurement errors

NASA Astrophysics Data System (ADS)

Simmons, B. E.

1981-08-01

This report derives equations predicting satellite ephemeris error as a function of measurement errors of space-surveillance sensors. These equations lend themselves to rapid computation with modest computer resources. They are applicable over prediction times such that measurement errors, rather than uncertainties of atmospheric drag and of Earth shape, dominate in producing ephemeris error. This report describes the specialization of these equations underlying the ANSER computer program, SEEM (Satellite Ephemeris Error Model). The intent is that this report be of utility to users of SEEM for interpretive purposes, and to computer programmers who may need a mathematical point of departure for limited generalization of SEEM.

78 FR 41265 - Energy Conservation Program for Consumer Products: Test Procedures for Residential Furnaces and...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-07-10

... 750 employees. DOE surveyed the AHRI certification directories for furnaces and boilers, as well as... calculation computer program to account for the new equations. 78 FR 7681, 7690 (Feb. 4, 2013). In the NOPR... quotes obtained from computer programmers familiar with the AFUE calculation program that is currently...

A real-time digital computer program for the simulation of a single rotor helicopter

NASA Technical Reports Server (NTRS)

Houck, J. A.; Gibson, L. H.; Steinmetz, G. G.

1974-01-01

A computer program was developed for the study of a single-rotor helicopter on the Langley Research Center real-time digital simulation system. Descriptions of helicopter equations and data, program subroutines (including flow charts and listings), real-time simulation system routines, and program operation are included. Program usage is illustrated by standard check cases and a representative flight case.

A Multi-Fidelity Surrogate Model for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S."bala"

2016-11-01

The explosive dispersal of particles is an example of a complex multiphase and multi-species fluid flow problem. This problem has many engineering applications including particle-laden explosives. In these flows, the detonation products of the explosive cannot be treated as a perfect gas so a real gas equation of state is used to close the governing equations (unlike air, which uses the ideal gas equation for closure). As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both of the state equations must be satisfied. One of the more accurate, yet computationally expensive, methods to deal with this is a scheme that iterates between the two equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work strives to create a multi-fidelity surrogate model of this process. We then study the performance of the model with respect to the iterative method by performing both gas-only and particle laden flow simulations using an Eulerian-Lagrangian approach with a finite volume code. Specifically, the model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel modeling approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

The National Flood Frequency Program, version 3 : a computer program for estimating magnitude and frequency of floods for ungaged sites

USGS Publications Warehouse

Ries, Kernell G.; Crouse, Michele Y.

2002-01-01

For many years, the U.S. Geological Survey (USGS) has been developing regional regression equations for estimating flood magnitude and frequency at ungaged sites. These regression equations are used to transfer flood characteristics from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory or predictor variables. Generally, these equations have been developed on a Statewide or metropolitan-area basis as part of cooperative study programs with specific State Departments of Transportation. In 1994, the USGS released a computer program titled the National Flood Frequency Program (NFF), which compiled all the USGS available regression equations for estimating the magnitude and frequency of floods in the United States and Puerto Rico. NFF was developed in cooperation with the Federal Highway Administration and the Federal Emergency Management Agency. Since the initial release of NFF, the USGS has produced new equations for many areas of the Nation. A new version of NFF has been developed that incorporates these new equations and provides additional functionality and ease of use. NFF version 3 provides regression-equation estimates of flood-peak discharges for unregulated rural and urban watersheds, flood-frequency plots, and plots of typical flood hydrographs for selected recurrence intervals. The Program also provides weighting techniques to improve estimates of flood-peak discharges for gaging stations and ungaged sites. The information provided by NFF should be useful to engineers and hydrologists for planning and design applications. This report describes the flood-regionalization techniques used in NFF and provides guidance on the applicability and limitations of the techniques. The NFF software and the documentation for the regression equations included in NFF are available at http://water.usgs.gov/software/nff.html.

Reduze - Feynman integral reduction in C++

NASA Astrophysics Data System (ADS)

Studerus, C.

2010-07-01

Reduze is a computer program for reducing Feynman integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel. Program summaryProgram title:Reduze Catalogue identifier: AEGE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:: yes No. of lines in distributed program, including test data, etc.: 55 433 No. of bytes in distributed program, including test data, etc.: 554 866 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Unix/Linux Number of processors used: The number of processors is problem dependent. More than one possible but not arbitrary many. RAM: Depends on the complexity of the system. Classification: 4.4, 5 External routines: CLN ( http://www.ginac.de/CLN/), GiNaC ( http://www.ginac.de/) Nature of problem: Solving large systems of linear equations with Feynman integrals as unknowns and rational polynomials as prefactors. Solution method: Using a Gauss/Laporta algorithm to solve the system of equations. Restrictions: Limitations depend on the complexity of the system (number of equations, number of kinematic invariants). Running time: Depends on the complexity of the system.

The use of numerical programs in research and academic institutions

NASA Astrophysics Data System (ADS)

Scupi, A. A.

2016-08-01

This paper is conceived on the idea that numerical programs using computer models of physical processes can be used both for scientific research and academic teaching to study different phenomena. Computational Fluid Dynamics (CFD) is used today on a large scale in research and academic institutions. CFD development is not limited to computer simulations of fluid flow phenomena. Analytical solutions for most fluid dynamics problems are already available for ideal or simplified situations for different situations. CFD is based on the Navier- Stokes (N-S) equations characterizing the flow of a single phase of any liquid. For multiphase flows the integrated N-S equations are complemented with equations of the Volume of Fluid Model (VOF) and with energy equations. Different turbulent models were used in the paper, each one of them with practical engineering applications: the flow around aerodynamic surfaces used as unconventional propulsion system, multiphase flows in a settling chamber and pneumatic transport systems, heat transfer in a heat exchanger etc. Some of them numerical results were validated by experimental results. Numerical programs are also used in academic institutions where certain aspects of various phenomena are presented to students (Bachelor, Master and PhD) for a better understanding of the phenomenon itself.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral equations and finite difference methods for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite difference solution of the transonic small perturbation equation, the integral equation program is given primary emphasis here because it is less well known.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral-equations and finite-difference method for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite-difference solution of the transonic small-perturbation equation, the integral-equation program is given primary emphasis here because it is less well known.

Chaotic Calculations.

ERIC Educational Resources Information Center

Chenery, Gordon

1991-01-01

Uses chaos theory to investigate the nonlinear phenomenon of population growth fluctuation. Illustrates the use of computers and computer programs to make calculations in a nonlinear difference equation system. (MDH)

Parallel aeroelastic computations for wing and wing-body configurations

NASA Technical Reports Server (NTRS)

Byun, Chansup

1994-01-01

The objective of this research is to develop computationally efficient methods for solving fluid-structural interaction problems by directly coupling finite difference Euler/Navier-Stokes equations for fluids and finite element dynamics equations for structures on parallel computers. This capability will significantly impact many aerospace projects of national importance such as Advanced Subsonic Civil Transport (ASCT), where the structural stability margin becomes very critical at the transonic region. This research effort will have direct impact on the High Performance Computing and Communication (HPCC) Program of NASA in the area of parallel computing.

Numerical simulation code for self-gravitating Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Madarassy, Enikő J. M.; Toth, Viktor T.

2013-04-01

We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson’s equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subsequent time iterations, previously computed values of the gravitational field serve as very good initial estimates. The code is robust (as evidenced by its stability on coarse grids) and efficient enough to simulate the evolution of a system over the course of 109 years using a finer (100×100×100) spatial grid, in less than a day of processor time on a contemporary desktop computer. Catalogue identifier: AEOR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOR_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5248 No. of bytes in distributed program, including test data, etc.: 715402 Distribution format: tar.gz Programming language: C++ or FORTRAN. Computer: PCs or workstations. Operating system: Linux or Windows. Classification: 1.5. Nature of problem: Simulation of a self-gravitating Bose-Einstein condensate by simultaneous solution of the Gross-Pitaevskii and Poisson equations in three dimensions. Solution method: The Gross-Pitaevskii equation is solved numerically using the Crank-Nicholson method; Poisson’s equation is solved using the relaxation method. The time evolution of the system is governed by the Gross-Pitaevskii equation; the solution of Poisson’s equation at each time step is used as an initial estimate for the next time step, which dramatically increases the efficiency of the relaxation method. Running time: Depends on the chosen size of the problem. On a typical personal computer, a 100×100×100 grid can be solved with a time span of 10 Gyr in approx. a day of running time.

SAGUARO: a finite-element computer program for partially saturated porous flow problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eaton, R.R.; Gartling, D.K.; Larson, D.E.

1983-06-01

SAGUARO is a finite element computer program designed to calculate two-dimensional flow of mass and energy through porous media. The media may be saturated or partially saturated. SAGUARO solves the parabolic time-dependent mass transport equation which accounts for the presence of partially saturated zones through the use of highly non-linear material characteristic curves. The energy equation accounts for the possibility of partially saturated regions by adjusting the thermal capacitances and thermal conductivities according to the volume fraction of water present in the local pores. Program capabilities, user instructions and a sample problem are presented in this manual.

Computation of high Reynolds number internal/external flows

NASA Technical Reports Server (NTRS)

Cline, M. C.; Wilmoth, R. G.

1981-01-01

A general, user oriented computer program, called VNAP2, has been developed to calculate high Reynolds number, internal/external flows. VNAP2 solves the two-dimensional, time-dependent Navier-Stokes equations. The turbulence is modeled with either a mixing-length, a one transport equation, or a two transport equation model. Interior grid points are computed using the explicit MacCormack scheme with special procedures to speed up the calculation in the fine grid. All boundary conditions are calculated using a reference plane characteristic scheme with the viscous terms treated as source terms. Several internal, and internal/external flow calculations are presented.

An analytical procedure and automated computer code used to design model nozzles which meet MSFC base pressure similarity parameter criteria. [space shuttle

NASA Technical Reports Server (NTRS)

Sulyma, P. R.

1980-01-01

Fundamental equations and similarity definition and application are described as well as the computational steps of a computer program developed to design model nozzles for wind tunnel tests conducted to define power-on aerodynamic characteristics of the space shuttle over a range of ascent trajectory conditions. The computer code capabilities, a user's guide for the model nozzle design program, and the output format are examined. A program listing is included.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Refinement Of Hexahedral Cells In Euler Flow Computations

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1996-01-01

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

Estimating Relative Positions of Outer-Space Structures

NASA Technical Reports Server (NTRS)

Balian, Harry; Breckenridge, William; Brugarolas, Paul

2009-01-01

A computer program estimates the relative position and orientation of two structures from measurements, made by use of electronic cameras and laser range finders on one structure, of distances and angular positions of fiducial objects on the other structure. The program was written specifically for use in determining errors in the alignment of large structures deployed in outer space from a space shuttle. The program is based partly on equations for transformations among the various coordinate systems involved in the measurements and on equations that account for errors in the transformation operators. It computes a least-squares estimate of the relative position and orientation. Sequential least-squares estimates, acquired at a measurement rate of 4 Hz, are averaged by passing them through a fourth-order Butterworth filter. The program is executed in a computer aboard the space shuttle, and its position and orientation estimates are displayed to astronauts on a graphical user interface.

User's guide to the NOZL3D and NOZLIC computer programs

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1980-01-01

Complete FORTRAN listings and running instructions are given for a set of computer programs that perform an implicit numerical solution to the unsteady Navier-Stokes equations to predict the flow characteristics and performance of nonaxisymmetric nozzles. The set includes the NOZL3D program, which performs the flow computations; the NOZLIC program, which sets up the flow field initial conditions for general nozzle configurations, and also generates the computational grid for simple two dimensional and axisymmetric configurations; and the RGRIDD program, which generates the computational grid for complicated three dimensional configurations. The programs are designed specifically for the NASA-Langley CYBER 175 computer, and employ auxiliary disk files for primary data storage. Input instructions and computed results are given for four test cases that include two dimensional, three dimensional, and axisymmetric configurations.

IMP: Interactive mass properties program. Volume 1: Program description

NASA Technical Reports Server (NTRS)

Stewart, W. A.

1976-01-01

A method of computing a weights and center of gravity analysis of a flight vehicle using interactive graphical capabilities of the Adage 340 computer is described. The equations used to calculate area, volume, and mass properties are based on elemental surface characteristics. The input/output methods employ the graphic support of the Adage computer. Several interactive program options are available for analyzing the mass properties of a vehicle. These options are explained.

Introduction to the Application of the Dynalist Computer Program to the Analysis of Rail Systems Dynamics

DOT National Transportation Integrated Search

1974-08-01

DYNALIST, a computer program that extracts complex eigenvalues and eigenvectors for dynamic systems described in terms of matrix equations of motion, has been acquired and made operational at TSC. In this report, simple dynamic systems are used to de...

A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1974-01-01

The equations of motion are derived, in vector-dyadic format, for a topological tree of coupled rigid bodies, point masses, and symmetrical momentum wheels. These equations were programmed, and form the basis for the general-purpose digital computer program N-BOD. A complete derivation of the equations of motion is included along with a description of the methods used for kinematics, constraint elimination, and for the inclusion of nongyroscope forces and torques acting external or internal to the system.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

HEMP 3D: A finite difference program for calculating elastic-plastic flow, appendix B

NASA Astrophysics Data System (ADS)

Wilkins, Mark L.

1993-05-01

The HEMP 3D program can be used to solve problems in solid mechanics involving dynamic plasticity and time dependent material behavior and problems in gas dynamics. The equations of motion, the conservation equations, and the constitutive relations listed below are solved by finite difference methods following the format of the HEMP computer simulation program formulated in two space dimensions and time.

Solution of the equation of heat conduction with time dependent sources: Programmed application to planetary thermal history

NASA Technical Reports Server (NTRS)

Conel, J. E.

1975-01-01

A computer program (Program SPHERE) solving the inhomogeneous equation of heat conduction with radiation boundary condition on a thermally homogeneous sphere is described. The source terms are taken to be exponential functions of the time. Thermal properties are independent of temperature. The solutions are appropriate to studying certain classes of planetary thermal history. Special application to the moon is discussed.

GRUMFOIL: A computer code for the viscous transonic flow over airfoils

NASA Technical Reports Server (NTRS)

Mead, H. R.; Melnik, R. E.

1985-01-01

A user's manual which describes the operation of the computer program, GRUMFOIL is presented. The program computes the viscous transonic flow over two dimensional airfoils using a boundary layer type viscid-inviscid interaction approach. The inviscid solution is obtained by a multigrid method for the full potential equation. The boundary layer solution is based on integral entrainment methods.

FastChem: A computer program for efficient complex chemical equilibrium calculations in the neutral/ionized gas phase with applications to stellar and planetary atmospheres

NASA Astrophysics Data System (ADS)

Stock, Joachim W.; Kitzmann, Daniel; Patzer, A. Beate C.; Sedlmayr, Erwin

2018-06-01

For the calculation of complex neutral/ionized gas phase chemical equilibria, we present a semi-analytical versatile and efficient computer program, called FastChem. The applied method is based on the solution of a system of coupled nonlinear (and linear) algebraic equations, namely the law of mass action and the element conservation equations including charge balance, in many variables. Specifically, the system of equations is decomposed into a set of coupled nonlinear equations in one variable each, which are solved analytically whenever feasible to reduce computation time. Notably, the electron density is determined by using the method of Nelder and Mead at low temperatures. The program is written in object-oriented C++ which makes it easy to couple the code with other programs, although a stand-alone version is provided. FastChem can be used in parallel or sequentially and is available under the GNU General Public License version 3 at https://github.com/exoclime/FastChem together with several sample applications. The code has been successfully validated against previous studies and its convergence behavior has been tested even for extreme physical parameter ranges down to 100 K and up to 1000 bar. FastChem converges stable and robust in even most demanding chemical situations, which posed sometimes extreme challenges for previous algorithms.

Analysis of a Multi-Fidelity Surrogate for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S.

2017-06-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the detonation products of the explosive must be treated as real gas while the ideal gas equation of state is used for the surrounding air. As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both state equations must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between both equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work aims to use a multi-fidelity surrogate model to replace this process. A Kriging model is used to produce a curve fit which interpolates selected data from the iterative algorithm using Bayesian statistics. We study the model performance with respect to the iterative method in simulations using a finite volume code. The model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel approach. Also, optimizing the combination of model accuracy and computational speed through the choice of sampling points is explained. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program as a Cooperative Agreement under the Predictive Science Academic Alliance Program under Contract No. DE-NA0002378.

A Computer Program for Preliminary Data Analysis

Treesearch

Dennis L. Schweitzer

1967-01-01

ABSTRACT. -- A computer program written in FORTRAN has been designed to summarize data. Class frequencies, means, and standard deviations are printed for as many as 100 independent variables. Cross-classifications of an observed dependent variable and of a dependent variable predicted by a multiple regression equation can also be generated.

Continued development and correlation of analytically based weight estimation codes for wings and fuselages

NASA Technical Reports Server (NTRS)

Mullen, J., Jr.

1978-01-01

The implementation of the changes to the program for Wing Aeroelastic Design and the development of a program to estimate aircraft fuselage weights are described. The equations to implement the modified planform description, the stiffened panel skin representation, the trim loads calculation, and the flutter constraint approximation are presented. A comparison of the wing model with the actual F-5A weight material distributions and loads is given. The equations and program techniques used for the estimation of aircraft fuselage weights are described. These equations were incorporated as a computer code. The weight predictions of this program are compared with data from the C-141.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

GYC: A program to compute the turbulent boundary layer on a rotating cone

NASA Technical Reports Server (NTRS)

Sullivan, R. D.

1976-01-01

A computer program, GYC, which is capable of computing the properties of a compressible turbulent boundary layer on a rotating axisymmetric cone-cylinder body, according to the principles of invariant modeling was studied. The program is extended to include the calculation of the turbulence scale by a differential equation. GYC is in operation on the CDC-7600 computer and has undergone several corrections and improvements as a result of the experience gained. The theoretical basis for the program and the method of implementation, as well as information on its operation are given.

Culvert analysis program for indirect measurement of discharge

USGS Publications Warehouse

Fulford, Janice M.; ,

1993-01-01

A program based on the U.S. Geological Survey (USGS) methods for indirectly computing peak discharges through culverts allows users to employ input data formats used by the water surface profile program (WSPRO). The program can be used to compute discharge rating surfaces or curves that describe the behavior of flow through a particular culvert or to compute discharges from measurements of upstream of the gradually varied flow equations and has been adapted slightly to provide solutions that minimize the need for the user to determine between different flow regimes. The program source is written in Fortran 77 and has been run on mini-computers and personal computers. The program does not use or require graphics capability, a color monitor, or a mouse.

Basic research and data analysis for the National Geodetic Satellite program and for the Earth Surveys program

NASA Technical Reports Server (NTRS)

1972-01-01

Current research is reported on precise and accurate descriptions of the earth's surface and gravitational field and on time variations of geophysical parameters. A new computer program was written in connection with the adjustment of the BC-4 worldwide geometric satellite triangulation net. The possibility that an increment to accuracy could be transferred from a super-control net to the basic geodetic (first-order triangulation) was investigated. Coordinates of the NA9 solution were computed and were transformed to the NAD datum, based on GEOS 1 observations. Normal equations from observational data of several different systems and constraint equations were added and a single solution was obtained for the combined systems. Transformation parameters with constraints were determined, and the impact of computers on surveying and mapping is discussed.

Activity computer program for calculating ion irradiation activation

NASA Astrophysics Data System (ADS)

Palmer, Ben; Connolly, Brian; Read, Mark

2017-07-01

A computer program, Activity, was developed to predict the activity and gamma lines of materials irradiated with an ion beam. It uses the TENDL (Koning and Rochman, 2012) [1] proton reaction cross section database, the Stopping and Range of Ions in Matter (SRIM) (Biersack et al., 2010) code, a Nuclear Data Services (NDS) radioactive decay database (Sonzogni, 2006) [2] and an ENDF gamma decay database (Herman and Chadwick, 2006) [3]. An extended version of Bateman's equation is used to calculate the activity at time t, and this equation is solved analytically, with the option to also solve by numeric inverse Laplace Transform as a failsafe. The program outputs the expected activity and gamma lines of the activated material.

Prediction of elemental creep. [steady state and cyclic data from regression analysis

NASA Technical Reports Server (NTRS)

Davis, J. W.; Rummler, D. R.

1975-01-01

Cyclic and steady-state creep tests were performed to provide data which were used to develop predictive equations. These equations, describing creep as a function of stress, temperature, and time, were developed through the use of a least squares regression analyses computer program for both the steady-state and cyclic data sets. Comparison of the data from the two types of tests, revealed that there was no significant difference between the cyclic and steady-state creep strains for the L-605 sheet under the experimental conditions investigated (for the same total time at load). Attempts to develop a single linear equation describing the combined steady-state and cyclic creep data resulted in standard errors of estimates higher than obtained for the individual data sets. A proposed approach to predict elemental creep in metals uses the cyclic creep equation and a computer program which applies strain and time hardening theories of creep accumulation.

Discrete sensitivity derivatives of the Navier-Stokes equations with a parallel Krylov solver

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Taylor, Arthur C., III

1994-01-01

This paper solves an 'incremental' form of the sensitivity equations derived by differentiating the discretized thin-layer Navier Stokes equations with respect to certain design variables of interest. The equations are solved with a parallel, preconditioned Generalized Minimal RESidual (GMRES) solver on a distributed-memory architecture. The 'serial' sensitivity analysis code is parallelized by using the Single Program Multiple Data (SPMD) programming model, domain decomposition techniques, and message-passing tools. Sensitivity derivatives are computed for low and high Reynolds number flows over a NACA 1406 airfoil on a 32-processor Intel Hypercube, and found to be identical to those computed on a single-processor Cray Y-MP. It is estimated that the parallel sensitivity analysis code has to be run on 40-50 processors of the Intel Hypercube in order to match the single-processor processing time of a Cray Y-MP.

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Cole, Helen; Chen, C. P.

2005-01-01

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Equations of motion for coupled n-body systems

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1980-01-01

Computer program, developed to analyze spacecraft attitude dynamics, can be applied to large class of problems involving objects that can be simplified into component parts. Systems of coupled rigid bodies, point masses, symmetric wheels, and elastically flexible bodies can be analyzed. Program derives complete set of non-linear equations of motion in vectordyadic format. Numerical solutions may be printed out. Program is in FORTRAN IV for batch execution and has been implemented on IBM 360.

DYNGEN: A program for calculating steady-state and transient performance of turbojet and turbofan engines

NASA Technical Reports Server (NTRS)

Sellers, J. F.; Daniele, C. J.

1975-01-01

The DYNGEN, a digital computer program for analyzing the steady state and transient performance of turbojet and turbofan engines, is described. The DYNGEN is based on earlier computer codes (SMOTE, GENENG, and GENENG 2) which are capable of calculating the steady state performance of turbojet and turbofan engines at design and off-design operating conditions. The DYNGEN has the combined capabilities of GENENG and GENENG 2 for calculating steady state performance; to these the further capability for calculating transient performance was added. The DYNGEN can be used to analyze one- and two-spool turbojet engines or two- and three-spool turbofan engines without modification to the basic program. A modified Euler method is used by DYNGEN to solve the differential equations which model the dynamics of the engine. This new method frees the programmer from having to minimize the number of equations which require iterative solution. As a result, some of the approximations normally used in transient engine simulations can be eliminated. This tends to produce better agreement when answers are compared with those from purely steady state simulations. The modified Euler method also permits the user to specify large time steps (about 0.10 sec) to be used in the solution of the differential equations. This saves computer execution time when long transients are run. Examples of the use of the program are included, and program results are compared with those from an existing hybrid-computer simulation of a two-spool turbofan.

Correlation of Experimental and Theoretical Steady-State Spinning Motion for a Current Fighter Airplane Using Rotation-Balance Aerodynamic Data

DTIC Science & Technology

1978-07-01

were input into the computer program. The program was numerically intergrated with time by using a fourth-order Runge-Kutta integration algorithm with...equations of motion are numerically intergrated to provide time histories of the aircraft spinning motion. A.2 EQUATIONS DEFINING THE FORCE AND MOMENT...by Cy or Cn. 50 AE DC-TR-77-126 A . 4 where EQUATIONS FOR TRANSFERRING AERODYNAMIC DATA INPUTS TO THE PROPER HORIZONTAL CENTER OF GRAVITY

Sizing-tube-fin space radiators

NASA Technical Reports Server (NTRS)

Peoples, J. A.

1978-01-01

Temperature and size considerations of the tube fin space radiator were characterized by charts and equations. An approach of accurately assessing rejection capability commensurate with a phase A/B level output is reviewed. A computer program, based on Mackey's equations, is also presented which sizes the rejection area for a given thermal load. The program also handles the flow and thermal considerations of the film coefficient.

Path-Following Solutions Of Nonlinear Equations

NASA Technical Reports Server (NTRS)

Barger, Raymond L.; Walters, Robert W.

1989-01-01

Report describes some path-following techniques for solution of nonlinear equations and compares with other methods. Use of multipurpose techniques applicable at more than one stage of path-following computation results in system relatively simple to understand, program, and use. Comparison of techniques with method of parametric differentiation (MPD) reveals definite advantages for path-following methods. Emphasis in investigation on multiuse techniques being applied at more than one stage of path-following computation. Incorporation of multipurpose techniques results in concise computer code relatively simple to use.

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1991-01-01

The three dimensional quasi-analytical sensitivity analysis and the ancillary driver programs are developed needed to carry out the studies and perform comparisons. The code is essentially contained in one unified package which includes the following: (1) a three dimensional transonic wing analysis program (ZEBRA); (2) a quasi-analytical portion which determines the matrix elements in the quasi-analytical equations; (3) a method for computing the sensitivity coefficients from the resulting quasi-analytical equations; (4) a package to determine for comparison purposes sensitivity coefficients via the finite difference approach; and (5) a graphics package.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation

NASA Technical Reports Server (NTRS)

Chesler, L.; Pierce, S.

1971-01-01

Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program.

MSFC crack growth analysis computer program, version 2 (users manual)

NASA Technical Reports Server (NTRS)

Creager, M.

1976-01-01

An updated version of the George C. Marshall Space Flight Center Crack Growth Analysis Program is described. The updated computer program has significantly expanded capabilities over the original one. This increased capability includes an extensive expansion of the library of stress intensity factors, plotting capability, increased design iteration capability, and the capability of performing proof test logic analysis. The technical approaches used within the computer program are presented, and the input and output formats and options are described. Details of the stress intensity equations, example data, and example problems are presented.

Computer Series, 67: Bits and Pieces, 27.

ERIC Educational Resources Information Center

Moore, John W., Ed.

1986-01-01

Discusses a computer interfacing course using Commodore 64 microcomputers; a computer program for radioactive equilibrium; analysis of near infrared spectrum of hydrochloric acid molecules using Apple II microcomputers; microcomputer approach to conductivity titrations; balancing equations with Commodore 64's; formulation of mathematical…

Metabolic balance analysis program

NASA Technical Reports Server (NTRS)

Rombach, J.

1971-01-01

Computer program calculates 28 day diet for life support consumables requirements and waste removal. Equations representing food breakdown into carbohydrates, fats, and proteins, modified to account for digestive materials and indigestible crude fibers, formulate total energy consumption. Program applications are listed.

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Levine, J. N.

1971-01-01

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

ROTRAN 1 - SOLUTION OF EQUATIONS FOR ROTARY TRANSFORMERS

NASA Technical Reports Server (NTRS)

Salomon, P. M.

1994-01-01

ROTRAN1 is a computer program to calculate the impedance and current gain of a simple transformer. Inputs to the program are primary resistance, primary inductance, secondary (load) resistance, secondary inductance, and mutual inductance. ROTRAN1 was written in BASICA for execution on the IBM PC personal computer. It was written in 1986.

A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg

NASA Technical Reports Server (NTRS)

Zoby, E. V.; Graves, R. A., Jr.

1973-01-01

A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.

Proof test of the computer program BUCKY for plasticity problems

NASA Technical Reports Server (NTRS)

Smith, James P.

1994-01-01

A theoretical equation describing the elastic-plastic deformation of a cantilever beam subject to a constant pressure is developed. The theoretical result is compared numerically to the computer program BUCKY for the case of an elastic-perfectly plastic specimen. It is shown that the theoretical and numerical results compare favorably in the plastic range. Comparisons are made to another research code to further validate the BUCKY results. This paper serves as a quality test for the computer program BUCKY developed at NASA Johnson Space Center.

Using Microcomputers to Teach Non-Linear Equations at Sixth Form Level.

ERIC Educational Resources Information Center

Cheung, Y. L.

1984-01-01

Promotes the use of the microcomputer in mathematics instruction, reviewing approaches to teaching nonlinear equations. Examples of computer diagrams are illustrated and compared to textbook samples. An example of a problem-solving program is included. (ML)

NASA Ames potential flow analysis (POTFAN) geometry program (POTGEM), version 1

NASA Technical Reports Server (NTRS)

Medan, R. T.; Bullock, R. B.

1976-01-01

A computer program known as POTGEM is reported which has been developed as an independent segment of a three-dimensional linearized, potential flow analysis system and which is used to generate a panel point description of arbitrary, three-dimensional bodies from convenient engineering descriptions consisting of equations and/or tables. Due to the independent, modular nature of the program, it may be used to generate corner points for other computer programs.

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

NASA Technical Reports Server (NTRS)

Koshigoe, S.; Murdock, J. W.; Akin, L. S.; Townsend, D. P.

1996-01-01

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

Computational simulation of probabilistic lifetime strength for aerospace materials subjected to high temperature, mechanical fatigue, creep and thermal fatigue

NASA Technical Reports Server (NTRS)

Boyce, Lola; Bast, Callie C.; Trimble, Greg A.

1992-01-01

This report presents the results of a fourth year effort of a research program, conducted for NASA-LeRC by the University of Texas at San Antonio (UTSA). The research included on-going development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subject to a number of effects or primitive variables. These primitive variables may include high temperature, fatigue or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation has been randomized and is included in the computer program, PROMISS. Also included in the research is the development of methodology to calibrate the above-described constitutive equation using actual experimental materials data together with regression analysis of that data, thereby predicting values for the empirical material constants for each effect or primitive variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from industry and the open literature for materials typically for applications in aerospace propulsion system components. Material data for Inconel 718 has been analyzed using the developed methodology.

Computational simulation of probabilistic lifetime strength for aerospace materials subjected to high temperature, mechanical fatigue, creep, and thermal fatigue

NASA Technical Reports Server (NTRS)

Boyce, Lola; Bast, Callie C.; Trimble, Greg A.

1992-01-01

The results of a fourth year effort of a research program conducted for NASA-LeRC by The University of Texas at San Antonio (UTSA) are presented. The research included on-going development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects or primitive variables. These primitive variables may include high temperature, fatigue, or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation was randomized and is included in the computer program, PROMISC. Also included in the research is the development of methodology to calibrate the above-described constitutive equation using actual experimental materials data together with regression analysis of that data, thereby predicting values for the empirical material constants for each effect or primitive variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from industry and the open literature for materials typically for applications in aerospace propulsion system components. Material data for Inconel 718 was analyzed using the developed methodology.

Computational simulation of coupled material degradation processes for probabilistic lifetime strength of aerospace materials

NASA Technical Reports Server (NTRS)

Boyce, Lola; Bast, Callie C.

1992-01-01

The research included ongoing development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects or primative variables. These primative variable may include high temperature, fatigue or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation has been randomized and is included in the computer program, PROMISS. Also included in the research is the development of methodology to calibrate the above described constitutive equation using actual experimental materials data together with linear regression of that data, thereby predicting values for the empirical material constraints for each effect or primative variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from the open literature for materials typically of interest to those studying aerospace propulsion system components. Material data for Inconel 718 was analyzed using the developed methodology.

A linear programming manual

NASA Technical Reports Server (NTRS)

Tuey, R. C.

1972-01-01

Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

Computing Gröbner and Involutive Bases for Linear Systems of Difference Equations

NASA Astrophysics Data System (ADS)

Yanovich, Denis

2018-02-01

The computation of involutive bases and Gröbner bases for linear systems of difference equations is solved and its importance for physical and mathematical problems is discussed. The algorithm and issues concerning its implementation in C are presented and calculation times are compared with the competing programs. The paper ends with consideration on the parallel version of this implementation and its scalability.

Parallel hyperbolic PDE simulation on clusters: Cell versus GPU

NASA Astrophysics Data System (ADS)

Rostrup, Scott; De Sterck, Hans

2010-12-01

Increasingly, high-performance computing is looking towards data-parallel computational devices to enhance computational performance. Two technologies that have received significant attention are IBM's Cell Processor and NVIDIA's CUDA programming model for graphics processing unit (GPU) computing. In this paper we investigate the acceleration of parallel hyperbolic partial differential equation simulation on structured grids with explicit time integration on clusters with Cell and GPU backends. The message passing interface (MPI) is used for communication between nodes at the coarsest level of parallelism. Optimizations of the simulation code at the several finer levels of parallelism that the data-parallel devices provide are described in terms of data layout, data flow and data-parallel instructions. Optimized Cell and GPU performance are compared with reference code performance on a single x86 central processing unit (CPU) core in single and double precision. We further compare the CPU, Cell and GPU platforms on a chip-to-chip basis, and compare performance on single cluster nodes with two CPUs, two Cell processors or two GPUs in a shared memory configuration (without MPI). We finally compare performance on clusters with 32 CPUs, 32 Cell processors, and 32 GPUs using MPI. Our GPU cluster results use NVIDIA Tesla GPUs with GT200 architecture, but some preliminary results on recently introduced NVIDIA GPUs with the next-generation Fermi architecture are also included. This paper provides computational scientists and engineers who are considering porting their codes to accelerator environments with insight into how structured grid based explicit algorithms can be optimized for clusters with Cell and GPU accelerators. It also provides insight into the speed-up that may be gained on current and future accelerator architectures for this class of applications. Program summaryProgram title: SWsolver Catalogue identifier: AEGY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL v3 No. of lines in distributed program, including test data, etc.: 59 168 No. of bytes in distributed program, including test data, etc.: 453 409 Distribution format: tar.gz Programming language: C, CUDA Computer: Parallel Computing Clusters. Individual compute nodes may consist of x86 CPU, Cell processor, or x86 CPU with attached NVIDIA GPU accelerator. Operating system: Linux Has the code been vectorised or parallelized?: Yes. Tested on 1-128 x86 CPU cores, 1-32 Cell Processors, and 1-32 NVIDIA GPUs. RAM: Tested on Problems requiring up to 4 GB per compute node. Classification: 12 External routines: MPI, CUDA, IBM Cell SDK Nature of problem: MPI-parallel simulation of Shallow Water equations using high-resolution 2D hyperbolic equation solver on regular Cartesian grids for x86 CPU, Cell Processor, and NVIDIA GPU using CUDA. Solution method: SWsolver provides 3 implementations of a high-resolution 2D Shallow Water equation solver on regular Cartesian grids, for CPU, Cell Processor, and NVIDIA GPU. Each implementation uses MPI to divide work across a parallel computing cluster. Additional comments: Sub-program numdiff is used for the test run.

a Recursive Approach to Compute Normal Forms

NASA Astrophysics Data System (ADS)

HSU, L.; MIN, L. J.; FAVRETTO, L.

2001-06-01

Normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations, particularly when singularities close to a bifurcation are to be characterized. However, the computation of a normal form up to an arbitrary order is numerically hard. This paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms. A computer program to reduce the system to its normal form on a center manifold is developed using the Maple symbolic language. However, it should be stressed that the program relies essentially on recursive numerical computations, while symbolic calculations are used only for minor tasks. Some strategies are proposed to save computation time. Examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension.

Computation of steady nozzle flow by a time-dependent method

NASA Technical Reports Server (NTRS)

Cline, M. C.

1974-01-01

The equations of motion governing steady, inviscid flow are of a mixed type, that is, hyperbolic in the supersonic region and elliptic in the subsonic region. These mathematical difficulties may be removed by using the so-called time-dependent method, where the governing equations become hyperbolic everywhere. The steady-state solution may be obtained as the asymptotic solution for large time. The object of this research was to develop a production type computer program capable of solving converging, converging-diverging, and plug two-dimensional nozzle flows in computational times of 1 min or less on a CDC 6600 computer.

A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1980-01-01

A method for generating two dimensional finite difference grids about airfoils and other shapes by the use of the Poisson differential equation is developed. The inhomogeneous terms are automatically chosen such that two important effects are imposed on the grid at both the inner and outer boundaries. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. A FORTRAN computer program has been written to use this method. A description of the program, a discussion of the control parameters, and a set of sample cases are included.

Accelerating numerical solution of stochastic differential equations with CUDA

NASA Astrophysics Data System (ADS)

Januszewski, M.; Kostur, M.

2010-01-01

Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the CUDA programming environment. We address general aspects of numerical programming on stream processors and illustrate them by two examples: the noisy phase dynamics in a Josephson junction and the noisy Kuramoto model. In presented cases the measured speedup can be as high as 675× compared to a typical CPU, which corresponds to several billion integration steps per second. This means that calculations which took weeks can now be completed in less than one hour. This brings stochastic simulation to a completely new level, opening for research a whole new range of problems which can now be solved interactively. Program summaryProgram title: SDE Catalogue identifier: AEFG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Gnu GPL v3 No. of lines in distributed program, including test data, etc.: 978 No. of bytes in distributed program, including test data, etc.: 5905 Distribution format: tar.gz Programming language: CUDA C Computer: any system with a CUDA-compatible GPU Operating system: Linux RAM: 64 MB of GPU memory Classification: 4.3 External routines: The program requires the NVIDIA CUDA Toolkit Version 2.0 or newer and the GNU Scientific Library v1.0 or newer. Optionally gnuplot is recommended for quick visualization of the results. Nature of problem: Direct numerical integration of stochastic differential equations is a computationally intensive problem, due to the necessity of calculating multiple independent realizations of the system. We exploit the inherent parallelism of this problem and perform the calculations on GPUs using the CUDA programming environment. The GPU's ability to execute hundreds of threads simultaneously makes it possible to speed up the computation by over two orders of magnitude, compared to a typical modern CPU. Solution method: The stochastic Runge-Kutta method of the second order is applied to integrate the equation of motion. Ensemble-averaged quantities of interest are obtained through averaging over multiple independent realizations of the system. Unusual features: The numerical solution of the stochastic differential equations in question is performed on a GPU using the CUDA environment. Running time: < 1 minute

Applications of Automation Methods for Nonlinear Fracture Test Analysis

NASA Technical Reports Server (NTRS)

Allen, Phillip A.; Wells, Douglas N.

2013-01-01

Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.

Digital computer program for generating dynamic turbofan engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.; Szuch, J. R.; Westerkamp, E. J.

1983-01-01

This report describes DIGTEM, a digital computer program that simulates two spool, two-stream turbofan engines. The turbofan engine model in DIGTEM contains steady-state performance maps for all of the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. Altogether there are 16 state variables and state equations. DIGTEM features a backward-differnce integration scheme for integrating stiff systems. It trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off-design points and iterates to a balanced engine condition. Transients can also be run. They are generated by defining controls as a function of time (open-loop control) in a user-written subroutine (TMRSP). DIGTEM has run on the IBM 370/3033 computer using implicit integration with time steps ranging from 1.0 msec to 1.0 sec. DIGTEM is generalized in the aerothermodynamic treatment of components.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Multi-dimensional computer simulation of MHD combustor hydrodynamics

NASA Astrophysics Data System (ADS)

Berry, G. F.; Chang, S. L.; Lottes, S. A.; Rimkus, W. A.

1991-04-01

Argonne National Laboratory is investigating the nonreacting jet gas mixing patterns in an MHD second stage combustor by using a 2-D multiphase hydrodynamics computer program and a 3-D single phase hydrodynamics computer program. The computer simulations are intended to enhance the understanding of flow and mixing patterns in the combustor, which in turn may lead to improvement of the downstream MHD channel performance. A 2-D steady state computer model, based on mass and momentum conservation laws for multiple gas species, is used to simulate the hydrodynamics of the combustor in which a jet of oxidizer is injected into an unconfined cross stream gas flow. A 3-D code is used to examine the effects of the side walls and the distributed jet flows on the non-reacting jet gas mixing patterns. The code solves the conservation equations of mass, momentum, and energy, and a transport equation of a turbulence parameter and allows permeable surfaces to be specified for any computational cell.

A Digital Simulation Program for Health Science Students to Follow Drug Levels in the Body

ERIC Educational Resources Information Center

Stavchansky, Salomon; And Others

1977-01-01

The Rayetheon Scientific Simulation Language (RSSL) program, an easily-used simulation on the CDC/6600 computer at the University of Texas at Austin, offers a simple method of solving differential equations on a digital computer. It is used by undergraduate biopharmaceutics-pharmacokinetics students and graduate students in all areas. (Author/LBH)

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

2013-01-01

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method with method-of-lines integration Running time: Determined by the size of the problem

Multibody dynamics model building using graphical interfaces

NASA Technical Reports Server (NTRS)

Macala, Glenn A.

1989-01-01

In recent years, the extremely laborious task of manually deriving equations of motion for the simulation of multibody spacecraft dynamics has largely been eliminated. Instead, the dynamicist now works with commonly available general purpose dynamics simulation programs which generate the equations of motion either explicitly or implicitly via computer codes. The user interface to these programs has predominantly been via input data files, each with its own required format and peculiarities, causing errors and frustrations during program setup. Recent progress in a more natural method of data input for dynamics programs: the graphical interface, is described.

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

NASA Technical Reports Server (NTRS)

Imlay, Scott T.; Roberts, Donald W.; Soetrisno, Moeljo; Eberhardt, Scott

1991-01-01

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

METal matrix composite ANalyzer (METCAN): Theoretical manual

NASA Technical Reports Server (NTRS)

Murthy, P. L. N.; Chamis, C. C.

1993-01-01

This manuscript is intended to be a companion volume to the 'METCAN User's Manual' and the 'METAN Demonstration Manual.' The primary purpose of the manual is to give details pertaining to micromechanics and macromechanics equations of high temperature metal matrix composites that are programmed in the METCAN computer code. The subroutines which contain the programmed equations are also mentioned in order to facilitate any future changes or modifications that the user may intend to incorporate in the code. Assumptions and derivations leading to the micromechanics equations are briefly mentioned.

Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations. Interim Revision, March 1976

NASA Technical Reports Server (NTRS)

Gordon, S.; Mcbride, B. J.

1976-01-01

A detailed description of the equations and computer program for computations involving chemical equilibria in complex systems is given. A free-energy minimization technique is used. The program permits calculations such as (1) chemical equilibrium for assigned thermodynamic states (T,P), (H,P), (S,P), (T,V), (U,V), or (S,V), (2) theoretical rocket performance for both equilibrium and frozen compositions during expansion, (3) incident and reflected shock properties, and (4) Chapman-Jouguet detonation properties. The program considers condensed species as well as gaseous species.

Further Improvement in 3DGRAPE

NASA Technical Reports Server (NTRS)

Alter, Stephen

2004-01-01

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

An investigation of constraint-based component-modeling for knowledge representation in computer-aided conceptual design

NASA Technical Reports Server (NTRS)

Kolb, Mark A.

1990-01-01

Originally, computer programs for engineering design focused on detailed geometric design. Later, computer programs for algorithmically performing the preliminary design of specific well-defined classes of objects became commonplace. However, due to the need for extreme flexibility, it appears unlikely that conventional programming techniques will prove fruitful in developing computer aids for engineering conceptual design. The use of symbolic processing techniques, such as object-oriented programming and constraint propagation, facilitate such flexibility. Object-oriented programming allows programs to be organized around the objects and behavior to be simulated, rather than around fixed sequences of function- and subroutine-calls. Constraint propagation allows declarative statements to be understood as designating multi-directional mathematical relationships among all the variables of an equation, rather than as unidirectional assignments to the variable on the left-hand side of the equation, as in conventional computer programs. The research has concentrated on applying these two techniques to the development of a general-purpose computer aid for engineering conceptual design. Object-oriented programming techniques are utilized to implement a user-extensible database of design components. The mathematical relationships which model both geometry and physics of these components are managed via constraint propagation. In addition, to this component-based hierarchy, special-purpose data structures are provided for describing component interactions and supporting state-dependent parameters. In order to investigate the utility of this approach, a number of sample design problems from the field of aerospace engineering were implemented using the prototype design tool, Rubber Airplane. The additional level of organizational structure obtained by representing design knowledge in terms of components is observed to provide greater convenience to the program user, and to result in a database of engineering information which is easier both to maintain and to extend.

The two-electron atomic systems. S-states

NASA Astrophysics Data System (ADS)

Liverts, Evgeny Z.; Barnea, Nir

2010-01-01

A simple Mathematica program for computing the S-state energies and wave functions of two-electron (helium-like) atoms (ions) is presented. The well-known method of projecting the Schrödinger equation onto the finite subspace of basis functions was applied. The basis functions are composed of the exponentials combined with integer powers of the simplest perimetric coordinates. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of results and computation time depend on the basis size. The precise energy values of 7-8 significant figures along with the corresponding wave functions can be computed on a single processor within a few minutes. The resultant wave functions have a simple analytical form consisting of elementary functions, that enables one to calculate the expectation values of arbitrary physical operators without any difficulties. Program summaryProgram title: TwoElAtom-S Catalogue identifier: AEFK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 185 No. of bytes in distributed program, including test data, etc.: 495 164 Distribution format: tar.gz Programming language: Mathematica 6.0; 7.0 Computer: Any PC Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0 RAM:⩾10 bytes Classification: 2.1, 2.2, 2.7, 2.9 Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or other physical attributes from quantum mechanical calculations. Solution method: The S-wave function is expanded into a triple basis set in three perimetric coordinates. Method of projecting the two-electron Schrödinger equation (for atoms/ions) onto a subspace of the basis functions enables one to obtain the set of homogeneous linear equations F.C=0 for the coefficients C of the above expansion. The roots of equation det(F)=0 yield the bound energies. Restrictions: First, the too large length of expansion (basis size) takes the too large computation time giving no perceptible improvement in accuracy. Second, the order of polynomial Ω (input parameter) in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive. Additional comments: The CPC Program Library includes "A program to calculate the eigenfunctions of the random phase approximation for two electron systems" (AAJD). It should be emphasized that this fortran code realizes a very rough approximation describing only the averaged electron density of the two electron systems. It does not characterize the properties of the individual electrons and has a number of input parameters including the Roothaan orbitals. Running time: ˜10 minutes (depends on basis size and computer speed)

Probabilistic Simulation for Nanocomposite Characterization

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Coroneos, Rula M.

2007-01-01

A unique probabilistic theory is described to predict the properties of nanocomposites. The simulation is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations have been programmed in a computer code. That computer code is used to simulate uniaxial strengths properties of a mononanofiber laminate. The results are presented graphically and discussed with respect to their practical significance. These results show smooth distributions.

A study of the geographic coverage properties of a satellite borne Doppler lidar wind velocity measuring system

NASA Technical Reports Server (NTRS)

Pate, T. H.

1982-01-01

Geographic coverage frequency and geographic shot density for a satellite borne Doppler lidar wind velocity measuring system are measured. The equations of motion of the light path on the ground were derived and a computer program devised to compute shot density and coverage frequency by latitude-longitude sections. The equations for the coverage boundaries were derived and a computer program developed to plot these boundaries, thus making it possible, after an application of a map coloring algorithm, to actually see the areas of multiple coverage. A theoretical cross-swath shot density function that gives close approximations in certain cases was also derived. This information should aid in the design of an efficient data-processing system for the Doppler lidar.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

Plotting equation for gaussian percentiles and a spreadsheet program for generating probability plots

USGS Publications Warehouse

Balsillie, J.H.; Donoghue, J.F.; Butler, K.M.; Koch, J.L.

2002-01-01

Two-dimensional plotting tools can be of invaluable assistance in analytical scientific pursuits, and have been widely used in the analysis and interpretation of sedimentologic data. We consider, in this work, the use of arithmetic probability paper (APP). Most statistical computer applications do not allow for the generation of APP plots, because of apparent intractable nonlinearity of the percentile (or probability) axis of the plot. We have solved this problem by identifying an equation(s) for determining plotting positions of Gaussian percentiles (or probabilities), so that APP plots can easily be computer generated. An EXCEL example is presented, and a programmed, simple-to-use EXCEL application template is hereby made publicly available, whereby a complete granulometric analysis including data listing, moment measure calculations, and frequency and cumulative APP plots, is automatically produced.

A Computer Simulation of the Trophic Dynamics of an Aquatic System.

ERIC Educational Resources Information Center

Bowker, D. W.; Randerson, P. F.

1989-01-01

Described is a computer program, AQUASIM, which simulates interaction between environmental factors, phytoplankton, zooplankton, and fish in an aquatic ecosystem. The conceptual flow, equations, variables, rate processes, and parameter manipulations are discussed. (CW)

Multispan Elevated Guideway Design for Passenger Transport Vehicles : Volume 2. Appendixes.

DOT National Transportation Integrated Search

1975-04-01

Contents: Appendix A - derivation of vehicle-guideway interaction equations; Appendix B - evaluation of pier support dynamics; Appendix C - computer simulation program of two-dimensional vehicle over a multi-span guideway; Appendix D - computer progr...

Houston Operations Predictor/Estimator (HOPE) programming manual, volume 1. [Apollo orbit determination

NASA Technical Reports Server (NTRS)

Daly, J. K.

1974-01-01

The programming techniques used to implement the equations and mathematical techniques of the Houston Operations Predictor/Estimator (HOPE) orbit determination program on the UNIVAC 1108 computer are described. Detailed descriptions are given of the program structure, the internal program structure, the internal program tables and program COMMON, modification and maintainence techniques, and individual subroutine documentation.

Numerical modeling of exciton-polariton Bose-Einstein condensate in a microcavity

NASA Astrophysics Data System (ADS)

Voronych, Oksana; Buraczewski, Adam; Matuszewski, Michał; Stobińska, Magdalena

2017-06-01

A novel, optimized numerical method of modeling of an exciton-polariton superfluid in a semiconductor microcavity was proposed. Exciton-polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge-Kutta method of 4th order, further optimized for efficient computations. The algorithms were implemented in form of C++ programs fitted for parallel environments and utilizing vector instructions. The programs form the EPCGP suite which has been used for theoretical investigation of exciton-polaritons. Catalogue identifier: AFBQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: BSD-3 No. of lines in distributed program, including test data, etc.: 2157 No. of bytes in distributed program, including test data, etc.: 498994 Distribution format: tar.gz Programming language: C++ with OpenMP extensions (main numerical program), Python (helper scripts). Computer: Modern PC (tested on AMD and Intel processors), HP BL2x220. Operating system: Unix/Linux and Windows. Has the code been vectorized or parallelized?: Yes (OpenMP) RAM: 200 MB for single run Classification: 7, 7.7. Nature of problem: An exciton-polariton superfluid is a novel, interesting physical system allowing investigation of high temperature Bose-Einstein condensation of exciton-polaritons-quasiparticles carrying spin. They have brought a lot of attention due to their unique properties and potential applications in polariton-based optoelectronic integrated circuits. This is an out-of-equilibrium quantum system confined within a semiconductor microcavity. It is described by a set of nonlinear differential equations similar in spirit to the Gross-Pitaevskii (GP) equation, but their unique properties do not allow standard GP solving frameworks to be utilized. Finding an accurate and efficient numerical algorithm as well as development of optimized numerical software is necessary for effective theoretical investigation of exciton-polaritons. Solution method: A Runge-Kutta method of 4th order was employed to solve the set of differential equations describing exciton-polariton superfluids. The method was fitted for the exciton-polariton equations and further optimized. The C++ programs utilize OpenMP extensions and vector operations in order to fully utilize the computer hardware. Running time: 6h for 100 ps evolution, depending on the values of parameters

Weighted triangulation adjustment

USGS Publications Warehouse

Anderson, Walter L.

1969-01-01

The variation of coordinates method is employed to perform a weighted least squares adjustment of horizontal survey networks. Geodetic coordinates are required for each fixed and adjustable station. A preliminary inverse geodetic position computation is made for each observed line. Weights associated with each observed equation for direction, azimuth, and distance are applied in the formation of the normal equations in-the least squares adjustment. The number of normal equations that may be solved is twice the number of new stations and less than 150. When the normal equations are solved, shifts are produced at adjustable stations. Previously computed correction factors are applied to the shifts and a most probable geodetic position is found for each adjustable station. Pinal azimuths and distances are computed. These may be written onto magnetic tape for subsequent computation of state plane or grid coordinates. Input consists of punch cards containing project identification, program options, and position and observation information. Results listed include preliminary and final positions, residuals, observation equations, solution of the normal equations showing magnitudes of shifts, and a plot of each adjusted and fixed station. During processing, data sets containing irrecoverable errors are rejected and the type of error is listed. The computer resumes processing of additional data sets.. Other conditions cause warning-errors to be issued, and processing continues with the current data set.

A computer program for predicting nonlinear uniaxial material responses using viscoplastic models

NASA Technical Reports Server (NTRS)

Chang, T. Y.; Thompson, R. L.

1984-01-01

A computer program was developed for predicting nonlinear uniaxial material responses using viscoplastic constitutive models. Four specific models, i.e., those due to Miller, Walker, Krieg-Swearengen-Rhode, and Robinson, are included. Any other unified model is easily implemented into the program in the form of subroutines. Analysis features include stress-strain cycling, creep response, stress relaxation, thermomechanical fatigue loop, or any combination of these responses. An outline is given on the theoretical background of uniaxial constitutive models, analysis procedure, and numerical integration methods for solving the nonlinear constitutive equations. In addition, a discussion on the computer program implementation is also given. Finally, seven numerical examples are included to demonstrate the versatility of the computer program developed.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

A hybrid computer program for rapidly solving flowing or static chemical kinetic problems involving many chemical species

NASA Technical Reports Server (NTRS)

Mclain, A. G.; Rao, C. S. R.

1976-01-01

A hybrid chemical kinetic computer program was assembled which provides a rapid solution to problems involving flowing or static, chemically reacting, gas mixtures. The computer program uses existing subroutines for problem setup, initialization, and preliminary calculations and incorporates a stiff ordinary differential equation solution technique. A number of check cases were recomputed with the hybrid program and the results were almost identical to those previously obtained. The computational time saving was demonstrated with a propane-oxygen-argon shock tube combustion problem involving 31 chemical species and 64 reactions. Information is presented to enable potential users to prepare an input data deck for the calculation of a problem.

Computer code for off-design performance analysis of radial-inflow turbines with rotor blade sweep

NASA Technical Reports Server (NTRS)

Meitner, P. L.; Glassman, A. J.

1983-01-01

The analysis procedure of an existing computer program was extended to include rotor blade sweep, to model the flow more accurately at the rotor exit, and to provide more detail to the loss model. The modeling changes are described and all analysis equations and procedures are presented. Program input and output are described and are illustrated by an example problem. Results obtained from this program and from a previous program are compared with experimental data.

A computer program for automated flutter solution and matched point determination

NASA Technical Reports Server (NTRS)

Bhatia, K. G.

1973-01-01

The use of a digital computer program (MATCH) for automated determination of the flutter velocity and the matched-point flutter density is described. The program is based on the use of the modified Laguerre iteration formula to converge to a flutter crossing or a matched-point density. A general description of the computer program is included and the purpose of all subroutines used is stated. The input required by the program and various input options are detailed, and the output description is presented. The program can solve flutter equations formulated with up to 12 vibration modes and obtain flutter solutions for up to 10 air densities. The program usage is illustrated by a sample run, and the FORTRAN program listing is included.

A computer program for fitting smooth surfaces to three-dimensional aircraft configurations

NASA Technical Reports Server (NTRS)

Craidon, C. B.; Smith, R. E., Jr.

1975-01-01

A computer program developed to fit smooth surfaces to the component parts of three-dimensional aircraft configurations was described. The resulting equation definition of an aircraft numerical model is useful in obtaining continuous two-dimensional cross section plots in arbitrarily defined planes, local tangents, enriched surface plots and other pertinent geometric information; the geometry organization used as input to the program has become known as the Harris Wave Drag Geometry.

Computer analysis speeds corrugated horn design

NASA Technical Reports Server (NTRS)

Loefer, G. R.; Newton, J. M.; Schuchardt, J. M.; Dees, J. W.

1976-01-01

A computer analysis program is developed for selecting the optimum flare angle and horn length of a corrugated horn design, the horn diameter, and the radiation pattern, before resorting to machining operations. The calculated antenna pattern is best suited to narrowband designs, and averaging of the E and H planes is recommended for wideband work. The program language used is BASIC. Some design examples are provided with representative data, printouts, and a rundown of the equations programmed.

The role of under-determined approximations in engineering and science application

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1992-01-01

There is currently a great deal of interest in using response surfaces in the optimization of aircraft performance. The objective function and/or constraint equations involved in these optimization problems may come from numerous disciplines such as structures, aerodynamics, environmental engineering, etc. In each of these disciplines, the mathematical complexity of the governing equations usually dictates that numerical results be obtained from large computer programs such as a finite element method program. Thus, when performing optimization studies, response surfaces are a convenient way of transferring information from the various disciplines to the optimization algorithm as opposed to bringing all the sundry computer programs together in a massive computer code. Response surfaces offer another advantage in the optimization of aircraft structures. A characteristic of these types of optimization problems is that evaluation of the objective function and response equations (referred to as a functional evaluation) can be very expensive in a computational sense. Because of the computational expense in obtaining functional evaluations, the present study was undertaken to investigate under-determinined approximations. An under-determined approximation is one in which there are fewer training pairs (pieces of information about a function) than there are undetermined parameters (coefficients or weights) associated with the approximation. Both polynomial approximations and neural net approximations were examined. Three main example problems were investigated: (1) a function of one design variable was considered; (2) a function of two design variables was considered; and (3) a 35 bar truss with 4 design variables was considered.

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

NASA Technical Reports Server (NTRS)

Harris, J. E.; Blanchard, D. K.

1982-01-01

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Finite element solution of torsion and other 2-D Poisson equations

NASA Technical Reports Server (NTRS)

Everstine, G. C.

1982-01-01

The NASTRAN structural analysis computer program may be used, without modification, to solve two dimensional Poisson equations such as arise in the classical Saint Venant torsion problem. The nonhomogeneous term (the right-hand side) in the Poisson equation can be handled conveniently by specifying a gravitational load in a "structural" analysis. The use of an analogy between the equations of elasticity and those of classical mathematical physics is summarized in detail.

HZETRN: Description of a free-space ion and nucleon transport and shielding computer program

NASA Technical Reports Server (NTRS)

Wilson, John W.; Badavi, Francis F.; Cucinotta, Francis A.; Shinn, Judy L.; Badhwar, Gautam D.; Silberberg, R.; Tsao, C. H.; Townsend, Lawrence W.; Tripathi, Ram K.

1995-01-01

The high-charge-and energy (HZE) transport computer program HZETRN is developed to address the problems of free-space radiation transport and shielding. The HZETRN program is intended specifically for the design engineer who is interested in obtaining fast and accurate dosimetric information for the design and construction of space modules and devices. The program is based on a one-dimensional space-marching formulation of the Boltzmann transport equation with a straight-ahead approximation. The effect of the long-range Coulomb force and electron interaction is treated as a continuous slowing-down process. Atomic (electronic) stopping power coefficients with energies above a few A MeV are calculated by using Bethe's theory including Bragg's rule, Ziegler's shell corrections, and effective charge. Nuclear absorption cross sections are obtained from fits to quantum calculations and total cross sections are obtained with a Ramsauer formalism. Nuclear fragmentation cross sections are calculated with a semiempirical abrasion-ablation fragmentation model. The relation of the final computer code to the Boltzmann equation is discussed in the context of simplifying assumptions. A detailed description of the flow of the computer code, input requirements, sample output, and compatibility requirements for non-VAX platforms are provided.

A rapid method for the computation of equilibrium chemical composition of air to 15000 K

NASA Technical Reports Server (NTRS)

Prabhu, Ramadas K.; Erickson, Wayne D.

1988-01-01

A rapid computational method has been developed to determine the chemical composition of equilibrium air to 15000 K. Eleven chemically reacting species, i.e., O2, N2, O, NO, N, NO+, e-, N+, O+, Ar, and Ar+ are included. The method involves combining algebraically seven nonlinear equilibrium equations and four linear elemental mass balance and charge neutrality equations. Computational speeds for determining the equilibrium chemical composition are significantly faster than the often used free energy minimization procedure. Data are also included from which the thermodynamic properties of air can be computed. A listing of the computer program together with a set of sample results are included.

Apollo Photograph Evaluation (APE) programming manual

NASA Technical Reports Server (NTRS)

Kim, I. J.

1974-01-01

This document describes the programming techniques used to implement the equations of the Apollo Photograph Evaluation (APE) program on the UNIVAC 1108 computer and contains detailed descriptions of the program structure, a User's Guide section to provide the necessary information for proper operation of the program, and information for the assessment of the program's adaptability to future problems.

A Programming Environment for Parallel Vision Algorithms

DTIC Science & Technology

1990-04-11

industrial arm on the market , while the unique head was designed by Rochester’s Computer Science and Mechanical Engineering Departments. 9a 4.1 Introduction...R. Constraining-Unification and the Programming Language Unicorn . In Logic Programming, Functions, Relations, and Equations, Degroot and Lind- strom

VMOMS — A computer code for finding moment solutions to the Grad-Shafranov equation

NASA Astrophysics Data System (ADS)

Lao, L. L.; Wieland, R. M.; Houlberg, W. A.; Hirshman, S. P.

1982-08-01

Title of program: VMOMS Catalogue number: ABSH Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland (See application form in this issue) Computer: PDP-10/KL10; Installation: ORNL Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA Operating system: TOPS 10 Programming language used: FORTRAN High speed storage required: 9000 words No. of bits in a word: 36 Overlay structure: none Peripherals used: line printer, disk drive No. of cards in combined program and test deck: 2839 Card punching code: ASCII

FORTRAN program for predicting off-design performance of radial-inflow turbines

NASA Technical Reports Server (NTRS)

Wasserbauer, C. A.; Glassman, A. J.

1975-01-01

The FORTRAN IV program uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. The program inputs needed are the design-point requirements and turbine geometry. The output includes performance and velocity-diagram parameters over a range of speed and pressure ratio. Computed performance is compared with the experimental data from two radial-inflow turbines and with the performance calculated by a previous computer program. The flow equations, program listing, and input and output for a sample problem are given.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

A Multi-Fidelity Surrogate Model for the Equation of State for Mixtures of Real Gases

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Koneru, Rahul; Balachandar, S.; Rollin, Bertrand

2017-11-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the products of detonated explosives must be treated as real gases while the ideal gas equation of state is used for the ambient air. As the products expand outward, they mix with the air and create a region where both state equations must be satisfied. One of the most accurate, yet expensive, methods to handle this problem is an algorithm that iterates between both state equations until both pressure and thermal equilibrium are achieved inside of each computational cell. This work creates a multi-fidelity surrogate model to replace this process. This is achieved by using a Kriging model to produce a curve fit which interpolates selected data from the iterative algorithm. The surrogate is optimized for computing speed and model accuracy by varying the number of sampling points chosen to construct the model. The performance of the surrogate with respect to the iterative method is tested in simulations using a finite volume code. The model's computational speed and accuracy are analyzed to show the benefits of this novel approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

Symbolic programming language in molecular multicenter integral problem

NASA Astrophysics Data System (ADS)

Safouhi, Hassan; Bouferguene, Ahmed

It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of three-center nuclear attraction and Coulomb integrals is the most frequently encountered. As the molecular system becomes larger, computation of these integrals becomes one of the most laborious and time-consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to further development in computational studies of large molecular systems. To develop fast and accurate algorithms for the numerical evaluation of these integrals over B functions, we used nonlinear transformations for improving convergence of highly oscillatory integrals. These methods form the basis of new methods for solving various problems that were unsolvable otherwise and have many applications as well. To apply these nonlinear transformations, the integrands should satisfy linear differential equations with coefficients having asymptotic power series in the sense of Poincaré, which in their turn should satisfy some limit conditions. These differential equations are very difficult to obtain explicitly. In the case of molecular integrals, we used a symbolic programming language (MAPLE) to demonstrate that all the conditions required to apply these nonlinear transformation methods are satisfied. Differential equations are obtained explicitly, allowing us to demonstrate that the limit conditions are also satisfied.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 3.0)

NASA Technical Reports Server (NTRS)

Epton, Michael A.; Magnus, Alfred E.

1990-01-01

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the Panel Aerodynamics (PAN AIR) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformation, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments. Principal revisions to version 3.0 are the following: (1) appendices H and K more fully describe the Aerodynamic Influence Coefficient (AIC) construction; (2) appendix L now provides a complete description of the AIC solution process; (3) appendix P is new and discusses the theory for the new FDP module (which calculates streamlines and offbody points); and (4) numerous small corrections and revisions reflecting the MAG module rewrite.

Computation of transonic potential flow about 3 dimensional inlets, ducts, and bodies

NASA Technical Reports Server (NTRS)

Reyhner, T. A.

1982-01-01

An analysis was developed and a computer code, P465 Version A, written for the prediction of transonic potential flow about three dimensional objects including inlet, duct, and body geometries. Finite differences and line relaxation are used to solve the complete potential flow equation. The coordinate system used for the calculations is independent of body geometry. Cylindrical coordinates are used for the computer code. The analysis is programmed in extended FORTRAN 4 for the CYBER 203 vector computer. The programming of the analysis is oriented toward taking advantage of the vector processing capabilities of this computer. Comparisons of computed results with experimental measurements are presented to verify the analysis. Descriptions of program input and output formats are also presented.

HARPA: A versatile three-dimensional Hamiltonian ray-tracing program for acoustic waves in the atmosphere above irregular terrain

NASA Astrophysics Data System (ADS)

Jones, R. M.; Riley, J. P.; Georges, T. M.

1986-08-01

The modular FORTRAN 77 computer program traces the three-dimensional paths of acoustic rays through continuous model atmospheres by numerically integrating Hamilton's equations (a differential expression of Fermat's principle). The user specifies an atmospheric model by writing closed-form formulas for its three-dimensional wind and temperature (or sound speed) distribution, and by defining the height of the reflecting terrain vs. geographic latitude and longitude. Some general-purpose models are provided, or users can readily design their own. In addition to computing the geometry of each raypath, HARPA can calculate pulse travel time, phase time, Doppler shift (if the medium varies in time), absorption, and geometrical path length. The program prints a step-by-step account of a ray's progress. The 410-page documentation describes the ray-tracing equations and the structure of the program, and provides complete instructions, illustrated by a sample case.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

PubMed Central

Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

2015-01-01

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology. PMID:26356082

Statistical computation of tolerance limits

NASA Technical Reports Server (NTRS)

Wheeler, J. T.

1993-01-01

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Large space structure damping design

NASA Technical Reports Server (NTRS)

Pilkey, W. D.; Haviland, J. K.

1983-01-01

Several FORTRAN subroutines and programs were developed which compute complex eigenvalues of a damped system using different approaches, and which rescale mode shapes to unit generalized mass and make rigid bodies orthogonal to each other. An analytical proof of a Minimum Constrained Frequency Criterion (MCFC) for a single damper is presented. A method to minimize the effect of control spill-over for large space structures is proposed. The characteristic equation of an undamped system with a generalized control law is derived using reanalysis theory. This equation can be implemented in computer programs for efficient eigenvalue analysis or control quasi synthesis. Methods to control vibrations in large space structure are reviewed and analyzed. The resulting prototype, using electromagnetic actuator, is described.

Method of fan sound mode structure determination

NASA Technical Reports Server (NTRS)

Pickett, G. F.; Sofrin, T. G.; Wells, R. W.

1977-01-01

A method for the determination of fan sound mode structure in the Inlet of turbofan engines using in-duct acoustic pressure measurements is presented. The method is based on the simultaneous solution of a set of equations whose unknowns are modal amplitude and phase. A computer program for the solution of the equation set was developed. An additional computer program was developed which calculates microphone locations the use of which results in an equation set that does not give rise to numerical instabilities. In addition to the development of a method for determination of coherent modal structure, experimental and analytical approaches are developed for the determination of the amplitude frequency spectrum of randomly generated sound models for use in narrow annulus ducts. Two approaches are defined: one based on the use of cross-spectral techniques and the other based on the use of an array of microphones.

Apollo lunar descent guidance

NASA Technical Reports Server (NTRS)

Klumpp, A. R.

1974-01-01

Apollo lunar-descent guidance transfers the Lunar Module from a near-circular orbit to touchdown, traversing a 17 deg central angle and a 15 km altitude in 11 min. A group of interactive programs in an onboard computer guide the descent, controlling altitude and the descent propulsion system throttle. A ground-based program pre-computes guidance targets. The concepts involved in this guidance are described. Explicit and implicit guidance are discussed, guidance equations are derived, and the earlier Apollo explicit equation is shown to be an inferior special case of the later implicit equation. Interactive guidance, by which the two-man crew selects a landing site in favorable terrain and directs the trajectory there, is discussed. Interactive terminal-descent guidance enables the crew to control the essentially vertical descent rate in order to land in minimum time with safe contact speed. The altitude maneuver routine uses concepts that make gimbal lock inherently impossible.

Users manual: Dynamics of two bodies connected by an elastic tether, six degrees of freedom forebody and five degrees of freedom decelerator

NASA Technical Reports Server (NTRS)

Doyle, G. R., Jr.; Burbick, J. W.

1974-01-01

The equations of motion and a computer program for the dynamics of a six degree of freedom body joined to a five degree of freedom body by a quasilinear elastic tether are presented. The forebody is assumed to be a completely general rigid body with six degrees of freedom; the decelerator is also assumed to be rigid, but with only five degrees of freedom (symmetric about its longitudinal axis). The tether is represented by a spring and dashpot in parallel, where the spring constant is a function of tether elongation. Lagrange's equation is used to derive the equations of motion with the Lagrange multiplier technique used to express the constraint provided by the tether. A computer program is included which provides a time history of the dynamics of both bodies and the tension in the tether.

A computer program for borehole compensation of dual-detector density well logs

USGS Publications Warehouse

Scott, James Henry

1978-01-01

The computer program described in this report was developed for applying a borehole-rugosity and mudcake compensation algorithm to dual-density logs using the following information: the water level in the drill hole, hole diameter (from a caliper log if available, or the nominal drill diameter if not), and the two gamma-ray count rate logs from the near and far detectors of the density probe. The equations that represent the compensation algorithm and the calibration of the two detectors (for converting countrate or density) were derived specifically for a probe manufactured by Comprobe Inc. (5.4 cm O.D. dual-density-caliper); they are not applicable to other probes. However, equivalent calibration and compensation equations can be empirically determined for any other similar two-detector density probes and substituted in the computer program listed in this report. * Use of brand names in this report does not necessarily constitute endorsement by the U.S. Geological Survey.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

An Introduction to Computational Physics

NASA Astrophysics Data System (ADS)

Pang, Tao

2010-07-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

PIFCGT: A PIF autopilot design program for general aviation aircraft

NASA Technical Reports Server (NTRS)

Broussard, J. R.

1983-01-01

This report documents the PIFCGT computer program. In FORTRAN, PIFCGT is a computer design aid for determing Proportional-Integral-Filter (PIF) control laws for aircraft autopilots implemented with a Command Generator Tracker (CGT). The program uses Linear-Quadratic-Regulator synthesis algorithms to determine feedback gains, and includes software to solve the feedforward matrix equation which is useful in determining the command generator tracker feedforward gains. The program accepts aerodynamic stability derivatives and computes the corresponding aerodynamic linear model. The nine autopilot modes that can be designed include four maneuver modes (ROLL SEL, PITCH SEL, HDG SEL, ALT SEL), four final approach models (APR GS, APR LOCI, APR LOCR, APR LOCP), and a BETA HOLD mode. The program has been compiled and executed on a CDC computer.

PAN AIR summary document (version 1.0)

NASA Technical Reports Server (NTRS)

Derbyshire, T.; Sidwell, K. W.

1982-01-01

The capabilities and limitations of the panel aerodynamics (PAN AIR) computer program system are summarized. This program uses a higher order panel method to solve boundary value problems involving the Prandtl-Glauert equation for subsonic and supersonic potential flows. Both aerodynamic and hydrodynamic problems can be solved using this modular software which is written for the CDC 6600 and 7600, and the CYBER 170 series computers.

A Fast Solution of the Lindley Equations for the M-Group Regression Problem. Technical Report 78-3, October 1977 through May 1978.

ERIC Educational Resources Information Center

Molenaar, Ivo W.

The technical problems involved in obtaining Bayesian model estimates for the regression parameters in m similar groups are studied. The available computer programs, BPREP (BASIC), and BAYREG, both written in FORTRAN, require an amount of computer processing that does not encourage regular use. These programs are analyzed so that the performance…

Computation of Southern Pine Site Index Using a TI-59 Calculator

Treesearch

Robert M. Farrar

1983-01-01

A program is described that permits computation of site index in the field using a Texas Instruments model TI-59 programmable, hand-held, battery-powered calculator. Based on a series of equations developed by R.M. Farrar, Jr., for the site index curves in USDA Miscellaneous Publication 50, the program can accommodate any index base age, tree age, and height within...

For operation of the Computer Software Management and Information Center (COSMIC)

NASA Technical Reports Server (NTRS)

Carmon, J. L.

1983-01-01

Computer programs for large systems of normal equations, an interactive digital signal process, structural analysis of cylindrical thrust chambers, swirling turbulent axisymmetric recirculating flows in practical isothermal combustor geometrics, computation of three dimensional combustor performance, a thermal radiation analysis system, transient response analysis, and a software design analysis are summarized.

Data Structures for Extreme Scale Computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kahan, Simon

As computing problems of national importance grow, the government meets the increased demand by funding the development of ever larger systems. The overarching goal of the work supported in part by this grant is to increase efficiency of programming and performing computations on these large computing systems. In past work, we have demonstrated that some of these computations once thought to require expensive hardware designs and/or complex, special-purpose programming may be executed efficiently on low-cost commodity cluster computing systems using a general-purpose “latency-tolerant” programming framework. One important developed application of the ideas underlying this framework is graph database technology supportingmore » social network pattern matching used by US intelligence agencies to more quickly identify potential terrorist threats. This database application has been spun out by the Pacific Northwest National Laboratory, a Department of Energy Laboratory, into a commercial start-up, Trovares Inc. We explore an alternative application of the same underlying ideas to a well-studied challenge arising in engineering: solving unstructured sparse linear equations. Solving these equations is key to predicting the behavior of large electronic circuits before they are fabricated. Predicting that behavior ahead of fabrication means that designs can optimized and errors corrected ahead of the expense of manufacture.« less

Verifying a Computer Algorithm Mathematically.

ERIC Educational Resources Information Center

Olson, Alton T.

1986-01-01

Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

An Ada Linear-Algebra Software Package Modeled After HAL/S

NASA Technical Reports Server (NTRS)

Klumpp, Allan R.; Lawson, Charles L.

1990-01-01

New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.

Probabilistic Simulation for Nanocomposite Fracture

NASA Technical Reports Server (NTRS)

Chamis, Christos C.

2010-01-01

A unique probabilistic theory is described to predict the uniaxial strengths and fracture properties of nanocomposites. The simulation is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations have been programmed in a computer code. That computer code is used to simulate uniaxial strengths and fracture of a nanofiber laminate. The results are presented graphically and discussed with respect to their practical significance. These results show smooth distributions from low probability to high.

Extended precision data types for the development of the original computer aided engineering applications

NASA Astrophysics Data System (ADS)

Pescaru, A.; Oanta, E.; Axinte, T.; Dascalescu, A.-D.

2015-11-01

Computer aided engineering is based on models of the phenomena which are expressed as algorithms. The implementations of the algorithms are usually software applications which are processing a large volume of numerical data, regardless the size of the input data. In this way, the finite element method applications used to have an input data generator which was creating the entire volume of geometrical data, starting from the initial geometrical information and the parameters stored in the input data file. Moreover, there were several data processing stages, such as: renumbering of the nodes meant to minimize the size of the band length of the system of equations to be solved, computation of the equivalent nodal forces, computation of the element stiffness matrix, assemblation of system of equations, solving the system of equations, computation of the secondary variables. The modern software application use pre-processing and post-processing programs to easily handle the information. Beside this example, CAE applications use various stages of complex computation, being very interesting the accuracy of the final results. Along time, the development of CAE applications was a constant concern of the authors and the accuracy of the results was a very important target. The paper presents the various computing techniques which were imagined and implemented in the resulting applications: finite element method programs, finite difference element method programs, applied general numerical methods applications, data generators, graphical applications, experimental data reduction programs. In this context, the use of the extended precision data types was one of the solutions, the limitations being imposed by the size of the memory which may be allocated. To avoid the memory-related problems the data was stored in files. To minimize the execution time, part of the file was accessed using the dynamic memory allocation facilities. One of the most important consequences of the paper is the design of a library which includes the optimized solutions previously tested, that may be used for the easily development of original CAE cross-platform applications. Last but not least, beside the generality of the data type solutions, there is targeted the development of a software library which may be used for the easily development of node-based CAE applications, each node having several known or unknown parameters, the system of equations being automatically generated and solved.

NASA-Ames three-dimensional potential flow analysis system (POTFAN) equation solver code (SOLN) version 1

NASA Technical Reports Server (NTRS)

Davis, J. E.; Bonnett, W. S.; Medan, R. T.

1976-01-01

A computer program known as SOLN was developed as an independent segment of the NASA-Ames three-dimensional potential flow analysis systems of linear algebraic equations. Methods used include: LU decomposition, Householder's method, a partitioning scheme, and a block successive relaxation method. Due to the independent modular nature of the program, it may be used by itself and not necessarily in conjunction with other segments of the POTFAN system.

Dynamic characteristics of a variable-mass flexible missile

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1970-01-01

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

Pressure model of a four-way spool valve for simulating electrohydraulic control systems

NASA Technical Reports Server (NTRS)

Gebben, V. D.

1976-01-01

An equation that relates the pressure flow characteristics of hydraulic spool valves was developed. The dependent variable is valve output pressure, and the independent variables are spool position and flow. This causal form of equation is preferred in applications that simulate the effects of hydraulic line dynamics. Results from this equation are compared with those from the conventional valve equation, whose dependent variable is flow. A computer program of the valve equations includes spool stops, leakage spool clearances, and dead-zone characteristics of overlap spools.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Computer program for flat sector thrust bearing performance

NASA Technical Reports Server (NTRS)

Presler, A. F.; Etsion, I.

1977-01-01

A versatile computer program is presented which achieves a rapid, numerical solution of the Reynolds equation for a flat sector thrust pad bearing with either compressible or liquid lubricants. Program input includes a range in values of the geometric and operating parameters of the sector bearing. Performance characteristics are obtained from the calculated bearing pressure distribution. These are the load capacity, center of pressure coordinates, frictional energy dissipation, and flow rates of liquid lubricant across the bearing edges. Two sample problems are described.

User's guide for a computer program to analyze the LRC 16 ft transonic dynamics tunnel cable mount system

NASA Technical Reports Server (NTRS)

Barbero, P.; Chin, J.

1973-01-01

The theoretical derivation of the set of equations is discussed which is applicable to modeling the dynamic characteristics of aeroelastically-scaled models flown on the two-cable mount system in a 16 ft transonic dynamics tunnel. The computer program provided for the analysis is also described. The program calculates model trim conditions as well as 3 DOF longitudinal and lateral/directional dynamic conditions for various flying cable and snubber cable configurations. Sample input and output are included.

Evaluation of out-of-core computer programs for the solution of symmetric banded linear equations. [simultaneous equations

NASA Technical Reports Server (NTRS)

Dunham, R. S.

1976-01-01

FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.

GRAPE- TWO-DIMENSIONAL GRIDS ABOUT AIRFOILS AND OTHER SHAPES BY THE USE OF POISSON'S EQUATION

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1994-01-01

The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids, including those about airfoils. In a grid used for computing aerodynamic flow over an airfoil, or any other body shape, the surface of the body is usually treated as an inner boundary and often cannot be easily represented as an analytic function. The GRAPE computer program was developed to incorporate a method for generating two-dimensional finite-difference grids about airfoils and other shapes by the use of the Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including a limited number of sharp corners. The GRAPE program has been developed to be numerically stable and computationally fast. GRAPE can provide the aerodynamic analyst with an efficient and consistent means of grid generation. The GRAPE procedure generates a grid between an inner and an outer boundary by utilizing an iterative procedure to solve the Poisson differential equation subject to geometrical restraints. In this method, the inhomogeneous terms of the equation are automatically chosen such that two important effects are imposed on the grid. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. Along with the iterative solution to Poisson's equation, a technique of coarse-fine sequencing is employed to accelerate numerical convergence. GRAPE program control cards and input data are entered via the NAMELIST feature. Each variable has a default value such that user supplied data is kept to a minimum. Basic input data consists of the boundary specification, mesh point spacings on the boundaries, and mesh line angles at the boundaries. Output consists of a dataset containing the grid data and, if requested, a plot of the generated mesh. The GRAPE program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 135K (octal) of 60 bit words. For plotted output the commercially available DISSPLA graphics software package is required. The GRAPE program was developed in 1980.

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

NASA Technical Reports Server (NTRS)

Grove, R. D.; Bowles, R. L.; Mayhew, S. C.

1972-01-01

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Transient Finite Element Computations on a Variable Transputer System

NASA Technical Reports Server (NTRS)

Smolinski, Patrick J.; Lapczyk, Ireneusz

1993-01-01

A parallel program to analyze transient finite element problems was written and implemented on a system of transputer processors. The program uses the explicit time integration algorithm which eliminates the need for equation solving, making it more suitable for parallel computations. An interprocessor communication scheme was developed for arbitrary two dimensional grid processor configurations. Several 3-D problems were analyzed on a system with a small number of processors.

Computer program for calculating thermodynamic and transport properties of fluids

NASA Technical Reports Server (NTRS)

Hendricks, R. C.; Braon, A. K.; Peller, I. C.

1975-01-01

Computer code has been developed to provide thermodynamic and transport properties of liquid argon, carbon dioxide, carbon monoxide, fluorine, helium, methane, neon, nitrogen, oxygen, and parahydrogen. Equation of state and transport coefficients are updated and other fluids added as new material becomes available.

PC-CUBE: A Personal Computer Based Hypercube

NASA Technical Reports Server (NTRS)

Ho, Alex; Fox, Geoffrey; Walker, David; Snyder, Scott; Chang, Douglas; Chen, Stanley; Breaden, Matt; Cole, Terry

1988-01-01

PC-CUBE is an ensemble of IBM PCs or close compatibles connected in the hypercube topology with ordinary computer cables. Communication occurs at the rate of 115.2 K-band via the RS-232 serial links. Available for PC-CUBE is the Crystalline Operating System III (CrOS III), Mercury Operating System, CUBIX and PLOTIX which are parallel I/O and graphics libraries. A CrOS performance monitor was developed to facilitate the measurement of communication and computation time of a program and their effects on performance. Also available are CXLISP, a parallel version of the XLISP interpreter; GRAFIX, some graphics routines for the EGA and CGA; and a general execution profiler for determining execution time spent by program subroutines. PC-CUBE provides a programming environment similar to all hypercube systems running CrOS III, Mercury and CUBIX. In addition, every node (personal computer) has its own graphics display monitor and storage devices. These allow data to be displayed or stored at every processor, which has much instructional value and enables easier debugging of applications. Some application programs which are taken from the book Solving Problems on Concurrent Processors (Fox 88) were implemented with graphics enhancement on PC-CUBE. The applications range from solving the Mandelbrot set, Laplace equation, wave equation, long range force interaction, to WaTor, an ecological simulation.

Multigrid calculation of internal flows in complex geometries

NASA Technical Reports Server (NTRS)

Smith, K. M.; Vanka, S. P.

1992-01-01

The development, validation, and application of a general purpose multigrid solution algorithm and computer program for the computation of elliptic flows in complex geometries is presented. This computer program combines several desirable features including a curvilinear coordinate system, collocated arrangement of the variables, and Full Multi-Grid/Full Approximation Scheme (FMG/FAS). Provisions are made for the inclusion of embedded obstacles and baffles inside the flow domain. The momentum and continuity equations are solved in a decoupled manner and a pressure corrective equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. Despite the computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence results in reduced overall CPU time. The numerical scheme and selected results of several validation flows are presented. Finally, the procedure is applied to study the flowfield in a side-inlet dump combustor and twin jet impingement from a simulated aircraft fuselage.

OpenMx: An Open Source Extended Structural Equation Modeling Framework

ERIC Educational Resources Information Center

Boker, Steven; Neale, Michael; Maes, Hermine; Wilde, Michael; Spiegel, Michael; Brick, Timothy; Spies, Jeffrey; Estabrook, Ryne; Kenny, Sarah; Bates, Timothy; Mehta, Paras; Fox, John

2011-01-01

OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the "R" statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are…

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

An Evaluation of Three Approximate Item Response Theory Models for Equating Test Scores.

ERIC Educational Resources Information Center

Marco, Gary L.; And Others

Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…

Electromagnetic Scattering from Two Dielectric Spheres: Comparison between Theory and Experiment,

DTIC Science & Technology

1982-08-30

struct, a very complex computer program to perform the calculations. It should be noted that several errors (probably typographical) were disco - vered in...their equations and virtually all of them had to be rederived. In a future publication we will present a corrected set of equations along with several

Logistic Achievement Test Scaling and Equating with Fixed versus Estimated Lower Asymptotes.

ERIC Educational Resources Information Center

Phillips, S. E.

This study compared the lower asymptotes estimated by the maximum likelihood procedures of the LOGIST computer program with those obtained via application of the Norton methodology. The study also compared the equating results from the three-parameter logistic model with those obtained from the equipercentile, Rasch, and conditional…

Teacher's Corner: Structural Equation Modeling with the Sem Package in R

ERIC Educational Resources Information Center

Fox, John

2006-01-01

R is free, open-source, cooperatively developed software that implements the S statistical programming language and computing environment. The current capabilities of R are extensive, and it is in wide use, especially among statisticians. The sem package provides basic structural equation modeling facilities in R, including the ability to fit…

Application of a soft computing technique in predicting the percentage of shear force carried by walls in a rectangular channel with non-homogeneous roughness.

PubMed

Khozani, Zohreh Sheikh; Bonakdari, Hossein; Zaji, Amir Hossein

2016-01-01

Two new soft computing models, namely genetic programming (GP) and genetic artificial algorithm (GAA) neural network (a combination of modified genetic algorithm and artificial neural network methods) were developed in order to predict the percentage of shear force in a rectangular channel with non-homogeneous roughness. The ability of these methods to estimate the percentage of shear force was investigated. Moreover, the independent parameters' effectiveness in predicting the percentage of shear force was determined using sensitivity analysis. According to the results, the GP model demonstrated superior performance to the GAA model. A comparison was also made between the GP program determined as the best model and five equations obtained in prior research. The GP model with the lowest error values (root mean square error ((RMSE) of 0.0515) had the best function compared with the other equations presented for rough and smooth channels as well as smooth ducts. The equation proposed for rectangular channels with rough boundaries (RMSE of 0.0642) outperformed the prior equations for smooth boundaries.

Computational chemistry

NASA Technical Reports Server (NTRS)

Arnold, J. O.

1987-01-01

With the advent of supercomputers, modern computational chemistry algorithms and codes, a powerful tool was created to help fill NASA's continuing need for information on the properties of matter in hostile or unusual environments. Computational resources provided under the National Aerodynamics Simulator (NAS) program were a cornerstone for recent advancements in this field. Properties of gases, materials, and their interactions can be determined from solutions of the governing equations. In the case of gases, for example, radiative transition probabilites per particle, bond-dissociation energies, and rates of simple chemical reactions can be determined computationally as reliably as from experiment. The data are proving to be quite valuable in providing inputs to real-gas flow simulation codes used to compute aerothermodynamic loads on NASA's aeroassist orbital transfer vehicles and a host of problems related to the National Aerospace Plane Program. Although more approximate, similar solutions can be obtained for ensembles of atoms simulating small particles of materials with and without the presence of gases. Computational chemistry has application in studying catalysis, properties of polymers, all of interest to various NASA missions, including those previously mentioned. In addition to discussing these applications of computational chemistry within NASA, the governing equations and the need for supercomputers for their solution is outlined.

Shuttle program: Computing atmospheric scale height for refraction corrections

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Methods for computing the atmospheric scale height to determine radio wave refraction were investigated for different atmospheres, and different angles of elevation. Tables of refractivity versus altitude are included. The equations used to compute the refraction corrections are given. It is concluded that very accurate corrections are determined with the assumption of an exponential atmosphere.

PyR@TE. Renormalization group equations for general gauge theories

NASA Astrophysics Data System (ADS)

Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

2014-03-01

Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)

Hybrid 3-D rocket trajectory program. Part 1: Formulation and analysis. Part 2: Computer programming and user's instruction. [computerized simulation using three dimensional motion analysis

NASA Technical Reports Server (NTRS)

Huang, L. C. P.; Cook, R. A.

1973-01-01

Models utilizing various sub-sets of the six degrees of freedom are used in trajectory simulation. A 3-D model with only linear degrees of freedom is especially attractive, since the coefficients for the angular degrees of freedom are the most difficult to determine and the angular equations are the most time consuming for the computer to evaluate. A computer program is developed that uses three separate subsections to predict trajectories. A launch rail subsection is used until the rocket has left its launcher. The program then switches to a special 3-D section which computes motions in two linear and one angular degrees of freedom. When the rocket trims out, the program switches to the standard, three linear degrees of freedom model.

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations

NASA Astrophysics Data System (ADS)

Vergara-Perez, Sandra; Marucho, Marcelo

2016-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson-Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post-analysis of structural and electrical properties of biomolecules.

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations

PubMed Central

Vergara-Perez, Sandra; Marucho, Marcelo

2015-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post- analysis of structural and electrical properties of biomolecules. PMID:26924848

MPBEC, a Matlab Program for Biomolecular Electrostatic Calculations.

PubMed

Vergara-Perez, Sandra; Marucho, Marcelo

2016-01-01

One of the most used and efficient approaches to compute electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation. There are several software packages available that solve the PB equation for molecules in aqueous electrolyte solutions. Most of these software packages are useful for scientists with specialized training and expertise in computational biophysics. However, the user is usually required to manually take several important choices, depending on the complexity of the biological system, to successfully obtain the numerical solution of the PB equation. This may become an obstacle for researchers, experimentalists, even students with no special training in computational methodologies. Aiming to overcome this limitation, in this article we present MPBEC, a free, cross-platform, open-source software that provides non-experts in the field an easy and efficient way to perform biomolecular electrostatic calculations on single processor computers. MPBEC is a Matlab script based on the Adaptative Poisson Boltzmann Solver, one of the most popular approaches used to solve the PB equation. MPBEC does not require any user programming, text editing or extensive statistical skills, and comes with detailed user-guide documentation. As a unique feature, MPBEC includes a useful graphical user interface (GUI) application which helps and guides users to configure and setup the optimal parameters and approximations to successfully perform the required biomolecular electrostatic calculations. The GUI also incorporates visualization tools to facilitate users pre- and post- analysis of structural and electrical properties of biomolecules.

Study-simulation of space station dynamics

NASA Technical Reports Server (NTRS)

Gaitens, M. J.

1971-01-01

Matrix algebra translator and executor /MATE/ takes equations describing structural control system environmental interaction problem for flexible spacecraft components and loads them into self programming computer.

Tray estimates for low reflux

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barna, B.A.; Ginn, R.F.

1985-05-01

In computer programs which perform shortcut calculations for multicomponent distillation, the Gilliland correlation continues to be used even though errors of up to 60% (compared with rigorous plate-to-plate calculations) were shown by Erbar and Maddox. Average absolute differences were approximately 30% for Gilliland's correlation versus 4% for the Erbar-Maddox method. The reason the Gilliland correlation continues to be used appears to be due to the availability of an equation by Eduljee which facilitates the correlation's use in computer program. A new equation is presented in this paper that represents the Erbar-Maddox correlation of trays with reflux for multicomponent distillation. Atmore » low reflux ratios, results show more trays are needed than would be estimated by Gilliland's method.« less

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

Requirements for Kalman filtering on the GE-701 whole word computer

NASA Technical Reports Server (NTRS)

Pines, S.; Schmidt, S. F.

1978-01-01

The results of a study to determine scaling, storage, and word length requirements for programming the Kalman filter on the GE-701 Whole Word Computer are reported. Simulation tests are presented which indicate that the Kalman filter, using a square root formulation with process noise added, utilizing MLS, radar altimeters, and airspeed as navigation aids, may be programmed for the GE-701 computer to successfully navigate and control the Boeing B737-100 during landing approach, landing rollout, and turnoff. The report contains flow charts, equations, computer storage, scaling, and word length recommendations for the Kalman filter on the GE-701 Whole Word computer.

Turbulence modeling of free shear layers for high-performance aircraft

NASA Technical Reports Server (NTRS)

Sondak, Douglas L.

1993-01-01

The High Performance Aircraft (HPA) Grand Challenge of the High Performance Computing and Communications (HPCC) program involves the computation of the flow over a high performance aircraft. A variety of free shear layers, including mixing layers over cavities, impinging jets, blown flaps, and exhaust plumes, may be encountered in such flowfields. Since these free shear layers are usually turbulent, appropriate turbulence models must be utilized in computations in order to accurately simulate these flow features. The HPCC program is relying heavily on parallel computers. A Navier-Stokes solver (POVERFLOW) utilizing the Baldwin-Lomax algebraic turbulence model was developed and tested on a 128-node Intel iPSC/860. Algebraic turbulence models run very fast, and give good results for many flowfields. For complex flowfields such as those mentioned above, however, they are often inadequate. It was therefore deemed that a two-equation turbulence model will be required for the HPA computations. The k-epsilon two-equation turbulence model was implemented on the Intel iPSC/860. Both the Chien low-Reynolds-number model and a generalized wall-function formulation were included.

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Multidimensional computer simulation of Stirling cycle engines

NASA Technical Reports Server (NTRS)

Hall, C. A.; Porsching, T. A.; Medley, J.; Tew, R. C.

1990-01-01

The computer code ALGAE (algorithms for the gas equations) treats incompressible, thermally expandable, or locally compressible flows in complicated two-dimensional flow regions. The solution method, finite differencing schemes, and basic modeling of the field equations in ALGAE are applicable to engineering design settings of the type found in Stirling cycle engines. The use of ALGAE to model multiple components of the space power research engine (SPRE) is reported. Videotape computer simulations of the transient behavior of the working gas (helium) in the heater-regenerator-cooler complex of the SPRE demonstrate the usefulness of such a program in providing information on thermal and hydraulic phenomena in multiple component sections of the SPRE.

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 2: Development of theory for wing shielding

NASA Technical Reports Server (NTRS)

Amiet, R. K.

1991-01-01

A unified theory for aerodynamics and noise of advanced turboprops is presented. The theory and a computer code developed for evaluation at the shielding benefits that might be expected by an aircraft wing in a wing-mounted propeller installation are presented. Several computed directivity patterns are presented to demonstrate the theory. Recently with the advent of the concept of using the wing of an aircraft for noise shielding, the case of diffraction by a surface in a flow has been given attention. The present analysis is based on the case of diffraction of no flow. By combining a Galilean and a Lorentz transform, the wave equation with a mean flow can be reduced to the ordinary equation. Allowance is also made in the analysis for the case of a swept wing. The same combination of Galilean and Lorentz transforms lead to a problem with no flow but a different sweep. The solution procedures for the cases of leading and trailing edges are basically the same. Two normalizations of the solution are given by the computer program. FORTRAN computer programs are presented with detailed documentation. The output from these programs compares favorably with the results of other investigators.

COMMIX-PPC: A three-dimensional transient multicomponent computer program for analyzing performance of power plant condensers. Volume 1, Equations and numerics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chien, T.H.; Domanus, H.M.; Sha, W.T.

1993-02-01

The COMMIX-PPC computer pregrain is an extended and improved version of earlier COMMIX codes and is specifically designed for evaluating the thermal performance of power plant condensers. The COMMIX codes are general-purpose computer programs for the analysis of fluid flow and heat transfer in complex Industrial systems. In COMMIX-PPC, two major features have been added to previously published COMMIX codes. One feature is the incorporation of one-dimensional equations of conservation of mass, momentum, and energy on the tube stile and the proper accounting for the thermal interaction between shell and tube side through the porous-medium approach. The other added featuremore » is the extension of the three-dimensional conservation equations for shell-side flow to treat the flow of a multicomponent medium. COMMIX-PPC is designed to perform steady-state and transient. Three-dimensional analysis of fluid flow with heat transfer tn a power plant condenser. However, the code is designed in a generalized fashion so that, with some modification, it can be used to analyze processes in any heat exchanger or other single-phase engineering applications. Volume I (Equations and Numerics) of this report describes in detail the basic equations, formulation, solution procedures, and models for a phenomena. Volume II (User`s Guide and Manual) contains the input instruction, flow charts, sample problems, and descriptions of available options and boundary conditions.« less

Using regression equations built from summary data in the psychological assessment of the individual case: extension to multiple regression.

PubMed

Crawford, John R; Garthwaite, Paul H; Denham, Annie K; Chelune, Gordon J

2012-12-01

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because (a) not all psychologists are aware that regression equations can be built not only from raw data but also using only basic summary data for a sample, and (b) the computations involved are tedious and prone to error. In an attempt to overcome these barriers, Crawford and Garthwaite (2007) provided methods to build and apply simple linear regression models using summary statistics as data. In the present study, we extend this work to set out the steps required to build multiple regression models from sample summary statistics and the further steps required to compute the associated statistics for drawing inferences concerning an individual case. We also develop, describe, and make available a computer program that implements these methods. Although there are caveats associated with the use of the methods, these need to be balanced against pragmatic considerations and against the alternative of either entirely ignoring a pertinent data set or using it informally to provide a clinical "guesstimate." Upgraded versions of earlier programs for regression in the single case are also provided; these add the point and interval estimates of effect size developed in the present article.

The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories

NASA Technical Reports Server (NTRS)

Dyer, J.; Danchick, R.; Pierce, S.; Haney, R.

1972-01-01

An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered.

Coupled bending-torsion steady-state response of pretwisted, nonuniform rotating beams using a transfer-matrix method

NASA Technical Reports Server (NTRS)

Gray, Carl E., Jr.

1988-01-01

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

TEMPEST: A three-dimensional time-dependent computer program for hydrothermal analysis: Volume 1, Numerical methods and input instructions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trent, D.S.; Eyler, L.L.; Budden, M.J.

This document describes the numerical methods, current capabilities, and the use of the TEMPEST (Version L, MOD 2) computer program. TEMPEST is a transient, three-dimensional, hydrothermal computer program that is designed to analyze a broad range of coupled fluid dynamic and heat transfer systems of particular interest to the Fast Breeder Reactor thermal-hydraulic design community. The full three-dimensional, time-dependent equations of motion, continuity, and heat transport are solved for either laminar or turbulent fluid flow, including heat diffusion and generation in both solid and liquid materials. 10 refs., 22 figs., 2 tabs.

Bio-inspired computational heuristics to study Lane-Emden systems arising in astrophysics model.

PubMed

Ahmad, Iftikhar; Raja, Muhammad Asif Zahoor; Bilal, Muhammad; Ashraf, Farooq

2016-01-01

This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane-Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an unsupervised manner. The proposed approximated solutions of higher order ordinary differential equation are calculated with the weights of neural networks trained with genetic algorithm, and pattern search hybrid with sequential quadratic programming for rapid local convergence. The results of proposed solvers for solving the nonlinear singular systems are in good agreements with the standard solutions. Accuracy and convergence the design schemes are demonstrated by the results of statistical performance measures based on the sufficient large number of independent runs.

A computationally efficient modelling of laminar separation bubbles

NASA Technical Reports Server (NTRS)

Maughmer, Mark D.

1988-01-01

The goal of this research is to accurately predict the characteristics of the laminar separation bubble and its effects on airfoil performance. To this end, a model of the bubble is under development and will be incorporated in the analysis section of the Eppler and Somers program. As a first step in this direction, an existing bubble model was inserted into the program. It was decided to address the problem of the short bubble before attempting the prediction of the long bubble. In the second place, an integral boundary-layer method is believed more desirable than a finite difference approach. While these two methods achieve similar prediction accuracy, finite-difference methods tend to involve significantly longer computer run times than the integral methods. Finally, as the boundary-layer analysis in the Eppler and Somers program employs the momentum and kinetic energy integral equations, a short-bubble model compatible with these equations is most preferable.

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.

1986-01-01

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

A Fortran 90 Hartree-Fock program for one-dimensional periodic π-conjugated systems using Pariser-Parr-Pople model

NASA Astrophysics Data System (ADS)

Kondayya, Gundra; Shukla, Alok

2012-03-01

Pariser-Parr-Pople (P-P-P) model Hamiltonian is employed frequently to study the electronic structure and optical properties of π-conjugated systems. In this paper we describe a Fortran 90 computer program which uses the P-P-P model Hamiltonian to solve the Hartree-Fock (HF) equation for infinitely long, one-dimensional, periodic, π-electron systems. The code is capable of computing the band structure, as also the linear optical absorption spectrum, by using the tight-binding and the HF methods. Furthermore, using our program the user can solve the HF equation in the presence of a finite external electric field, thereby, allowing the simulation of gated systems. We apply our code to compute various properties of polymers such as trans-polyacetylene, poly- para-phenylene, and armchair and zigzag graphene nanoribbons, in the infinite length limit. Program summaryProgram title: ppp_bulk.x Catalogue identifier: AEKW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 464 No. of bytes in distributed program, including test data, etc.: 2 046 933 Distribution format: tar.gz Programming language: Fortran 90 Computer: PCs and workstations Operating system: Linux, Code was developed and tested on various recent versions of 64-bit Fedora including Fedora 14 (kernel version 2.6.35.12-90). Classification: 7.3 External routines: This program needs to link with LAPACK/BLAS libraries compiled with the same compiler as the program. For the Intel Fortran Compiler we used the ACML library version 4.4.0, while for the gfortran compiler we used the libraries supplied with the Fedora distribution. Nature of problem: The electronic structure of one-dimensional periodic π-conjugated systems is an intense area of research at present because of the tremendous interest in the physics of conjugated polymers and graphene nanoribbons. The computer program described in this paper provides an efficient way of solving the Hartree-Fock equations for such systems within the P-P-P model. In addition to the Bloch orbitals, band structure, and the density of states, the program can also compute quantities such as the linear absorption spectrum, and the electro-absorption spectrum of these systems. Solution method: For a one-dimensional periodic π-conjugated system lying in the xy-plane, the single-particle Bloch orbitals are expressed as linear combinations of p-orbitals of individual atoms. Then using various parameters defining the P-P-P Hamiltonian, the Hartree-Fock equations are set up as a matrix eigenvalue problem in the k-space. Thereby, its solutions are obtained in a self-consistent manner, using the iterative diagonalizing technique at several k points. The band structure and the corresponding Bloch orbitals thus obtained are used to perform a variety of calculations such as the density of states, linear optical absorption spectrum, electro-absorption spectrum, etc. Running time: Most of the examples provided take only a few seconds to run. For a large system, however, depending on the system size, the run time may be a few minutes to a few hours.

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

Three-dimensional computer simulation of non-reacting jet-gas flow mixing in an MHD second stage combustor

NASA Astrophysics Data System (ADS)

Chang, S. L.; Lottes, S. A.; Berry, G. F.

Argonne National Laboratory is investigating the non-reacting jet-gas mixing patterns in a magnetohydrodynamics (MHD) second stage combustor by using a three-dimensional single-phase hydrodynamics computer program. The computer simulation is intended to enhance the understanding of flow and mixing patterns in the combustor, which in turn may improve downstream MHD channel performance. The code is used to examine the three-dimensional effects of the side walls and the distributed jet flows on the non-reacting jet-gas mixing patterns. The code solves the conservation equations of mass, momentum, and energy, and a transport equation of a turbulence parameter and allows permeable surfaces to be specified for any computational cell.

The theory of the gravitational potential applied to orbit prediction

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.

Rotor dynamic simulation and system identification methods for application to vacuum whirl data

NASA Technical Reports Server (NTRS)

Berman, A.; Giansante, N.; Flannelly, W. G.

1980-01-01

Methods of using rotor vacuum whirl data to improve the ability to model helicopter rotors were developed. The work consisted of the formulation of the equations of motion of elastic blades on a hub using a Galerkin method; the development of a general computer program for simulation of these equations; the study and implementation of a procedure for determining physical parameters based on measured data; and the application of a method for computing the normal modes and natural frequencies based on test data.

Modeling of the WSTF frictional heating apparatus in high pressure systems

NASA Technical Reports Server (NTRS)

Skowlund, Christopher T.

1992-01-01

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

PAGOSA physics manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weseloh, Wayne N.; Clancy, Sean P.; Painter, James W.

2010-08-01

PAGOSA is a computational fluid dynamics computer program developed at Los Alamos National Laboratory (LANL) for the study of high-speed compressible flow and high-rate material deformation. PAGOSA is a three-dimensional Eulerian finite difference code, solving problems with a wide variety of equations of state (EOSs), material strength, and explosive modeling options.

A Pulsatile Cardiovascular Computer Model for Teaching Heart-Blood Vessel Interaction.

ERIC Educational Resources Information Center

Campbell, Kenneth; And Others

1982-01-01

Describes a model which gives realistic predictions of pulsatile pressure, flow, and volume events in the cardiovascular system. Includes computer oriented laboratory exercises for veterinary and graduate students; equations of the dynamic and algebraic models; and a flow chart for the cardiovascular teaching program. (JN)

Computer program for Stirling engine performance calculations

NASA Technical Reports Server (NTRS)

Tew, R. C., Jr.

1983-01-01

The thermodynamic characteristics of the Stirling engine were analyzed and modeled on a computer to support its development as a possible alternative to the automobile spark ignition engine. The computer model is documented. The documentation includes a user's manual, symbols list, a test case, comparison of model predictions with test results, and a description of the analytical equations used in the model.

An Interactive Excel Program for Tracking a Single Droplet in Crossflow Computation

NASA Technical Reports Server (NTRS)

Urip, E.; Yang, S. L.; Marek, C. J.

2002-01-01

Spray jet in crossflow has been a subject of research because of its wide application in systems involving pollutant dispersion, jet mixing in the dilution zone of combustors, and fuel injection strategies. The focus of this work is to investigate dispersion of a 2-dimensional atomized spray jet into a 2-dimensional crossflow. A quick computational method is developed using available software. The spreadsheet can be used for any 2D droplet trajectory problem where the drop is injected into the free stream eventually coming to the free stream conditions. During the transverse injection of a spray into high velocity airflow, the droplets (carried along and deflected by a gaseous stream of co-flowing air) are subjected to forces that affect their motion in the flow field. Based on the Newton's Second Law of motion, four ordinary differential equations were used. These equations were then solved by a fourth-order Runge-Kutta method using Excel software. Visual basic programming and Excel macrocode to produce the data facilitate Excel software to plot graphs describing the droplet's motion in the flow field. This program computes and plots the data sequentially without forcing users to open other types of plotting programs. A user's manual on how to use the program is also included in this report.

Star adaptation for two-algorithms used on serial computers

NASA Technical Reports Server (NTRS)

Howser, L. M.; Lambiotte, J. J., Jr.

1974-01-01

Two representative algorithms used on a serial computer and presently executed on the Control Data Corporation 6000 computer were adapted to execute efficiently on the Control Data STAR-100 computer. Gaussian elimination for the solution of simultaneous linear equations and the Gauss-Legendre quadrature formula for the approximation of an integral are the two algorithms discussed. A description is given of how the programs were adapted for STAR and why these adaptations were necessary to obtain an efficient STAR program. Some points to consider when adapting an algorithm for STAR are discussed. Program listings of the 6000 version coded in 6000 FORTRAN, the adapted STAR version coded in 6000 FORTRAN, and the STAR version coded in STAR FORTRAN are presented in the appendices.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

NASA Technical Reports Server (NTRS)

Baker, A. J.

1982-01-01

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

Equation-based languages – A new paradigm for building energy modeling, simulation and optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wetter, Michael; Bonvini, Marco; Nouidui, Thierry S.

Most of the state-of-the-art building simulation programs implement models in imperative programming languages. This complicates modeling and excludes the use of certain efficient methods for simulation and optimization. In contrast, equation-based modeling languages declare relations among variables, thereby allowing the use of computer algebra to enable much simpler schematic modeling and to generate efficient code for simulation and optimization. We contrast the two approaches in this paper. We explain how such manipulations support new use cases. In the first of two examples, we couple models of the electrical grid, multiple buildings, HVAC systems and controllers to test a controller thatmore » adjusts building room temperatures and PV inverter reactive power to maintain power quality. In the second example, we contrast the computing time for solving an optimal control problem for a room-level model predictive controller with and without symbolic manipulations. As a result, exploiting the equation-based language led to 2, 200 times faster solution« less

Preconditioned implicit solvers for the Navier-Stokes equations on distributed-memory machines

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Liou, Meng-Sing; Dyson, Rodger W.

1994-01-01

The GMRES method is parallelized, and combined with local preconditioning to construct an implicit parallel solver to obtain steady-state solutions for the Navier-Stokes equations of fluid flow on distributed-memory machines. The new implicit parallel solver is designed to preserve the convergence rate of the equivalent 'serial' solver. A static domain-decomposition is used to partition the computational domain amongst the available processing nodes of the parallel machine. The SPMD (Single-Program Multiple-Data) programming model is combined with message-passing tools to develop the parallel code on a 32-node Intel Hypercube and a 512-node Intel Delta machine. The implicit parallel solver is validated for internal and external flow problems, and is found to compare identically with flow solutions obtained on a Cray Y-MP/8. A peak computational speed of 2300 MFlops/sec has been achieved on 512 nodes of the Intel Delta machine,k for a problem size of 1024 K equations (256 K grid points).

An efficient algorithm using matrix methods to solve wind tunnel force-balance equations

NASA Technical Reports Server (NTRS)

Smith, D. L.

1972-01-01

An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.

Equation-based languages – A new paradigm for building energy modeling, simulation and optimization

DOE PAGES

Wetter, Michael; Bonvini, Marco; Nouidui, Thierry S.

2016-04-01

Most of the state-of-the-art building simulation programs implement models in imperative programming languages. This complicates modeling and excludes the use of certain efficient methods for simulation and optimization. In contrast, equation-based modeling languages declare relations among variables, thereby allowing the use of computer algebra to enable much simpler schematic modeling and to generate efficient code for simulation and optimization. We contrast the two approaches in this paper. We explain how such manipulations support new use cases. In the first of two examples, we couple models of the electrical grid, multiple buildings, HVAC systems and controllers to test a controller thatmore » adjusts building room temperatures and PV inverter reactive power to maintain power quality. In the second example, we contrast the computing time for solving an optimal control problem for a room-level model predictive controller with and without symbolic manipulations. As a result, exploiting the equation-based language led to 2, 200 times faster solution« less

Finding all solutions of nonlinear equations using the dual simplex method

NASA Astrophysics Data System (ADS)

Yamamura, Kiyotaka; Fujioka, Tsuyoshi

2003-03-01

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

Unsteady flow model for circulation-control airfoils

NASA Technical Reports Server (NTRS)

Rao, B. M.

1979-01-01

An analysis and a numerical lifting surface method are developed for predicting the unsteady airloads on two-dimensional circulation control airfoils in incompressible flow. The analysis and the computer program are validated by correlating the computed unsteady airloads with test data and also with other theoretical solutions. Additionally, a mathematical model for predicting the bending-torsion flutter of a two-dimensional airfoil (a reference section of a wing or rotor blade) and a computer program using an iterative scheme are developed. The flutter program has a provision for using the CC airfoil airloads program or the Theodorsen hard flap solution to compute the unsteady lift and moment used in the flutter equations. The adopted mathematical model and the iterative scheme are used to perform a flutter analysis of a typical CC rotor blade reference section. The program seems to work well within the basic assumption of the incompressible flow.

Aerodynamic design guidelines and computer program for estimation of subsonic wind tunnel performance

NASA Technical Reports Server (NTRS)

Eckert, W. T.; Mort, K. W.; Jope, J.

1976-01-01

General guidelines are given for the design of diffusers, contractions, corners, and the inlets and exits of non-return tunnels. A system of equations, reflecting the current technology, has been compiled and assembled into a computer program (a user's manual for this program is included) for determining the total pressure losses. The formulation presented is applicable to compressible flow through most closed- or open-throat, single-, double-, or non-return wind tunnels. A comparison of estimated performance with that actually achieved by several existing facilities produced generally good agreement.

A flexible computer aid for conceptual design based on constraint propagation and component-modeling. [of aircraft in three dimensions

NASA Technical Reports Server (NTRS)

Kolb, Mark A.

1988-01-01

The Rubber Airplane program, which combines two symbolic processing techniques with a component-based database of design knowledge, is proposed as a computer aid for conceptual design. Using object-oriented programming, programs are organized around the objects and behavior to be simulated, and using constraint propagation, declarative statements designate mathematical relationships among all the equation variables. It is found that the additional level of organizational structure resulting from the arrangement of the design information in terms of design components provides greater flexibility and convenience.

SPIP: A computer program implementing the Interaction Picture method for simulation of light-wave propagation in optical fibre

NASA Astrophysics Data System (ADS)

Balac, Stéphane; Fernandez, Arnaud

2016-02-01

The computer program SPIP is aimed at solving the Generalized Non-Linear Schrödinger equation (GNLSE), involved in optics e.g. in the modelling of light-wave propagation in an optical fibre, by the Interaction Picture method, a new efficient alternative method to the Symmetric Split-Step method. In the SPIP program a dedicated costless adaptive step-size control based on the use of a 4th order embedded Runge-Kutta method is implemented in order to speed up the resolution.

COMMIX-PPC: A three-dimensional transient multicomponent computer program for analyzing performance of power plant condensers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chien, T.H.; Domanus, H.M.; Sha, W.T.

1993-02-01

The COMMIX-PPC computer pregrain is an extended and improved version of earlier COMMIX codes and is specifically designed for evaluating the thermal performance of power plant condensers. The COMMIX codes are general-purpose computer programs for the analysis of fluid flow and heat transfer in complex Industrial systems. In COMMIX-PPC, two major features have been added to previously published COMMIX codes. One feature is the incorporation of one-dimensional equations of conservation of mass, momentum, and energy on the tube stile and the proper accounting for the thermal interaction between shell and tube side through the porous-medium approach. The other added featuremore » is the extension of the three-dimensional conservation equations for shell-side flow to treat the flow of a multicomponent medium. COMMIX-PPC is designed to perform steady-state and transient. Three-dimensional analysis of fluid flow with heat transfer tn a power plant condenser. However, the code is designed in a generalized fashion so that, with some modification, it can be used to analyze processes in any heat exchanger or other single-phase engineering applications. Volume I (Equations and Numerics) of this report describes in detail the basic equations, formulation, solution procedures, and models for a phenomena. Volume II (User's Guide and Manual) contains the input instruction, flow charts, sample problems, and descriptions of available options and boundary conditions.« less

Demonstrating the Gas Laws.

ERIC Educational Resources Information Center

Holko, David A.

1982-01-01

Presents a complete computer program demonstrating the relationship between volume/pressure for Boyle's Law, volume/temperature for Charles' Law, and volume/moles of gas for Avagadro's Law. The programing reinforces students' application of gas laws and equates a simulated moving piston to theoretical values derived using the ideal gas law.…

User's manual for XTRAN2L (version 1.2): A program for solving the general-frequency unsteady transonic small-disturbance equation

NASA Technical Reports Server (NTRS)

Seidel, D. A.; Batina, J. T.

1986-01-01

The development, use and operation of the XTRAN2L program that solves the two dimensional unsteady transonic small disturbance potential equation are described. The XTRAN2L program is used to calculate steady and unsteady transonic flow fields about airfoils and is capable of performing self contained transonic flutter calculations. Operation of the XTRAN2L code is described, and tables defining all input variables, including default values, are presented. Sample cases that use various program options are shown to illustrate operation of XTRAN2L. Computer listings containing input and selected output are included as an aid to the user.

Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Beşliu, C.; Jipa, Al.; Felea, D.; Grossu, I. V.

2008-05-01

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE. Program summaryProgram title: Chaos Catalogue identifier: AEAP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 885 No. of bytes in distributed program, including test data, etc.: 5925 Distribution format: tar.gz Programming language: Scilab 3.1.1 Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 100 Megabytes Classification: 6.2 Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem. Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

NASA Technical Reports Server (NTRS)

Ball, R. E.

1972-01-01

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Computer programs for smoothing and scaling airfoil coordinates

NASA Technical Reports Server (NTRS)

Morgan, H. L., Jr.

1983-01-01

Detailed descriptions are given of the theoretical methods and associated computer codes of a program to smooth and a program to scale arbitrary airfoil coordinates. The smoothing program utilizes both least-squares polynomial and least-squares cubic spline techniques to smooth interatively the second derivatives of the y-axis airfoil coordinates with respect to a transformed x-axis system which unwraps the airfoil and stretches the nose and trailing-edge regions. The corresponding smooth airfoil coordinates are then determined by solving a tridiagonal matrix of simultaneous cubic-spline equations relating the y-axis coordinates and their corresponding second derivatives. A technique for computing the camber and thickness distribution of the smoothed airfoil is also discussed. The scaling program can then be used to scale the thickness distribution generated by the smoothing program to a specific maximum thickness which is then combined with the camber distribution to obtain the final scaled airfoil contour. Computer listings of the smoothing and scaling programs are included.

Effect of misalignment on mechanical behavior of metals in creep. [computer programs

NASA Technical Reports Server (NTRS)

Wu, H. C.

1979-01-01

Application of the endochronic theory of viscoplasticity to creep, creep recovery, and stress relaxation at the small strain and short time range produced the following results: (1) The governing constitutive equations for constant-strain-rate stress-strain behavior, creep, creep recovery, and stress relaxation were derived by imposing appropriate constraints on the general constitutive equation of the endochronic theory. (2) A set of material constants was found which correlate strain-hardening, creep, creep recovery, and stress relaxation. (3) The theory predicts with reasonable accuracy the creep and creep recovery behaviors at short time. (4) The initial strain history prior to the creep stage affects the subsequent creep significantly. (5) A critical stress was established for creep recovery. A computer program, written for the misalignment problem is reported.

Cascade flow analysis by Navier-Stokes equation

NASA Astrophysics Data System (ADS)

Nozaki, Osamu

1987-06-01

As the performance of the large electronic computer has improved, numerical simulation of the flow around the blade of the aircraft, for instance, is being actively conducted. In the compressor and turbine cascades of aircraft engine, multiple blades are put side by side closely, and the pressure gradient in the flow direction is large. Thus they have more complicated properties than the independent blade. At present, therefore, it is the mainstream to use potential, Euler's equation, etc., as the basic equation but, for knowing the phenomenon caused by the viscosity like the interference of shock waves and boundary layers, it is necessary to solve the Navier-Stokes (N-S) equation. A two-dimensional cascade analysis program was developed by the N-S equation by expanding the two-dimensional high Reynolds number transonic profile analysis code NSFOIL and the lattice formation program AFMESH for the independent blade, which were already developed so as to fit the cascade flow.

The N-BOD2 user's and programmer's manual

NASA Technical Reports Server (NTRS)

Frisch, H. P.

1978-01-01

A general purpose digital computer program was developed and designed to aid in the analysis of spacecraft attitude dynamics. The program provides the analyst with the capability of automatically deriving and numerically solving the equations of motion of any system that can be modeled as a topological tree of coupled rigid bodies, flexible bodies, point masses, and symmetrical momentum wheels. Two modes of output are available. The composite system equations of motion may be outputted on a line printer in a symbolic form that may be easily translated into common vector-dyadic notation, or the composite system equations of motion may be solved numerically and any desirable set of system state variables outputted as a function of time.

Application of the sequential quadratic programming algorithm for reconstructing the distribution of optical parameters based on the time-domain radiative transfer equation.

PubMed

Qi, Hong; Qiao, Yao-Bin; Ren, Ya-Tao; Shi, Jing-Wen; Zhang, Ze-Yu; Ruan, Li-Ming

2016-10-17

Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Transonic flow analysis for rotors. Part 1: Three-dimensional quasi-steady, full-potential calculation

NASA Technical Reports Server (NTRS)

Chang, I. C.

1984-01-01

A new computer program is presented for calculating the quasi-steady transonic flow past a helicopter rotor blade in hover as well as in forward flight. The program is based on the full potential equations in a blade attached frame of reference and is capable of treating a very general class of rotor blade geometries. Computed results show good agreement with available experimental data for both straight and swept tip blade geometries.

A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model

USGS Publications Warehouse

McDonald, Michael G.; Harbaugh, Arlen W.; Guo, Weixing; Lu, Guoping

1988-01-01

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

Algorthms and prigrams complex for chaotic dynamics investigation of the Earth artificial sat-ellites. (Russian Title: Комплекс алгоритмов и программ для исследования хаотичности в динамике искусственных спутников Земли )

NASA Astrophysics Data System (ADS)

Bordovitsyna, T. V.; Aleksandrova, A. G.; Chuvashov, I. N.

2010-12-01

In this paper complex of algorithms and programs for revelation and investigation of dynamical chaotic state in the motion of the Earth artificial satellites by parallel computing is presented. Complex has been based on the program "Numerical model of the system artificial satellites motion" for cluster "Skiff Cyberia". Factor MEGNO as main indicator of chaotic state has been used. The factor is computed by combined numerical integration of equations of the motion, equations in variation and equations of MEGNO parameters. The results of program complex testing in the problem of MEGNO parameters calculation for different types of geostationary orbits are presented.

A program for calculating load coefficient matrices utilizing the force summation method, L218 (LOADS). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Miller, R. D.; Anderson, L. R.

1979-01-01

The LOADS program L218, a digital computer program that calculates dynamic load coefficient matrices utilizing the force summation method, is described. The load equations are derived for a flight vehicle in straight and level flight and excited by gusts and/or control motions. In addition, sensor equations are calculated for use with an active control system. The load coefficient matrices are calculated for the following types of loads: translational and rotational accelerations, velocities, and displacements; panel aerodynamic forces; net panel forces; shears and moments. Program usage and a brief description of the analysis used are presented. A description of the design and structure of the program to aid those who will maintain and/or modify the program in the future is included.

Solution of quadratic matrix equations for free vibration analysis of structures.

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1973-01-01

An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries

NASA Technical Reports Server (NTRS)

Lilley, D. G.; Rhode, D. L.

1982-01-01

A primitive pressure-velocity variable finite difference computer code was developed to predict swirling recirculating inert turbulent flows in axisymmetric combustors in general, and for application to a specific idealized combustion chamber with sudden or gradual expansion. The technique involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation k-epsilon turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. A user's manual, dealing with the computational problem, showing how the mathematical basis and computational scheme may be translated into a computer program is presented. A flow chart, FORTRAN IV listing, notes about various subroutines and a user's guide are supplied as an aid to prospective users of the code.

Aeroelasticity of wing and wing-body configurations on parallel computers

NASA Technical Reports Server (NTRS)

Byun, Chansup

1995-01-01

The objective of this research is to develop computationally efficient methods for solving aeroelasticity problems on parallel computers. Both uncoupled and coupled methods are studied in this research. For the uncoupled approach, the conventional U-g method is used to determine the flutter boundary. The generalized aerodynamic forces required are obtained by the pulse transfer-function analysis method. For the coupled approach, the fluid-structure interaction is obtained by directly coupling finite difference Euler/Navier-Stokes equations for fluids and finite element dynamics equations for structures. This capability will significantly impact many aerospace projects of national importance such as Advanced Subsonic Civil Transport (ASCT), where the structural stability margin becomes very critical at the transonic region. This research effort will have direct impact on the High Performance Computing and Communication (HPCC) Program of NASA in the area of parallel computing.

Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB

NASA Technical Reports Server (NTRS)

Rose, Geoffrey K.; Nguyen, Duc T.; Newman, Brett A.

2017-01-01

Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.

Analysis of the possibilities and limits of the Moldflow method

NASA Astrophysics Data System (ADS)

Brierre, M.

1982-01-01

The Moldflow information and computation service is presented. Moldflow is a computer program and data bank available as a computer aid to dimensioning thermoplastic injection molding equipment and processes. It is based on the simultaneous solution of thermal and rheological equations and is intended to completely simulate the injection process. The Moldflow system is described and algorithms are discussed, based on Moldflow listings.

A finite element approach for solution of the 3D Euler equations

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.; Dechaumphai, P.

1986-01-01

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

Free geometric adjustment of the SECOR Equatorial Network (Solution SECOR-27)

NASA Technical Reports Server (NTRS)

Mueller, I. I.; Kumar, M.; Soler, T.

1973-01-01

The basic purpose of this experiment is to compute reduced normal equations from the observational data of the SECOR Equatorial Network obtained from DMA/Topographic Center, D/Geodesy, Geosciences Div. Washington, D.C. These reduced normal equations are to be combined with reduced normal equations of other satellite networks of the National Geodetic Satellite Program to provide station coordinates from a single least square adjustment. An individual SECOR solution was also obtained and is presented in this report, using direction constraints computed from BC-4 optical data from stations collocated with SECOR stations. Due to the critical configuration present in the range observations, weighted height constraints were also applied in order to break the near coplanarity of the observing stations.

GCKP84-general chemical kinetics code for gas-phase flow and batch processes including heat transfer effects

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1984-01-01

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

Computing Robust, Bootstrap-Adjusted Fit Indices for Use with Nonnormal Data

ERIC Educational Resources Information Center

Walker, David A.; Smith, Thomas J.

2017-01-01

Nonnormality of data presents unique challenges for researchers who wish to carry out structural equation modeling. The subsequent SPSS syntax program computes bootstrap-adjusted fit indices (comparative fit index, Tucker-Lewis index, incremental fit index, and root mean square error of approximation) that adjust for nonnormality, along with the…

MMA-EoS: A Computational Framework for Mineralogical Thermodynamics

NASA Astrophysics Data System (ADS)

Chust, T. C.; Steinle-Neumann, G.; Dolejš, D.; Schuberth, B. S. A.; Bunge, H.-P.

2017-12-01

We present a newly developed software framework, MMA-EoS, that evaluates phase equilibria and thermodynamic properties of multicomponent systems by Gibbs energy minimization, with application to mantle petrology. The code is versatile in terms of the equation-of-state and mixing properties and allows for the computation of properties of single phases, solution phases, and multiphase aggregates. Currently, the open program distribution contains equation-of-state formulations widely used, that is, Caloric-Murnaghan, Caloric-Modified-Tait, and Birch-Murnaghan-Mie-Grüneisen-Debye models, with published databases included. Through its modular design and easily scripted database, MMA-EoS can readily be extended with new formulations of equations-of-state and changes or extensions to thermodynamic data sets. We demonstrate the application of the program by reproducing and comparing physical properties of mantle phases and assemblages with previously published work and experimental data, successively increasing complexity, up to computing phase equilibria of six-component compositions. Chemically complex systems allow us to trace the budget of minor chemical components in order to explore whether they lead to the formation of new phases or extend stability fields of existing ones. Self-consistently computed thermophysical properties for a homogeneous mantle and a mechanical mixture of slab lithologies show no discernible differences that require a heterogeneous mantle structure as has been suggested previously. Such examples illustrate how thermodynamics of mantle mineralogy can advance the study of Earth's interior.

The Computer Bulletin Board.

ERIC Educational Resources Information Center

Batt, Russell H., Ed.

1990-01-01

Described is how spreadsheet and problem solver microcomputer programs may assist students in performing mathematical calculations. Discussed is the application of the equation solver "MathCAD" to various areas in the undergraduate curriculum. (KR)

Computer programs for the solution of systems of linear algebraic equations

NASA Technical Reports Server (NTRS)

Sequi, W. T.

1973-01-01

FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

Fragility Analysis of a Concrete Gravity Dam Embedded in Rock and Its System Response Curve Computed by the Analytical Program GDLAD_Foundation

DTIC Science & Technology

2012-06-01

According to the Bernoulli equation for ideal flows, i.e. steady, frictionless, incompressible flows, the total head, H, at any point can be determined...centerline and using the Bernoulli equation for ideal flow with an assumption that the velocity is small, the total head equals the pressure head...the Bernoulli equation for ideal flows, i.e. steady, frictionless, incompressible flows, the total head, H, at any point can be determined by

Dynamic analysis of a system of hinge-connected rigid bodies with nonrigid appendages. [equations of motion

NASA Technical Reports Server (NTRS)

Likins, P. W.

1974-01-01

Equations of motion are derived for use in simulating a spacecraft or other complex electromechanical system amenable to idealization as a set of hinge-connected rigid bodies of tree topology, with rigid axisymmetric rotors and nonrigid appendages attached to each rigid body in the set. In conjunction with a previously published report on finite-element appendage vibration equations, this report provides a complete minimum-dimension formulation suitable for generic programming for digital computer numerical integration.

User's manual for a TEACH computer program for the analysis of turbulent, swirling reacting flow in a research combustor

NASA Technical Reports Server (NTRS)

Chiappetta, L. M.

1983-01-01

Described is a computer program for the analysis of the subsonic, swirling, reacting turbulent flow in an axisymmetric, bluff-body research combustor. The program features an improved finite-difference procedure designed to reduce the effects of numerical diffusion and a new algorithm for predicting the pressure distribution within the combustor. A research version of the computer program described in the report was supplied to United Technologies Research Center by Professor A. D. Gosman and his students, R. Benodeker and R. I. Issa, of Imperial College, London. The Imperial College staff also supplied much of the program documentation. Presented are a description of the mathematical model for flow within an axisymmetric bluff-body combustor, the development of the finite-difference procedure used to represent the system of equations, an outline of the algorithm for determining the static pressure distribution within the combustor, a description of the computer program including its input format, and the results for representative test cases.

Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program

NASA Astrophysics Data System (ADS)

Asinari, Pietro

2010-10-01

The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both these corrections make possible to derive very accurate reference solutions for this test case. Moreover this work aims to distribute an open-source program (called HOMISBOLTZ), which can be redistributed and/or modified for dealing with different applications, under the terms of the GNU General Public License. The program has been purposely designed in order to be minimal, not only with regards to the reduced number of lines (less than 1000), but also with regards to the coding style (as simple as possible). Program summaryProgram title: HOMISBOLTZ Catalogue identifier: AEGN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 23 340 No. of bytes in distributed program, including test data, etc.: 7 635 236 Distribution format: tar.gz Programming language: Tested with Matlab version ⩽6.5. However, in principle, any recent version of Matlab or Octave should work Computer: All supporting Matlab or Octave Operating system: All supporting Matlab or Octave RAM: 300 MBytes Classification: 23 Nature of problem: The problem consists in integrating the homogeneous Boltzmann equation for a generic collisional kernel in case of isotropic symmetry, by a deterministic direct method. Difficulties arise from the multi-dimensionality of the collisional operator and from satisfying the conservation of particle number and energy (momentum is trivial for this test case) as accurately as possible, in order to preserve the late dynamics. Solution method: The solution is based on the method proposed by Aristov (2001) [1], but with two substantial improvements: (a) the original problem is reformulated in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium). Both these corrections make possible to derive very accurate reference solutions for this test case. Restrictions: The nonlinear Boltzmann equation is extremely challenging from the computational point of view, in particular for deterministic methods, despite the increased computational power of recent hardware. In this work, only the homogeneous isotropic case is considered, for making possible the development of a minimal program (by a simple scripting language) and allowing the user to check the advantages of the proposed improvements beyond Aristov's (2001) method [1]. The initial conditions are supposed parameterized according to a fixed analytical expression, but this can be easily modified. Running time: From minutes to hours (depending on the adopted discretization of the kinetic energy space). For example, on a 64 bit workstation with Intel CoreTM i7-820Q Quad Core CPU at 1.73 GHz and 8 MBytes of RAM, the provided test run (with the corresponding binary data file storing the pre-computed relaxation rates) requires 154 seconds. References:V.V. Aristov, Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows, Kluwer Academic Publishers, 2001.

OPMILL - MICRO COMPUTER PROGRAMMING ENVIRONMENT FOR CNC MILLING MACHINES THREE AXIS EQUATION PLOTTING CAPABILITIES

NASA Technical Reports Server (NTRS)

Ray, R. B.

1994-01-01

OPMILL is a computer operating system for a Kearney and Trecker milling machine that provides a fast and easy way to program machine part manufacture with an IBM compatible PC. The program gives the machinist an "equation plotter" feature which plots any set of equations that define axis moves (up to three axes simultaneously) and converts those equations to a machine milling program that will move a cutter along a defined path. Other supported functions include: drill with peck, bolt circle, tap, mill arc, quarter circle, circle, circle 2 pass, frame, frame 2 pass, rotary frame, pocket, loop and repeat, and copy blocks. The system includes a tool manager that can handle up to 25 tools and automatically adjusts tool length for each tool. It will display all tool information and stop the milling machine at the appropriate time. Information for the program is entered via a series of menus and compiled to the Kearney and Trecker format. The program can then be loaded into the milling machine, the tool path graphically displayed, and tool change information or the program in Kearney and Trecker format viewed. The program has a complete file handling utility that allows the user to load the program into memory from the hard disk, save the program to the disk with comments, view directories, merge a program on the disk with one in memory, save a portion of a program in memory, and change directories. OPMILL was developed on an IBM PS/2 running DOS 3.3 with 1 MB of RAM. OPMILL was written for an IBM PC or compatible 8088 or 80286 machine connected via an RS-232 port to a Kearney and Trecker Data Mill 700/C Control milling machine. It requires a "D:" drive (fixed-disk or virtual), a browse or text display utility, and an EGA or better display. Users wishing to modify and recompile the source code will also need Turbo BASIC, Turbo C, and Crescent Software's QuickPak for Turbo BASIC. IBM PC and IBM PS/2 are registered trademarks of International Business Machines. Turbo BASIC and Turbo C are trademarks of Borland International.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Computational fluid dynamics at NASA Ames and the numerical aerodynamic simulation program

NASA Technical Reports Server (NTRS)

Peterson, V. L.

1985-01-01

Computers are playing an increasingly important role in the field of aerodynamics such as that they now serve as a major complement to wind tunnels in aerospace research and development. Factors pacing advances in computational aerodynamics are identified, including the amount of computational power required to take the next major step in the discipline. The four main areas of computational aerodynamics research at NASA Ames Research Center which are directed toward extending the state of the art are identified and discussed. Example results obtained from approximate forms of the governing equations are presented and discussed, both in the context of levels of computer power required and the degree to which they either further the frontiers of research or apply to programs of practical importance. Finally, the Numerical Aerodynamic Simulation Program--with its 1988 target of achieving a sustained computational rate of 1 billion floating-point operations per second--is discussed in terms of its goals, status, and its projected effect on the future of computational aerodynamics.

Numerical solution of differential equations by artificial neural networks

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1995-01-01

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Performance of a parallel code for the Euler equations on hypercube computers

NASA Technical Reports Server (NTRS)

Barszcz, Eric; Chan, Tony F.; Jesperson, Dennis C.; Tuminaro, Raymond S.

1990-01-01

The performance of hypercubes were evaluated on a computational fluid dynamics problem and the parallel environment issues were considered that must be addressed, such as algorithm changes, implementation choices, programming effort, and programming environment. The evaluation focuses on a widely used fluid dynamics code, FLO52, which solves the two dimensional steady Euler equations describing flow around the airfoil. The code development experience is described, including interacting with the operating system, utilizing the message-passing communication system, and code modifications necessary to increase parallel efficiency. Results from two hypercube parallel computers (a 16-node iPSC/2, and a 512-node NCUBE/ten) are discussed and compared. In addition, a mathematical model of the execution time was developed as a function of several machine and algorithm parameters. This model accurately predicts the actual run times obtained and is used to explore the performance of the code in interesting but yet physically realizable regions of the parameter space. Based on this model, predictions about future hypercubes are made.

Automating the parallel processing of fluid and structural dynamics calculations

NASA Technical Reports Server (NTRS)

Arpasi, Dale J.; Cole, Gary L.

1987-01-01

The NASA Lewis Research Center is actively involved in the development of expert system technology to assist users in applying parallel processing to computational fluid and structural dynamic analysis. The goal of this effort is to eliminate the necessity for the physical scientist to become a computer scientist in order to effectively use the computer as a research tool. Programming and operating software utilities have previously been developed to solve systems of ordinary nonlinear differential equations on parallel scalar processors. Current efforts are aimed at extending these capabilities to systems of partial differential equations, that describe the complex behavior of fluids and structures within aerospace propulsion systems. This paper presents some important considerations in the redesign, in particular, the need for algorithms and software utilities that can automatically identify data flow patterns in the application program and partition and allocate calculations to the parallel processors. A library-oriented multiprocessing concept for integrating the hardware and software functions is described.

Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow

USGS Publications Warehouse

Wexler, Eliezer J.

1992-01-01

Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems having uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of selected solutions, source codes for the computer programs, and samples of program input and output also are included.

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual. [Green function

NASA Technical Reports Server (NTRS)

Morino, L.

1980-01-01

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Thermal-stress analysis for a wood composite blade

NASA Technical Reports Server (NTRS)

Fu, K. C.; Harb, A.

1984-01-01

A thermal-stress analysis of a wind turbine blade made of wood composite material is reported. First, the governing partial differential equation on heat conduction is derived, then, a finite element procedure using variational approach is developed for the solution of the governing equation. Thus, the temperature distribution throughout the blade is determined. Next, based on the temperature distribution, a finite element procedure using potential energy approach is applied to determine the thermal-stress distribution. A set of results is obtained through the use of a computer, which is considered to be satisfactory. All computer programs are contained in the report.

Summer Faculty Systems Design Program. Integrating Wind Tunnels and Computers. Volume 2. Details of Summer Design Study USAF/OSR/ASEE

DTIC Science & Technology

1977-08-01

level is given in the report by El- Ramly and Rainbird of Carleton University in Ontario Canada (Ref. 2.48). This report comments on an investigation of...RefT 3, Äp r i 1 1976. 2.48. El- Ramly , Z. M. and Rainbird, W. J. "Computer-Controlled System for the Investigation of the Flow Behind Wings...detailed studies of "model" equations (such as the Burgers ’ equation) which include all the essential aspects of the actual problem of interest have

Utilization of parallel processing in solving the inviscid form of the average-passage equation system for multistage turbomachinery

NASA Technical Reports Server (NTRS)

Mulac, Richard A.; Celestina, Mark L.; Adamczyk, John J.; Misegades, Kent P.; Dawson, Jef M.

1987-01-01

A procedure is outlined which utilizes parallel processing to solve the inviscid form of the average-passage equation system for multistage turbomachinery along with a description of its implementation in a FORTRAN computer code, MSTAGE. A scheme to reduce the central memory requirements of the program is also detailed. Both the multitasking and I/O routines referred to are specific to the Cray X-MP line of computers and its associated SSD (Solid-State Disk). Results are presented for a simulation of a two-stage rocket engine fuel pump turbine.

Composite Nanomechanics: A Mechanistic Properties Prediction

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Handler, Louis M.; Manderscheid, Jane M.

2007-01-01

A unique mechanistic theory is described to predict the properties of nanocomposites. The theory is based on composite micromechanics with progressive substructuring down to a nanoscale slice of a nanofiber where all the governing equations are formulated. These equations hav e been programmed in a computer code. That computer code is used to predict 25 properties of a mononanofiber laminate. The results are pr esented graphically and discussed with respect to their practical sig nificance. Most of the results show smooth distributions. Results for matrix-dependent properties show bimodal through-the-thickness distr ibution with discontinuous changes from mode to mode.

SCI Identification (SCIDNT) program user's guide. [maximum likelihood method for linear rotorcraft models

NASA Technical Reports Server (NTRS)

1979-01-01

The computer program Linear SCIDNT which evaluates rotorcraft stability and control coefficients from flight or wind tunnel test data is described. It implements the maximum likelihood method to maximize the likelihood function of the parameters based on measured input/output time histories. Linear SCIDNT may be applied to systems modeled by linear constant-coefficient differential equations. This restriction in scope allows the application of several analytical results which simplify the computation and improve its efficiency over the general nonlinear case.

A Model for High Frequency Radar Auroral Clutter

DTIC Science & Technology

1980-03-01

PROGRAM ELEMENT PROJECT. TA9K Deputy for Electronic Technology (HADCEEP) AREA A WORK UNIT Hansco AF13 02Fl II CONTROLLING OFFICE NAME AND ADDRESS W...region is sometimes referred to as the "polar cavity." 16 I wf, 2. RKlIO PROPA(ArION CONSIDERATIONS An essential element in computing the incidence and...called liaselgrove equations. 8 This is :iccomplished nume’rically by use of a computer program originally developed by ,lTnes .11rd later modified

A computer program to evaluate optical systems

NASA Technical Reports Server (NTRS)

Innes, D.

1972-01-01

A computer program is used to evaluate a 25.4 cm X-ray telescope at a field angle of 20 minutes of arc by geometrical analysis. The object is regarded as a point source of electromagnetic radiation, and the optical surfaces are treated as boundary conditions in the solution of the electromagnetic wave propagation equation. The electric field distribution is then determined in the region of the image and the intensity distribution inferred. A comparison of wave analysis results and photographs taken through the telescope shows excellent agreement.

Quantitative Measurements of the Effects of Variations in Panel Density and Distributions for Panel Method Computer Programs

DTIC Science & Technology

1980-01-01

AND ADDRESS 1 .PROGRAM ELEMENT. PROJECT, TASK AREA & WORK UNIT NUMBERS Aircraft and -.rew Systems Technology Di r. (C:ode 60 E61-.U o A0 Naval Air...0 . . . . . . . . . . . B- 1 B-If Input Statistics For Equations 5 and 6 .... ....... B- 2 B-Ill Computation of Coefficients of...trapezoidal panels and the formula for PAR can be derived for the case where equal spanwise and chordwise divisions are used: PAR (N/2M)/( 1 +X ( 2 = ( 2

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

High precision series solutions of differential equations: Ordinary and regular singular points of second order ODEs

NASA Astrophysics Data System (ADS)

Noreen, Amna; Olaussen, Kåre

2012-10-01

A subroutine for a very-high-precision numerical solution of a class of ordinary differential equations is provided. For a given evaluation point and equation parameters the memory requirement scales linearly with precision P, and the number of algebraic operations scales roughly linearly with P when P becomes sufficiently large. We discuss results from extensive tests of the code, and how one, for a given evaluation point and equation parameters, may estimate precision loss and computing time in advance. Program summary Program title: seriesSolveOde1 Catalogue identifier: AEMW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 991 No. of bytes in distributed program, including test data, etc.: 488116 Distribution format: tar.gz Programming language: C++ Computer: PC's or higher performance computers. Operating system: Linux and MacOS RAM: Few to many megabytes (problem dependent). Classification: 2.7, 4.3 External routines: CLN — Class Library for Numbers [1] built with the GNU MP library [2], and GSL — GNU Scientific Library [3] (only for time measurements). Nature of problem: The differential equation -s2({d2}/{dz2}+{1-ν+-ν-}/{z}{d}/{dz}+{ν+ν-}/{z2})ψ(z)+{1}/{z} ∑n=0N vnznψ(z)=0, is solved numerically to very high precision. The evaluation point z and some or all of the equation parameters may be complex numbers; some or all of them may be represented exactly in terms of rational numbers. Solution method: The solution ψ(z), and optionally ψ'(z), is evaluated at the point z by executing the recursion A(z)={s-2}/{(m+1+ν-ν+)(m+1+ν-ν-)} ∑n=0N Vn(z)A(z), ψ(z)=ψ(z)+A(z), to sufficiently large m. Here ν is either ν+ or ν-, and Vn(z)=vnz. The recursion is initialized by A(z)=δzν,for n=0,1,…,N ψ(z)=A0(z). Restrictions: No solution is computed if z=0, or s=0, or if ν=ν- (assuming Reν+≥Reν-) with ν+-ν- an integer, except when ν+-ν-=1 and v =0 (i.e. when z is an ordinary point for zψ(z)). Additional comments: The code of the main algorithm is in the file seriesSolveOde1.cc, which "#include" the file checkForBreakOde1.cc. These routines, and the programs using them, must "#include" the file seriesSolveOde1.cc. Running time: On a Linux PC that is a few years old, at y=√{10} to an accuracy of P=200 decimal digits, evaluating the ground state wavefunction of the anharmonic oscillator (with the eigenvalue known in advance); (cf. Eq. (6)) takes about 2 ms, and about 40 min at an accuracy of P=100000 decimal digits. References: [1] B. Haible and R.B. Kreckel, CLN — Class Library for Numbers, http://www.ginac.de/CLN/ [2] T. Granlund and collaborators, GMP — The GNU Multiple Precision Arithmetic Library, http://gmplib.org/ [3] M. Galassi et al., GNU Scientific Library Reference Manual (3rd Ed.), ISBN 0954612078., http://www.gnu.org/software/gsl/

RMS massless arm dynamics capability in the SVDS. [equations of motion

NASA Technical Reports Server (NTRS)

Flanders, H. A.

1977-01-01

The equations of motion for the remote manipulator system, assuming that the masses and inertias of the arm can be neglected, are developed for implementation into the space vehicle dynamics simulation (SVDS) program for the Orbiter payload system. The arm flexibility is incorporated into the equations by the computation of flexibility terms for use in the joint servo model. The approach developed in this report is based on using the Jacobian transformation matrix to transform force and velocity terms between the configuration space and the task space to simplify the form of the equations.

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations

DOE PAGES

Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; ...

2012-01-01

A template-based generic programming approach was presented in Part I of this series of papers [Sci. Program. 20 (2012), 197–219] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertaintymore » quantification results for a 3D PDE application.« less

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

NASA Technical Reports Server (NTRS)

Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

1988-01-01

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Abrashkevich, A. G.; Amaya-Tapia, A.; Kaschiev, M. S.; Larsen, S. Y.; Vinitsky, S. I.

2007-10-01

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4224 No. of bytes in distributed program, including test data, etc.: 31 232 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986] Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite-element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions for such systems of coupled differential equations. Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points; and (d) the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively. Running time: The running time depends critically upon: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points on interval [0,ρ]; and (d) the number of eigensolutions required. The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.

Molecular dynamics studies of transport properties and equation of state of supercritical fluids

NASA Astrophysics Data System (ADS)

Nwobi, Obika C.

Many chemical propulsion systems operate with one or more of the reactants above the critical point in order to enhance their performance. Most of the computational fluid dynamics (CFD) methods used to predict these flows require accurate information on the transport properties and equation of state at these supercritical conditions. This work involves the determination of transport coefficients and equation of state of supercritical fluids by equilibrium molecular dynamics (MD) simulations on parallel computers using the Green-Kubo formulae and the virial equation of state, respectively. MD involves the solution of equations of motion of a system of molecules that interact with each other through an intermolecular potential. Provided that an accurate potential can be found for the system of interest, MD can be used regardless of the phase and thermodynamic conditions of the substances involved. The MD program uses the effective Lennard-Jones potential, with system sizes of 1000-1200 molecules and, simulations of 2,000,000 time-steps for computing transport coefficients and 200,000 time-steps for pressures. The computer code also uses linked cell lists for efficient sorting of molecules, periodic boundary conditions, and a modified velocity Verlet algorithm for particle displacement. Particle decomposition is used for distributing the molecules to different processors of a parallel computer. Simulations have been carried out on pure argon, nitrogen, oxygen and ethylene at various supercritical conditions, with self-diffusion coefficients, shear viscosity coefficients, thermal conductivity coefficients and pressures computed for most of the conditions. Results compare well with experimental and the National Institute of Standards and Technology (NIST) values. The results show that the number of molecules and the potential cut-off radius have no significant effect on the computed coefficients, while long-time integration is necessary for accurate determination of the coefficients.

A real-time digital computer program for the simulation of automatic spacecraft reentries

NASA Technical Reports Server (NTRS)

Kaylor, J. T.; Powell, L. F.; Powell, R. W.

1977-01-01

The automatic reentry flight dynamics simulator, a nonlinear, six-degree-of-freedom simulation, digital computer program, has been developed. The program includes a rotating, oblate earth model for accurate navigation calculations and contains adjustable gains on the aerodynamic stability and control parameters. This program uses a real-time simulation system and is designed to examine entries of vehicles which have constant mass properties whose attitudes are controlled by both aerodynamic surfaces and reaction control thrusters, and which have automatic guidance and control systems. The program has been used to study the space shuttle orbiter entry. This report includes descriptions of the equations of motion used, the control and guidance schemes that were implemented, the program flow and operation, and the hardware involved.

User's manual for three-dimensional analysis of propeller flow fields

NASA Technical Reports Server (NTRS)

Chaussee, D. S.; Kutler, P.

1983-01-01

A detailed operating manual is presented for the prop-fan computer code (in addition to supporting programs) recently developed by Kutler, Chaussee, Sorenson, and Pulliam while at the NASA'S Ames Research Center. This code solves the inviscid Euler equations using an implicit numerical procedure developed by Beam and Warming of Ames. A description of the underlying theory, numerical techniques, and boundary conditions with equations, formulas, and methods for the mesh generation program (MGP), three dimensional prop-fan flow field program (3DPFP), and data reduction program (DRP) is provided, together with complete operating instructions. In addition, a programmer's manual is also provided to assist the user interested in modifying the codes. Included in the programmer's manual for each program is a description of the input and output variables, flow charts, program listings, sample input and output data, and operating hints.

Fortran Programs for Weapon Systems Analysis

DTIC Science & Technology

1990-06-01

interested in ballistics and related work. The programs include skeletal combat models , a set of discrete-event timing routines, mathematical and...32 4.3 LinEqs: Solve Linear Equations Like a Textbook ........................................................................... 34...military applications as it is of computer science. This crisis occurs in all fields, including the modeling of logistics, mobility, ballistics, and combat

Far-Field Lorenz-Mie Scattering in an Absorbing Host Medium: Theoretical Formalism and FORTRAN Program

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenzâ€"Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

Far-field Lorenz-Mie scattering in an absorbing host medium: Theoretical formalism and FORTRAN program

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yang, Ping

2018-01-01

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenz-Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html, and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations.

A Review of Recent Aeroelastic Analysis Methods for Propulsion at NASA Lewis Research Center

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, Milind A.; Srivastava, R.; Mehmed, Oral; Stefko, George L.

1993-01-01

This report reviews aeroelastic analyses for propulsion components (propfans, compressors and turbines) being developed and used at NASA LeRC. These aeroelastic analyses include both structural and aerodynamic models. The structural models include a typical section, a beam (with and without disk flexibility), and a finite-element blade model (with plate bending elements). The aerodynamic models are based on the solution of equations ranging from the two-dimensional linear potential equation to the three-dimensional Euler equations for multibladed configurations. Typical calculated results are presented for each aeroelastic model. Suggestions for further research are made. Many of the currently available aeroelastic models and analysis methods are being incorporated in a unified computer program, APPLE (Aeroelasticity Program for Propulsion at LEwis).

PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

This report documents PCG2 : a numerical code to be used with the U.S. Geological Survey modular three-dimensional, finite-difference, ground-water flow model . PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow conditions may be simulated. PCG2 includes two reconditioning options : modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers . Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.

1999-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are derived. These equations are then modified to allow the plate reference surface to be located a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described. The terms of the plate stiffness matrix using both classical plate theory (CPT) and first-order shear-deformation plate theory (SDPT) are presented. The effects of in-plane transverse and in-plane shear loads are included in the in-plane stability equations. Numerical results for several example problems with different loading states are presented. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPT are made. The computational effort required by the new analysis is compared to that of the analysis currently in the VICONOPT program. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

Computations of Wall Distances Based on Differential Equations

NASA Technical Reports Server (NTRS)

Tucker, Paul G.; Rumsey, Chris L.; Spalart, Philippe R.; Bartels, Robert E.; Biedron, Robert T.

2004-01-01

The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

Two-Dimensional Grids About Airfoils and Other Shapes

NASA Technical Reports Server (NTRS)

Sorenson, R.

1982-01-01

GRAPE computer program generates two-dimensional finite-difference grids about airfoils and other shapes by use of Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including limited number of sharp corners. Numerically stable and computationally fast, GRAPE provides aerodynamic analyst with efficient and consistant means of grid generation.

Reliability computation using fault tree analysis

NASA Technical Reports Server (NTRS)

Chelson, P. O.

1971-01-01

A method is presented for calculating event probabilities from an arbitrary fault tree. The method includes an analytical derivation of the system equation and is not a simulation program. The method can handle systems that incorporate standby redundancy and it uses conditional probabilities for computing fault trees where the same basic failure appears in more than one fault path.

Computation of Flow Through Water-Control Structures Using Program DAMFLO.2

USGS Publications Warehouse

Sanders, Curtis L.; Feaster, Toby D.

2004-01-01

As part of its mission to collect, analyze, and store streamflow data, the U.S. Geological Survey computes flow through several dam structures throughout the country. Flows are computed using hydraulic equations that describe flow through sluice and Tainter gates, crest gates, lock gates, spillways, locks, pumps, and siphons, which are calibrated using flow measurements. The program DAMFLO.2 was written to compute, tabulate, and plot flow through dam structures using data that describe the physical properties of dams and various hydraulic parameters and ratings that use time-varying data, such as lake elevations or gate openings. The program uses electronic computer files of time-varying data, such as lake elevation or gate openings, retrieved from the U.S. Geological Survey Automated Data Processing System. Computed time-varying flow data from DAMFLO.2 are output in flat files, which can be entered into the Automated Data Processing System database. All computations are made in units of feet and seconds. DAMFLO.2 uses the procedures and language developed by the SAS Institute Inc.

An experimental and computational investigation of the flow field about a transonic airfoil in supercritical flow with turbulent boundary-layer separation

NASA Technical Reports Server (NTRS)

Rubesin, M. W.; Okuno, A. F.; Levy, L. L., Jr.; Mcdevitt, J. B.; Seegmiller, H. L.

1976-01-01

A combined experimental and computational research program is described for testing and guiding turbulence modeling within regions of separation induced by shock waves incident in turbulent boundary layers. Specifically, studies are made of the separated flow the rear portion of an 18%-thick circular-arc airfoil at zero angle of attack in high Reynolds number supercritical flow. The measurements include distributions of surface static pressure and local skin friction. The instruments employed include highfrequency response pressure cells and a large array of surface hot-wire skin-friction gages. Computations at the experimental flow conditions are made using time-dependent solutions of ensemble-averaged Navier-Stokes equations, plus additional equations for the turbulence modeling.

DEKFIS user's guide: Discrete Extended Kalman Filter/Smoother program for aircraft and rotorcraft data consistency

NASA Technical Reports Server (NTRS)

1979-01-01

The computer program DEKFIS (discrete extended Kalman filter/smoother), formulated for aircraft and helicopter state estimation and data consistency, is described. DEKFIS is set up to pre-process raw test data by removing biases, correcting scale factor errors and providing consistency with the aircraft inertial kinematic equations. The program implements an extended Kalman filter/smoother using the Friedland-Duffy formulation.

Bridge-scour analysis using the water surface profile (WSPRO) model

USGS Publications Warehouse

Mueller, David S.; ,

1993-01-01

A program was developed to extract hydraulic information required for bridge-scour computations, from the Water-Surface Profile computation model (WSPRO). The program is written in compiled BASIC and is menu driven. Using only ground points, the program can compute average ground elevation, cross-sectional area below a specified datum, or create a Drawing Exchange Format (DXF) fie of cross section. Using both ground points ad hydraulic information form the equal-conveyance tubes computed by WSPRO, the program can compute hydraulic parameters at a user-specified station or in a user-specified subsection of the cross section. The program can identify the maximum velocity in a cross section and the velocity and depth at a user-specified station. The program also can identify the maximum velocity in the cross section and the average velocity, average depth, average ground elevation, width perpendicular to the flow, cross-sectional area of flow, and discharge in a subsection of the cross section. This program does not include any help or suggestions as to what data should be extracted; therefore, the used must understand the scour equations and associated variables to the able to extract the proper information from the WSPRO output.

Chemistry Notes.

ERIC Educational Resources Information Center

School Science Review, 1983

1983-01-01

Presents chemistry experiments, laboratory procedures, demonstrations, teaching suggestions, and classroom materials/activities. These include: game for teaching ionic formulas; method for balancing equations; description of useful redox series; computer programs (with listings) for water electrolysis simulation and for determining chemical…

An Improved Newton's Method.

ERIC Educational Resources Information Center

Mathews, John H.

1989-01-01

Describes Newton's method to locate roots of an equation using the Newton-Raphson iteration formula. Develops an adaptive method overcoming limitations of the iteration method. Provides the algorithm and computer program of the adaptive Newton-Raphson method. (YP)

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Gerdt, V. P.; Rostovtsev, V. A.; Vinitsky, S. I.; Abrashkevich, A. G.; Kaschiev, M. S.; Serov, V. V.

2008-02-01

A FORTRAN 77 program is presented which calculates with the relative machine precision potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. The potential curves are eigenvalues corresponding to the angular oblate spheroidal functions that compose adiabatic basis which depends on the radial variable as a parameter. The matrix elements of radial coupling are integrals in angular variables of the following two types: product of angular functions and the first derivative of angular functions in parameter, and product of the first derivatives of angular functions in parameter, respectively. The program calculates also the angular part of the dipole transition matrix elements (in the length form) expressed as integrals in angular variables involving product of a dipole operator and angular functions. Moreover, the program calculates asymptotic regular and irregular matrix solutions of the coupled adiabatic radial equations at the end of interval in radial variable needed for solving a multi-channel scattering problem by the generalized R-matrix method. Potential curves and radial matrix elements computed by the POTHMF program can be used for solving the bound state and multi-channel scattering problems. As a test desk, the program is applied to the calculation of the energy values, a short-range reaction matrix and corresponding wave functions with the help of the KANTBP program. Benchmark calculations for the known photoionization cross-sections are presented. Program summaryProgram title:POTHMF Catalogue identifier:AEAA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAA_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:8123 No. of bytes in distributed program, including test data, etc.:131 396 Distribution format:tar.gz Programming language:FORTRAN 77 Computer:Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system:OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM:Depends on the number of radial differential equations; the number and order of finite elements; the number of radial points. Test run requires 4 MB Classification:2.5 External routines:POTHMF uses some Lapack routines, copies of which are included in the distribution (see README file for details). Nature of problem:In the multi-channel adiabatic approach the Schrödinger equation for a hydrogen-like atom in a homogeneous magnetic field of strength γ ( γ=B/B, B≅2.35×10 T is a dimensionless parameter which determines the field strength B) is reduced by separating the radial coordinate, r, from the angular variables, (θ,φ), and using a basis of the angular oblate spheroidal functions [3] to a system of second-order ordinary differential equations which contain first-derivative coupling terms [4]. The purpose of this program is to calculate potential curves and matrix elements of radial coupling needed for calculating the low-lying bound and scattering states of hydrogen-like atoms in a homogeneous magnetic field of strength 0<γ⩽1000 within the adiabatic approach [5]. The program evaluates also asymptotic regular and irregular matrix radial solutions of the multi-channel scattering problem needed to extract from the R-matrix a required symmetric shortrange open-channel reaction matrix K [6] independent from matching point [7]. In addition, the program computes the dipole transition matrix elements in the length form between the basis functions that are needed for calculating the dipole transitions between the low-lying bound and scattering states and photoionization cross sections [8]. Solution method:The angular oblate spheroidal eigenvalue problem depending on the radial variable is solved using a series expansion in the Legendre polynomials [3]. The resulting tridiagonal symmetric algebraic eigenvalue problem for the evaluation of selected eigenvalues, i.e. the potential curves, is solved by the LDLT factorization using the DSTEVR program [2]. Derivatives of the eigenfunctions with respect to the radial variable which are contained in matrix elements of the coupled radial equations are obtained by solving the inhomogeneous algebraic equations. The corresponding algebraic problem is solved by using the LDLT factorization with the help of the DPTTRS program [2]. Asymptotics of the matrix elements at large values of radial variable are computed using a series expansion in the associated Laguerre polynomials [9]. The corresponding matching points between the numeric and asymptotic solutions are found automatically. These asymptotics are used for the evaluation of the asymptotic regular and irregular matrix radial solutions of the multi-channel scattering problem [7]. As a test desk, the program is applied to the calculation of the energy values of the ground and excited bound states and reaction matrix of multi-channel scattering problem for a hydrogen atom in a homogeneous magnetic field using the KANTBP program [10]. Restrictions:The computer memory requirements depend on: the number of radial differential equations; the number and order of finite elements; the total number of radial points. Restrictions due to dimension sizes can be changed by resetting a small number of PARAMETER statements before recompiling (see Introduction and listing for details). Running time:The running time depends critically upon: the number of radial differential equations; the number and order of finite elements; the total number of radial points on interval [r,r]. The test run which accompanies this paper took 7 s required for calculating of potential curves, radial matrix elements, and dipole transition matrix elements on a finite-element grid on interval [ r=0, r=100] used for solving discrete and continuous spectrum problems and obtaining asymptotic regular and irregular matrix radial solutions at r=100 for continuous spectrum problem on the Intel Pentium IV 2.4 GHz. The number of radial differential equations was equal to 6. The accompanying test run using the KANTBP program took 2 s for solving discrete and continuous spectrum problems using the above calculated potential curves, matrix elements and asymptotic regular and irregular matrix radial solutions. Note, that in the accompanied benchmark calculations of the photoionization cross-sections from the bound states of a hydrogen atom in a homogeneous magnetic field to continuum we have used interval [ r=0, r=1000] for continuous spectrum problem. The total number of radial differential equations was varied from 10 to 18. References:W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. http://www.netlib.org/lapack/. M. Abramovits, I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965. U. Fano, Colloq. Int. C.N.R.S. 273 (1977) 127; A.F. Starace, G.L. Webster, Phys. Rev. A 19 (1979) 1629-1640; C.V. Clark, K.T. Lu, A.F. Starace, in: H.G. Beyer, H. Kleinpoppen (Eds.), Progress in Atomic Spectroscopy, Part C, Plenum, New York, 1984, pp. 247-320; U. Fano, A.R.P. Rau, Atomic Collisions and Spectra, Academic Press, Florida, 1986. M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352; O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, V.V. Serov, T.V. Tupikova, S.I. Vinitsky, Proc. SPIE 6537 (2007) 653706-1-18. M.J. Seaton, Rep. Prog. Phys. 46 (1983) 167-257. M. Gailitis, J. Phys. B 9 (1976) 843-854; J. Macek, Phys. Rev. A 30 (1984) 1277-1278; S.I. Vinitsky, V.P. Gerdt, A.A. Gusev, M.S. Kaschiev, V.A. Rostovtsev, V.N. Samoylov, T.V. Tupikova, O. Chuluunbaatar, Programming and Computer Software 33 (2007) 105-116. H. Friedrich, Theoretical Atomic Physics, Springer, New York, 1991. R.J. Damburg, R.Kh. Propin, J. Phys. B 1 (1968) 681-691; J.D. Power, Phil. Trans. Roy. Soc. London A 274 (1973) 663-702. O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Comm. 177 (2007) 649-675.

Low-thrust trajectory analysis for the geosynchronous mission

NASA Technical Reports Server (NTRS)

Jasper, T. P.

1973-01-01

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

Exploiting loop level parallelism in nonprocedural dataflow programs

NASA Technical Reports Server (NTRS)

Gokhale, Maya B.

1987-01-01

Discussed are how loop level parallelism is detected in a nonprocedural dataflow program, and how a procedural program with concurrent loops is scheduled. Also discussed is a program restructuring technique which may be applied to recursive equations so that concurrent loops may be generated for a seemingly iterative computation. A compiler which generates C code for the language described below has been implemented. The scheduling component of the compiler and the restructuring transformation are described.

Teaching Computational Geophysics Classes using Active Learning Techniques

NASA Astrophysics Data System (ADS)

Keers, H.; Rondenay, S.; Harlap, Y.; Nordmo, I.

2016-12-01

We give an overview of our experience in teaching two computational geophysics classes at the undergraduate level. In particular we describe The first class is for most students the first programming class and assumes that the students have had an introductory course in geophysics. In this class the students are introduced to basic Matlab skills: use of variables, basic array and matrix definition and manipulation, basic statistics, 1D integration, plotting of lines and surfaces, making of .m files and basic debugging techniques. All of these concepts are applied to elementary but important concepts in earthquake and exploration geophysics (including epicentre location, computation of travel time curves for simple layered media plotting of 1D and 2D velocity models etc.). It is important to integrate the geophysics with the programming concepts: we found that this enhances students' understanding. Moreover, as this is a 3 year Bachelor program, and this class is taught in the 2nd semester, there is little time for a class that focusses on only programming. In the second class, which is optional and can be taken in the 4th or 6th semester, but often is also taken by Master students we extend the Matlab programming to include signal processing and ordinary and partial differential equations, again with emphasis on geophysics (such as ray tracing and solving the acoustic wave equation). This class also contains a project in which the students have to write a brief paper on a topic in computational geophysics, preferably with programming examples. When teaching these classes it was found that active learning techniques, in which the students actively participate in the class, either individually, in pairs or in groups, are indispensable. We give a brief overview of the various activities that we have developed when teaching theses classes.

Analytical solutions for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow

USGS Publications Warehouse

Wexler, Eliezer J.

1989-01-01

Analytical solutions to the advective-dispersive solute-transport equation are useful in predicting the fate of solutes in ground water. Analytical solutions compiled from available literature or derived by the author are presented in this report for a variety of boundary condition types and solute-source configurations in one-, two-, and three-dimensional systems with uniform ground-water flow. A set of user-oriented computer programs was created to evaluate these solutions and to display the results in tabular and computer-graphics format. These programs incorporate many features that enhance their accuracy, ease of use, and versatility. Documentation for the programs describes their operation and required input data, and presents the results of sample problems. Derivations of select solutions, source codes for the computer programs, and samples of program input and output also are included.

A user's guide to the SUDAN computer program for determining the vibration modes of structural systems. Ph.D. Thesis - Case Western Reserve Univ., Jun. 1963

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; Durling, B. J.

1978-01-01

The use of the SUDAN computer program for analyzing structural systems for their natural modes and frequencies of vibration is described. SUDAN is intended for structures which can be represented as an equivalent system of beam, spring, and rigid-body substructures. User-written constraint equations are used to analytically join the mass and stiffness matrices of the substructures to form the mass and stiffness matrices of the complete structure from which all the frequencies and modes of the system are determined. The SUDAN program can treat the case in which both the mass and stiffness matrices of the coupled system may be singular simultaneously. A general description of the FORTRAN IV program is given, the computer hardware and software specifications are indicated, and the input required by the program is described.

Algorithms for Computation of Fundamental Properties of Seawater. Endorsed by Unesco/SCOR/ICES/IAPSO Joint Panel on Oceanographic Tables and Standards and SCOR Working Group 51. Unesco Technical Papers in Marine Science, No. 44.

ERIC Educational Resources Information Center

Fofonoff, N. P.; Millard, R. C., Jr.

Algorithms for computation of fundamental properties of seawater, based on the practicality salinity scale (PSS-78) and the international equation of state for seawater (EOS-80), are compiled in the present report for implementing and standardizing computer programs for oceanographic data processing. Sample FORTRAN subprograms and tables are given…

Development of programs for computing characteristics of ultraviolet radiation

NASA Technical Reports Server (NTRS)

Dave, J. V.

1972-01-01

Efficient programs were developed for computing all four characteristics of the radiation scattered by a plane-parallel, turbid, terrestrial atmospheric model. They were developed (FORTRAN 4) and tested on the IBM /360 computers with 2314 direct access storage facility. The storage requirement varies between 200K and 750K bytes depending upon the task. The scattering phase matrix (or function) is expanded in a Fourier series whose number of terms depend upon the zenith angles of the incident and scattered radiations, as well as on the nature of aerosols. A Gauss-Seidel procedure is used for obtaining the numerical solution of the transfer equation.

An Improved Theoretical Aerodynamic Derivatives Computer Program for Sounding Rockets

NASA Technical Reports Server (NTRS)

Barrowman, J. S.; Fan, D. N.; Obosu, C. B.; Vira, N. R.; Yang, R. J.

1979-01-01

The paper outlines a Theoretical Aerodynamic Derivatives (TAD) computer program for computing the aerodynamics of sounding rockets. TAD outputs include normal force, pitching moment and rolling moment coefficient derivatives as well as center-of-pressure locations as a function of the flight Mach number. TAD is applicable to slender finned axisymmetric vehicles at small angles of attack in subsonic and supersonic flows. TAD improvement efforts include extending Mach number regions of applicability, improving accuracy, and replacement of some numerical integration algorithms with closed-form integrations. Key equations used in TAD are summarized and typical TAD outputs are illustrated for a second-stage Tomahawk configuration.

General chemical kinetics computer program for static and flow reactions, with application to combustion and shock-tube kinetics

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1972-01-01

A general chemical kinetics program is described for complex, homogeneous ideal-gas reactions in any chemical system. Its main features are flexibility and convenience in treating many different reaction conditions. The program solves numerically the differential equations describing complex reaction in either a static system or one-dimensional inviscid flow. Applications include ignition and combustion, shock wave reactions, and general reactions in a flowing or static system. An implicit numerical solution method is used which works efficiently for the extreme conditions of a very slow or a very fast reaction. The theory is described, and the computer program and users' manual are included.

Computer program for design analysis of radial-inflow turbines

NASA Technical Reports Server (NTRS)

Glassman, A. J.

1976-01-01

A computer program written in FORTRAN that may be used for the design analysis of radial-inflow turbines was documented. The following information is included: loss model (estimation of losses), the analysis equations, a description of the input and output data, the FORTRAN program listing and list of variables, and sample cases. The input design requirements include the power, mass flow rate, inlet temperature and pressure, and rotational speed. The program output data includes various diameters, efficiencies, temperatures, pressures, velocities, and flow angles for the appropriate calculation stations. The design variables include the stator-exit angle, rotor radius ratios, and rotor-exit tangential velocity distribution. The losses are determined by an internal loss model.

Computer Programs for Calculating the Isentropic Flow Properties for Mixtures of R-134a and Air

NASA Technical Reports Server (NTRS)

Kvaternik, Raymond G.

2000-01-01

Three computer programs for calculating the isentropic flow properties of R-134a/air mixtures which were developed in support of the heavy gas conversion of the Langley Transonic Dynamics Tunnel (TDT) from dichlorodifluoromethane (R-12) to 1,1,1,2 tetrafluoroethane (R-134a) are described. The first program calculates the Mach number and the corresponding flow properties when the total temperature, total pressure, static pressure, and mole fraction of R-134a in the mixture are given. The second program calculates tables of isentropic flow properties for a specified set of free-stream Mach numbers given the total pressure, total temperature, and mole fraction of R-134a. Real-gas effects are accounted for in these programs by treating the gases comprising the mixture as both thermally and calorically imperfect. The third program is a specialized version of the first program in which the gases are thermally perfect. It was written to provide a simpler computational alternative to the first program in those cases where real-gas effects are not important. The theory and computational procedures underlying the programs are summarized, the equations used to compute the flow quantities of interest are given, and sample calculated results that encompass the operating conditions of the TDT are shown.

Application of the CAP-TSD unsteady transonic small disturbance program to wing flutter. [Computational Aeroelasticity Program

NASA Technical Reports Server (NTRS)

Bennett, Robert M.; Batina, John T.

1989-01-01

The application and assessment of a computer program called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) for flutter predictions are described. Flutter calculations are presented for two thin swept-and-tapered wing planforms with well-defined modal properties. One planform is a series of 45-degree swept wings and the other planform is a clipped delta wing. Comparisons are made between the results of CAP-TSD using the linear equation and no airfoil thickness and the results obtained from a subsonic kernel function analysis. The calculations cover a Mach number range from low subsonic to low supersonic values, including the transonic range, and are compared with subsonic linear theory and experimental data. It is noted that since both wings have very thin airfoil sections, the effects of thickness are minimal.

Effect of virtual memory on efficient solution of two model problems

NASA Technical Reports Server (NTRS)

Lambiotte, J. J., Jr.

1977-01-01

Computers with virtual memory architecture allow programs to be written as if they were small enough to be contained in memory. Two types of problems are investigated to show that this luxury can lead to quite an inefficient performance if the programmer does not interact strongly with the characteristics of the operating system when developing the program. The two problems considered are the simultaneous solutions of a large linear system of equations by Gaussian elimination and a model three-dimensional finite-difference problem. The Control Data STAR-100 computer runs are made to demonstrate the inefficiencies of programming the problems in the manner one would naturally do if the problems were indeed, small enough to be contained in memory. Program redesigns are presented which achieve large improvements in performance through changes in the computational procedure and the data base arrangement.

Optimal low thrust geocentric transfer. [mission analysis computer program

NASA Technical Reports Server (NTRS)

Edelbaum, T. N.; Sackett, L. L.; Malchow, H. L.

1973-01-01

A computer code which will rapidly calculate time-optimal low thrust transfers is being developed as a mission analysis tool. The final program will apply to NEP or SEP missions and will include a variety of environmental effects. The current program assumes constant acceleration. The oblateness effect and shadowing may be included. Detailed state and costate equations are given for the thrust effect, oblateness effect, and shadowing. A simple but adequate model yields analytical formulas for power degradation due to the Van Allen radiation belts for SEP missions. The program avoids the classical singularities by the use of equinoctial orbital elements. Kryloff-Bogoliuboff averaging is used to facilitate rapid calculation. Results for selected cases using the current program are given.

KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Vinitsky, S. I.; Abrashkevich, A. G.

2008-11-01

A FORTRAN 77 program for calculating energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach is presented. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with homogeneous boundary conditions: (i) the Dirichlet, Neumann and third type at the left and right boundary points for continuous spectrum problem, (ii) the Dirichlet and Neumann type conditions at left boundary point and Dirichlet, Neumann and third type at the right boundary point for the discrete spectrum problem. The resulting system of radial equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reaction matrix and radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field. This version extends the previous version 1.0 of the KANTBP program [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675]. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 20 403 No. of bytes in distributed program, including test data, etc.: 147 563 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: This depends on the number of differential equations; the number and order of finite elements; the number of hyperradial points; and the number of eigensolutions required. The test run requires 2 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [2] Nature of problem: In the hyperspherical adiabatic approach [3-5], a multidimensional Schrödinger equation for a two-electron system [6] or a hydrogen atom in magnetic field [7-9] is reduced by separating radial coordinate ρ from the angular variables to a system of the second-order ordinary differential equations containing the potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions of the continuum spectrum for such systems of coupled differential equations on finite intervals of the radial variable ρ∈[ρ,ρ]. This approach can be used in the calculations of effects of electron screening on low-energy fusion cross sections [10-12]. Solution method: The boundary problems for the coupled second-order differential equations are solved by the finite element method using high-order accuracy approximations [13]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [14]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns ( λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [14]. As a test desk, the program is applied to the calculation of the reaction matrix and corresponding radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field described in [9] on finite intervals of the radial variable ρ∈[ρ,ρ]. For this benchmark model the required analytical expressions for asymptotics of the potential matrix elements and first-derivative coupling terms, and also asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: the number of differential equations; the number and order of finite elements; the total number of hyperradial points; and the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Section 3 and [1] for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should also supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMS0 and ASYMSC (when solving the scattering problem) which evaluate asymptotics of the radial wave functions at left and right boundary points in case of a boundary condition of the third type for the above problems. Running time: The running time depends critically upon: the number of differential equations; the number and order of finite elements; the total number of hyperradial points on interval [ ρ,ρ]; and the number of eigensolutions required. The test run which accompanies this paper took 2 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz. References: [1] O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; http://cpc.cs.qub.ac.uk/summaries/ADZHv10.html. [2] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. [3] J. Macek, J. Phys. B 1 (1968) 831-843. [4] U. Fano, Rep. Progr. Phys. 46 (1983) 97-165. [5] C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142. [6] A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Commun. 90 (1995) 311-339. [7] M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352. [8] O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov, S.I. Vinitsky, J. Phys. A 40 (2007) 11485-11524. [9] O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Commun. 178 (2007) 301 330; http://cpc.cs.qub.ac.uk/summaries/AEAAv10.html. [10] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461-468. [11] V. Melezhik, Nucl. Phys. A 550 (1992) 223-234. [12] L. Bracci, G. Fiorentini, V.S. Melezhik, G. Mezzorani, P. Pasini, Phys. Lett. A 153 (1991) 456-460. [13] A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40-64. [14] K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982.

FY06 NRL DoD High Performance Computing Modernization Program Annual Reports

DTIC Science & Technology

2007-10-31

our simulations yield important new information on the amount and form of the energy that is released by these explosive events. These results...coupled with the ideal-gas equation of state and a one-step Arrhenuis kinetics of energy release. The equations are solved using the explicit...practical applications, including hydrogen safety and pulse -detonation engines (PDE). For example, the results summarizing the effect of obstacle

Implementation of a 3D mixing layer code on parallel computers

NASA Technical Reports Server (NTRS)

Roe, K.; Thakur, R.; Dang, T.; Bogucz, E.

1995-01-01

This paper summarizes our progress and experience in the development of a Computational-Fluid-Dynamics code on parallel computers to simulate three-dimensional spatially-developing mixing layers. In this initial study, the three-dimensional time-dependent Euler equations are solved using a finite-volume explicit time-marching algorithm. The code was first programmed in Fortran 77 for sequential computers. The code was then converted for use on parallel computers using the conventional message-passing technique, while we have not been able to compile the code with the present version of HPF compilers.

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

NASA Technical Reports Server (NTRS)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

The utilization of parallel processing in solving the inviscid form of the average-passage equation system for multistage turbomachinery

NASA Technical Reports Server (NTRS)

Mulac, Richard A.; Celestina, Mark L.; Adamczyk, John J.; Misegades, Kent P.; Dawson, Jef M.

1987-01-01

A procedure is outlined which utilizes parallel processing to solve the inviscid form of the average-passage equation system for multistage turbomachinery along with a description of its implementation in a FORTRAN computer code, MSTAGE. A scheme to reduce the central memory requirements of the program is also detailed. Both the multitasking and I/O routines referred to in this paper are specific to the Cray X-MP line of computers and its associated SSD (Solid-state Storage Device). Results are presented for a simulation of a two-stage rocket engine fuel pump turbine.

Coupled 2-dimensional cascade theory for noise an d unsteady aerodynamics of blade row interaction in turbofans. Volume 2: Documentation for computer code CUP2D

NASA Technical Reports Server (NTRS)

Hanson, Donald B.

1994-01-01

A two dimensional linear aeroacoustic theory for rotor/stator interaction with unsteady coupling was derived and explored in Volume 1 of this report. Computer program CUP2D has been written in FORTRAN embodying the theoretical equations. This volume (Volume 2) describes the structure of the code, installation and running, preparation of the input file, and interpretation of the output. A sample case is provided with printouts of the input and output. The source code is included with comments linking it closely to the theoretical equations in Volume 1.

A decentralized process for finding equilibria given by linear equations.

PubMed Central

Reiter, S

1994-01-01

I present a decentralized process for finding the equilibria of an economy characterized by a finite number of linear equilibrium conditions. The process finds all equilibria or, if there are none, reports that, in a finite number of steps at most equal to the number of equations. The communication and computational complexity compare favorably with other decentralized processes. The process may also be interpreted as an algorithm for solving a distributed system of linear equations. Comparisons with the Linpack program for LU (lower and upper triangular decomposition of the matrix of the equation system, a version of Gaussian elimination) are presented. PMID:11607486

Property evaluations of hydrocarbon fuels under supercritical conditions based on cubic equation of state

NASA Astrophysics Data System (ADS)

Li, Haohan; Wu, Yong; Zeng, Xiaojun; Wang, Xiaohan; Zhao, Daiqing

2017-06-01

Thermophysical properties, such as density, specific heat, viscosity and thermal conductivity, vary sharply near critical point. To evaluate these properties of hydrocarbons accurately is crucial to the further research of fuel system. Comparison was made by the calculating program based on four widely used equations of state (EoS), and results indicated that calculations based on the Peng-Robinson (PR) equation of state achieve better prediction accuracy among the four equations of state. Due to the small computational amount and high accuracy, the evaluation method proposed in this paper can be implemented into practical application for the design of fuel system.

Modeling the complete Otto cycle: Preliminary version. [computer programming

NASA Technical Reports Server (NTRS)

Zeleznik, F. J.; Mcbride, B. J.

1977-01-01

A description is given of the equations and the computer program being developed to model the complete Otto cycle. The program incorporates such important features as: (1) heat transfer, (2) finite combustion rates, (3) complete chemical kinetics in the burned gas, (4) exhaust gas recirculation, and (5) manifold vacuum or supercharging. Changes in thermodynamic, kinetic and transport data as well as model parameters can be made without reprogramming. Preliminary calculations indicate that: (1) chemistry and heat transfer significantly affect composition and performance, (2) there seems to be a strong interaction among model parameters, and (3) a number of cycles must be calculated in order to obtain steady-state conditions.

APPLE - An aeroelastic analysis system for turbomachines and propfans

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, Milind A.; Srivastava, R.; Mehmed, Oral

1992-01-01

This paper reviews aeroelastic analysis methods for propulsion elements (advanced propellers, compressors and turbines) being developed and used at NASA Lewis Research Center. These aeroelastic models include both structural and aerodynamic components. The structural models include the typical section model, the beam model with and without disk flexibility, and the finite element blade model with plate bending elements. The aerodynamic models are based on the solution of equations ranging from the two-dimensional linear potential equation for a cascade to the three-dimensional Euler equations for multi-blade configurations. Typical results are presented for each aeroelastic model. Suggestions for further research are indicated. All the available aeroelastic models and analysis methods are being incorporated into a unified computer program named APPLE (Aeroelasticity Program for Propulsion at LEwis).

Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

NASA Technical Reports Server (NTRS)

Robertson, D. K.

1985-01-01

Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

Comparison of some optimal control methods for the design of turbine blades

NASA Technical Reports Server (NTRS)

Desilva, B. M. E.; Grant, G. N. C.

1977-01-01

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Survey of new vector computers: The CRAY 1S from CRAY research; the CYBER 205 from CDC and the parallel computer from ICL - architecture and programming

NASA Technical Reports Server (NTRS)

Gentzsch, W.

1982-01-01

Problems which can arise with vector and parallel computers are discussed in a user oriented context. Emphasis is placed on the algorithms used and the programming techniques adopted. Three recently developed supercomputers are examined and typical application examples are given in CRAY FORTRAN, CYBER 205 FORTRAN and DAP (distributed array processor) FORTRAN. The systems performance is compared. The addition of parts of two N x N arrays is considered. The influence of the architecture on the algorithms and programming language is demonstrated. Numerical analysis of magnetohydrodynamic differential equations by an explicit difference method is illustrated, showing very good results for all three systems. The prognosis for supercomputer development is assessed.

Simulation of mixing in the quick quench region of a rich burn-quick quench mix-lean burn combustor

NASA Technical Reports Server (NTRS)

Shih, Tom I.-P.; Nguyen, H. Lee; Howe, Gregory W.; Li, Z.

1991-01-01

A computer program was developed to study the mixing process in the quick quench region of a rich burn-quick quench mix-lean burn combustor. The computer program developed was based on the density-weighted, ensemble-averaged conservation equations of mass, momentum (full compressible Navier-Stokes), total energy, and species, closed by a k-epsilon turbulence model with wall functions. The combustion process was modeled by a two-step global reaction mechanism, and NO(x) formation was modeled by the Zeldovich mechanism. The formulation employed in the computer program and the essence of the numerical method of solution are described. Some results obtained for nonreacting and reacting flows with different main-flow to dilution-jet momentum flux ratios are also presented.

Markov Chain Monte Carlo from Lagrangian Dynamics.

PubMed

Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark

2015-04-01

Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper.

QuTiP 2: A Python framework for the dynamics of open quantum systems

NASA Astrophysics Data System (ADS)

Johansson, J. R.; Nation, P. D.; Nori, Franco

2013-04-01

We present version 2 of QuTiP, the Quantum Toolbox in Python. Compared to the preceding version [J.R. Johansson, P.D. Nation, F. Nori, Comput. Phys. Commun. 183 (2012) 1760.], we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch-Redfield and Floquet-Markov master equations. Here we introduce these new features, demonstrate their use, and give a summary of the important backward-incompatible API changes introduced in this version. Catalog identifier: AEMB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMB_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 33625 No. of bytes in distributed program, including test data, etc.: 410064 Distribution format: tar.gz Programming language: Python. Computer: i386, x86-64. Operating system: Linux, Mac OSX. RAM: 2+ Gigabytes Classification: 7. External routines: NumPy, SciPy, Matplotlib, Cython Catalog identifier of previous version: AEMB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1760 Does the new version supercede the previous version?: Yes Nature of problem: Dynamics of open quantum systems Solution method: Numerical solutions to Lindblad, Floquet-Markov, and Bloch-Redfield master equations, as well as the Monte Carlo wave function method. Reasons for new version: Compared to the preceding version we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch-Redfield and Floquet-Markov master equations. Restrictions: Problems must meet the criteria for using the master equation in Lindblad, Floquet-Markov, or Bloch-Redfield form. Running time: A few seconds up to several tens of hours, depending on size of the underlying Hilbert space.

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1985-01-01

Synopses are given for NASA supported work in computer science at the University of Virginia. Some areas of research include: error seeding as a testing method; knowledge representation for engineering design; analysis of faults in a multi-version software experiment; implementation of a parallel programming environment; two computer graphics systems for visualization of pressure distribution and convective density particles; task decomposition for multiple robot arms; vectorized incomplete conjugate gradient; and iterative methods for solving linear equations on the Flex/32.

Probabilistic methods for rotordynamics analysis

NASA Technical Reports Server (NTRS)

Wu, Y.-T.; Torng, T. Y.; Millwater, H. R.; Fossum, A. F.; Rheinfurth, M. H.

1991-01-01

This paper summarizes the development of the methods and a computer program to compute the probability of instability of dynamic systems that can be represented by a system of second-order ordinary linear differential equations. Two instability criteria based upon the eigenvalues or Routh-Hurwitz test functions are investigated. Computational methods based on a fast probability integration concept and an efficient adaptive importance sampling method are proposed to perform efficient probabilistic analysis. A numerical example is provided to demonstrate the methods.

User's Manual for Aerofcn: a FORTRAN Program to Compute Aerodynamic Parameters

NASA Technical Reports Server (NTRS)

Conley, Joseph L.

1992-01-01

The computer program AeroFcn is discussed. AeroFcn is a utility program that computes the following aerodynamic parameters: geopotential altitude, Mach number, true velocity, dynamic pressure, calibrated airspeed, equivalent airspeed, impact pressure, total pressure, total temperature, Reynolds number, speed of sound, static density, static pressure, static temperature, coefficient of dynamic viscosity, kinematic viscosity, geometric altitude, and specific energy for a standard- or a modified standard-day atmosphere using compressible flow and normal shock relations. Any two parameters that define a unique flight condition are selected, and their values are entered interactively. The remaining parameters are computed, and the solutions are stored in an output file. Multiple cases can be run, and the multiple case solutions can be stored in another output file for plotting. Parameter units, the output format, and primary constants in the atmospheric and aerodynamic equations can also be changed.

Computer Solution of the Schrodinger Equation--Two Useful Programs.

ERIC Educational Resources Information Center

Evans, D. E.

1980-01-01

Describes a general purpose algorithm which enables one to calculate the allowed energy eigenvalues for an arbitrary potential. Results of a calculation where a centrifugal potential is added to the hydrogenic Coulomb potential are discussed. (Author/HM)

Numerical Stimulation of Multicomponent Chromatography Using Spreadsheets.

ERIC Educational Resources Information Center

Frey, Douglas D.

1990-01-01

Illustrated is the use of spreadsheet programs for implementing finite difference numerical simulations of chromatography as an instructional tool in a separations course. Discussed are differential equations, discretization and integration, spreadsheet development, computer requirements, and typical simulation results. (CW)

Computer program system for dynamic simulation and stability analysis of passive and actively controlled spacecraft. Volume 1. Theory

NASA Technical Reports Server (NTRS)

Bodley, C. S.; Devers, D. A.; Park, C. A.

1975-01-01

A theoretical development and associated digital computer program system is presented. The dynamic system (spacecraft) is modeled as an assembly of rigid and/or flexible bodies not necessarily in a topological tree configuration. The computer program system may be used to investigate total system dynamic characteristics including interaction effects between rigid and/or flexible bodies, control systems, and a wide range of environmental loadings. Additionally, the program system may be used for design of attitude control systems and for evaluation of total dynamic system performance including time domain response and frequency domain stability analyses. Volume 1 presents the theoretical developments including a description of the physical system, the equations of dynamic equilibrium, discussion of kinematics and system topology, a complete treatment of momentum wheel coupling, and a discussion of gravity gradient and environmental effects. Volume 2, is a program users' guide and includes a description of the overall digital program code, individual subroutines and a description of required program input and generated program output. Volume 3 presents the results of selected demonstration problems that illustrate all program system capabilities.

Bulk-Flow Analysis of Hybrid Thrust Bearings for Advanced Cryogenic Turbopumps

NASA Technical Reports Server (NTRS)

SanAndres, Luis

1998-01-01

A bulk-flow analysis and computer program for prediction of the static load performance and dynamic force coefficients of angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings have been completed. The product of the research is an efficient computational tool for the design of high-speed thrust bearings for cryogenic fluid turbopumps. The study addresses the needs of a growing technology that requires of reliable fluid film bearings to provide the maximum operating life with optimum controllable rotordynamic characteristics at the lowest cost. The motion of a cryogenic fluid on the thin film lands of a thrust bearing is governed by a set of bulk-flow mass and momentum conservation and energy transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. The bulk-flow model includes flow turbulence with fluid inertia advection, Coriolis and centrifugal acceleration effects on the bearing recesses and film lands. The cryogenic fluid properties are obtained from realistic thermophysical equations of state. Turbulent bulk-flow shear parameters are based on Hirs' model with Moody's friction factor equations allowing a simple simulation for machined bearing surface roughness. A perturbation analysis leads to zeroth-order nonlinear equations governing the fluid flow for the thrust bearing operating at a static equilibrium position, and first-order linear equations describing the perturbed fluid flow for small amplitude shaft motions in the axial direction. Numerical solution to the zeroth-order flow field equations renders the bearing flow rate, thrust load, drag torque and power dissipation. Solution to the first-order equations determines the axial stiffness, damping and inertia force coefficients. The computational method uses well established algorithms and generic subprograms available from prior developments. The Fortran9O computer program hydrothrust runs on a Windows 95/NT personal computer. The program, help files and examples are licensed by Texas A&M University Technology License Office. The study of the static and dynamic performance of two hydrostatic/hydrodynamic bearings demonstrates the importance of centrifugal and advection fluid inertia effects for operation at high rotational speeds. The first example considers a conceptual hydrostatic thrust bearing for an advanced liquid hydrogen turbopump operating at 170,000 rpm. The large axial stiffness and damping coefficients of the bearing should provide accurate control and axial positioning of the turbopump and also allow for unshrouded impellers, therefore increasing the overall pump efficiency. The second bearing uses a refrigerant R134a, and its application in oil-free air conditioning compressors is of great technological importance and commercial value. The computed predictions reveal that the LH2 bearing load capacity and flow rate increase with the recess pressure (i.e. increasing orifice diameters). The bearing axial stiffness has a maximum for a recess pressure rati of approx. 0.55. while the axial damping coefficient decreases as the recess pressure ratio increases. The computer results from three flow models are compared. These models are a) inertialess, b) fluid inertia at recess edges only, and c) full fluid inertia at both recess edges and film lands. The full inertia model shows the lowest flow rates, axial load capacity and stiffness coefficient but on the other hand renders the largest damping coefficients and inertia coefficients. The most important findings are related to the reduction of the outflow through the inner radius and the appearance of subambient pressures. The performance of the refrigerant hybrid thrust bearing is evaluated at two operating speeds and pressure drops. The computed results are presented in dimensionless form to evidence consistent trends in the bearing performance characteristics. As the applied axial load increases, the bearing film thickness and flow rate decrease while the recess pressure increases. The axial stiffness coefficient shows a maximum for a certain intermediate load while the damping coefficient steadily increases. The computed results evidence the paramount of centrifugal fluid inertia at low recess pressures (i.e. low loads), and where there is actually an inflow through the bearing inner diameter, accompanied by subambient pressures just downstream of the bearing recess edge. These results are solely due to centrifugal fluid inertia and advection transport effects. Recommendations include the extension of the computer program to handle flexure pivot tilting pad hybrid bearings and the ability to calculate moment coefficients for shaft angular misalignments.

Computation of iodine species concentrations in water

NASA Technical Reports Server (NTRS)

Schultz, John R.; Mudgett, Paul D.; Flanagan, David T.; Sauer, Richard L.

1994-01-01

During an evaluation of the use of iodine as a water disinfectant and the development of methods for measuring various iodine species in water onboard Space Freedom, it became necessary to compute the concentration of the various species based on equilibrium principles alone. Of particular concern was the case when various amounts of iodine, iodide, strong acid, and strong base are added to water. Such solutions can be used to evaluate the performance of various monitoring methods being considered. The authors of this paper present an overview of aqueous iodine chemistry, a set of nonlinear equations which can be used to model the above case, and a computer program for solving this system of equations using the Newton-Raphson method. The program was validated by comparing results over a range of concentrations and pH values with those previously presented by Gottardi for a given pH. Use of this program indicated that there are multiple roots to many cases and selecting an appropriate initial guess is important. Comparison of program results with laboratory results for the case when only iodine is added to water indicates the program gives high pH values for the iodine concentrations normally used for water disinfection. Extending the model to include the effects of iodate formation results in the computer pH values being closer to those observed, but the model with iodate does not agree well for the case in which base is added in addition to iodine to raise the pH. Potential explanations include failure to obtain equilibrium conditions in the lab, inaccuracies in published values for the equilibrium constants, and inadequate model of iodine chemistry and/or the lack of adequate analytical methods for measuring the various iodine species in water.

The combustion program at CTR

NASA Technical Reports Server (NTRS)

Poinsot, Thierry J.

1993-01-01

Understanding and modeling of turbulent combustion are key problems in the computation of numerous practical systems. Because of the lack of analytical theories in this field and of the difficulty of performing precise experiments, direct numerical simulation (DNS) appears to be one of the most attractive tools to use in addressing this problem. The general objective of DNS of reacting flows is to improve our knowledge of turbulent combustion but also to use this information for turbulent combustion models. For the foreseeable future, numerical simulation of the full three-dimensional governing partial differential equations with variable density and transport properties as well as complex chemistry will remain intractable; thus, various levels of simplification will remain necessary. On one hand, the requirement to simplify is not necessarily a handicap: numerical simulations allow the researcher a degree of control in isolating specific physical phenomena that is inaccessible in experiments. CTR has pursued an intensive research program in the field of DNS for turbulent reacting flows since 1987. DNS of reacting flows is quite different from DNS of non-reacting flows: without reaction, the equations to solve are clearly the five conservation equations of the Navier Stokes system for compressible situations (four for incompressible cases), and the limitation of the approach is the Reynolds number (or in other words the number of points in the computation). For reacting flows, the choice of the equations, the species (each species will require one additional conservation equation), the chemical scheme, and the configuration itself is more complex.

Kleene Monads: Handling Iteration in a Framework of Generic Effects

NASA Astrophysics Data System (ADS)

Goncharov, Sergey; Schröder, Lutz; Mossakowski, Till

Monads are a well-established tool for modelling various computational effects. They form the semantic basis of Moggi’s computational metalanguage, the metalanguage of effects for short, which made its way into modern functional programming in the shape of Haskell’s do-notation. Standard computational idioms call for specific classes of monads that support additional control operations. Here, we introduce Kleene monads, which additionally feature nondeterministic choice and Kleene star, i.e. nondeterministic iteration, and we provide a metalanguage and a sound calculus for Kleene monads, the metalanguage of control and effects, which is the natural joint extension of Kleene algebra and the metalanguage of effects. This provides a framework for studying abstract program equality focussing on iteration and effects. These aspects are known to have decidable equational theories when studied in isolation. However, it is well known that decidability breaks easily; e.g. the Horn theory of continuous Kleene algebras fails to be recursively enumerable. Here, we prove several negative results for the metalanguage of control and effects; in particular, already the equational theory of the unrestricted metalanguage of control and effects over continuous Kleene monads fails to be recursively enumerable. We proceed to identify a fragment of this language which still contains both Kleene algebra and the metalanguage of effects and for which the natural axiomatisation is complete, and indeed the equational theory is decidable.

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model - User Guide to Modularization Concepts and the Ground-Water Flow Process

USGS Publications Warehouse

Harbaugh, Arlen W.; Banta, Edward R.; Hill, Mary C.; McDonald, Michael G.

2000-01-01

MODFLOW is a computer program that numerically solves the three-dimensional ground-water flow equation for a porous medium by using a finite-difference method. Although MODFLOW was designed to be easily enhanced, the design was oriented toward additions to the ground-water flow equation. Frequently there is a need to solve additional equations; for example, transport equations and equations for estimating parameter values that produce the closest match between model-calculated heads and flows and measured values. This report documents a new version of MODFLOW, called MODFLOW-2000, which is designed to accommodate the solution of equations in addition to the ground-water flow equation. This report is a user's manual. It contains an overview of the old and added design concepts, documents one new package, and contains input instructions for using the model to solve the ground-water flow equation.

Application of digital computer APU modeling techniques to control system design.

NASA Technical Reports Server (NTRS)

Bailey, D. A.; Burriss, W. L.

1973-01-01

Study of the required controls for a H2-O2 auxiliary power unit (APU) technology program for the Space Shuttle. A steady-state system digital computer program was prepared and used to optimize initial system design. Analytical models of each system component were included. The program was used to solve a nineteen-dimensional problem, and then time-dependent differential equations were added to the computer program to simulate transient APU system and control. Some system parameters were considered quasi-steady-state, and others were treated as differential variables. The dynamic control analysis proceeded from initial ideal control modeling (which considered one control function and assumed the others to be ideal), stepwise through the system (adding control functions), until all of the control functions and their interactions were considered. In this way, the adequacy of the final control design over the required wide range of APU operating conditions was established.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Technical Reports Server (NTRS)

Glass, Christopher E.

1990-01-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Astrophysics Data System (ADS)

Glass, Christopher E.

1990-08-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Lifetime Reliability Evaluation of Structural Ceramic Parts with the CARES/LIFE Computer Program

NASA Technical Reports Server (NTRS)

Nemeth, Noel N.; Powers, Lynn M.; Janosik, Lesley A.; Gyekenyesi, John P.

1993-01-01

The computer program CARES/LIFE calculates the time-dependent reliability of monolithic ceramic components subjected to thermomechanical and/or proof test loading. This program is an extension of the CARES (Ceramics Analysis and Reliability Evaluation of Structures) computer program. CARES/LIFE accounts for the phenomenon of subcritical crack growth (SCG) by utilizing the power law, Paris law, or Walker equation. The two-parameter Weibull cumulative distribution function is used to characterize the variation in component strength. The effects of multiaxial stresses are modeled using either the principle of independent action (PIA), Weibull's normal stress averaging method (NSA), or Batdorf's theory. Inert strength and fatigue parameters are estimated from rupture strength data of naturally flawed specimens loaded in static, dynamic, or cyclic fatigue. Two example problems demonstrating cyclic fatigue parameter estimation and component reliability analysis with proof testing are included.

Computers and the design of ion beam optical systems

NASA Astrophysics Data System (ADS)

White, Nicholas R.

Advances in microcomputers have made it possible to maintain a library of advanced ion optical programs which can be used on inexpensive computer hardware, which are suitable for the design of a variety of ion beam systems including ion implanters, giving excellent results. This paper describes in outline the steps typically involved in designing a complete ion beam system for materials modification applications. Two computer programs are described which, although based largely on algorithms which have been in use for many years, make possible detailed beam optical calculations using microcomputers, specifically the IBM PC. OPTICIAN is an interactive first-order program for tracing beam envelopes through complex optical systems. SORCERY is a versatile program for solving Laplace's and Poisson's equations by finite difference methods using successive over-relaxation. Ion and electron trajectories can be traced through these potential fields, and plots of beam emittance obtained.

A new version of Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Felea, D.; Beşliu, C.; Jipa, Al.; Grossu, I. V.

2009-11-01

This work presents a new version of a software package for the study of chaotic flows, maps and fractals [1]. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well-known examples are implemented, with the capability of the users inserting their own ODE or iterative equations. New version program summaryProgram title: Chaos v2.0 Catalogue identifier: AEAP_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1275 No. of bytes in distributed program, including test data, etc.: 7135 Distribution format: tar.gz Programming language: Scilab 5.1.1. Scilab 5.1.1 should be installed before running the program. Information about the installation can be found at http://wiki.scilab.org/howto/install/windows. Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 150 Megabytes Classification: 6.2 Catalogue identifier of previous version: AEAP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 788 Does the new version supersede the previous version?: Yes Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations for the study of chaotic flows. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincare sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Numerical solving of iterative equations for the study of maps and fractals. Reasons for new version: The program has been updated to use the new version 5.1.1 of Scilab with new graphical capabilities [2]. Moreover, new use cases have been added which make the handling of the program easier and more efficient. Summary of revisions: A new use case concerning coupled predator-prey models has been added [3]. Three new use cases concerning fractals (Sierpinsky gasket, Barnsley's Fern and Tree) have been added [3]. The graphical user interface (GUI) of the program has been reconstructed to include the new use cases. The program has been updated to use Scilab 5.1.1 with the new graphical capabilities. Additional comments: The program package contains 12 subprograms. interface.sce - the graphical user interface (GUI) that permits the choice of a routine as follows 1.sci - Lorenz dynamical system 2.sci - Chua dynamical system 3.sci - Rosler dynamical system 4.sci - Henon map 5.sci - Lyapunov exponents for Lorenz dynamical system 6.sci - Lyapunov exponent for the logistic map 7.sci - Shannon entropy for the logistic map 8.sci - Coupled predator-prey model 1f.sci - Sierpinsky gasket 2f.sci - Barnsley's Fern 3f.sci - Barnsley's Tree Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE, Lyapunov exponents calculation and fractals. References: C.C. Bordeianu, C. Besliu, Al. Jipa, D. Felea, I. V. Grossu, Comput. Phys. Comm. 178 (2008) 788. S. Campbell, J.P. Chancelier, R. Nikoukhah, Modeling and Simulation in Scilab/Scicos, Springer, 2006. R.H. Landau, M.J. Paez, C.C. Bordeianu, A Survey of Computational Physics, Introductory Computational Science, Princeton University Press, 2008.

Manual for computing bed load transport using BAGS (Bedload Assessment for Gravel-bed Streams) Software

Treesearch

John Pitlick; Yantao Cui; Peter Wilcock

2009-01-01

This manual provides background information and instructions on the use of a spreadsheet-based program for Bedload Assessment in Gravel-bed Streams (BAGS). The program implements six bed load transport equations developed specifically for gravel-bed rivers. Transport capacities are calculated on the basis of field measurements of channel geometry, reach-average slope,...

A program for calculating load coefficient matrices utilizing the force summation method, L218 (LOADS). Volume 2: Supplemental system design and maintenance document

NASA Technical Reports Server (NTRS)

Anderson, L. R.; Miller, R. D.

1979-01-01

The LOADS computer program L218 which calculates dynamic load coefficient matrices utilizing the force summation method is described. The load equations are derived for a flight vehicle in straight and level flight and excited by gusts and/or control motions. In addition, sensor equations are calculated for use with an active control system. The load coefficient matrices are calculated for the following types of loads: (1) translational and rotational accelerations, velocities, and displacements; (2) panel aerodynamic forces; (3) net panel forces; and (4) shears, bending moments, and torsions.

A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Bailey, John W.; Schallhorn, Paul; Steadman, Todd

1998-01-01

This paper describes a general purpose computer program for analyzing steady state and transient flow in a complex network. The program is capable of modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal. The program's preprocessor allows the user to interactively develop a fluid network simulation consisting of nodes and branches. Mass, energy and specie conservation equations are solved at the nodes; the momentum conservation equations are solved in the branches. The program contains subroutines for computing "real fluid" thermodynamic and thermophysical properties for 33 fluids. The fluids are: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride and ammonia. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. Seventeen different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include: pipe flow, flow through a restriction, non-circular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, and a Joule-Thompson device. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. This paper also illustrates the application and verification of the code by comparison with Hardy Cross method for steady state flow and analytical solution for unsteady flow.

Onboard Navigation Systems Characteristics

NASA Technical Reports Server (NTRS)

1979-01-01

The space shuttle onboard navigation systems characteristics are described. A standard source of equations and numerical data for use in error analyses and mission simulations related to space shuttle development is reported. The sensor characteristics described are used for shuttle onboard navigation performance assessment. The use of complete models in the studies depend on the analyses to be performed, the capabilities of the computer programs, and the availability of computer resources.

SALLY LEVEL II- COMPUTE AND INTEGRATE DISTURBANCE AMPLIFICATION RATES ON SWEPT AND TAPERED LAMINAR FLOW CONTROL WINGS WITH SUCTION

NASA Technical Reports Server (NTRS)

Srokowski, A. J.

1994-01-01

The computer program SALLY was developed to compute the incompressible linear stability characteristics and integrate the amplification rates of boundary layer disturbances on swept and tapered wings. For some wing designs, boundary layer disturbance can significantly alter the wing performance characteristics. This is particularly true for swept and tapered laminar flow control wings which incorporate suction to prevent boundary layer separation. SALLY should prove to be a useful tool in the analysis of these wing performance characteristics. The first step in calculating the disturbance amplification rates is to numerically solve the compressible laminar boundary-layer equation with suction for the swept and tapered wing. A two-point finite-difference method is used to solve the governing continuity, momentum, and energy equations. A similarity transformation is used to remove the wall normal velocity as a boundary condition and place it into the governing equations as a parameter. Thus the awkward nonlinear boundary condition is avoided. The resulting compressible boundary layer data is used by SALLY to compute the incompressible linear stability characteristics. The local disturbance growth is obtained from temporal stability theory and converted into a local growth rate for integration. The direction of the local group velocity is taken as the direction of integration. The amplification rate, or logarithmic disturbance amplitude ratio, is obtained by integration of the local disturbance growth over distance. The amplification rate serves as a measure of the growth of linear disturbances within the boundary layer and can serve as a guide in transition prediction. This program is written in FORTRAN IV and ASSEMBLER for batch execution and has been implemented on a CDC CYBER 70 series computer with a central memory requirement of approximately 67K (octal) of 60 bit words. SALLY was developed in 1979.

LENMODEL: A forward model for calculating length distributions and fission-track ages in apatite

NASA Astrophysics Data System (ADS)

Crowley, Kevin D.

1993-05-01

The program LENMODEL is a forward model for annealing of fission tracks in apatite. It provides estimates of the track-length distribution, fission-track age, and areal track density for any user-supplied thermal history. The program approximates the thermal history, in which temperature is represented as a continuous function of time, by a series of isothermal steps of various durations. Equations describing the production of tracks as a function of time and annealing of tracks as a function of time and temperature are solved for each step. The step calculations are summed to obtain estimates for the entire thermal history. Computational efficiency is maximized by performing the step calculations backwards in model time. The program incorporates an intuitive and easy-to-use graphical interface. Thermal history is input to the program using a mouse. Model options are specified by selecting context-sensitive commands from a bar menu. The program allows for considerable selection of equations and parameters used in the calculations. The program was written for PC-compatible computers running DOS TM 3.0 and above (and Windows TM 3.0 or above) with VGA or SVGA graphics and a Microsoft TM-compatible mouse. Single copies of a runtime version of the program are available from the author by written request as explained in the last section of this paper.

Numerical studies of unsteady two dimensional subsonic flows using the ICE method. Ph.D. Thesis - Toledo Univ.

NASA Technical Reports Server (NTRS)

Wieber, P. R.

1973-01-01

A numerical program was developed to compute transient compressible and incompressible laminar flows in two dimensions with multicomponent mixing and chemical reaction. The algorithm used the Los Alamos Scientific Laboratory ICE (Implicit Continuous-Fluid Eulerian) method as its base. The program can compute both high and low speed compressible flows. The numerical program incorporating the stabilization techniques was quite successful in treating both old and new problems. Detailed calculations of coaxial flow very close to the entry plane were possible. The program treated complex flows such as the formation and downstream growth of a recirculation cell. An implicit solution of the species equation predicted mixing and reaction rates which compared favorably with the literature.

Generalized three-dimensional experimental lightning code (G3DXL) user's manual

NASA Technical Reports Server (NTRS)

Kunz, Karl S.

1986-01-01

Information concerning the programming, maintenance and operation of the G3DXL computer program is presented and the theoretical basis for the code is described. The program computes time domain scattering fields and surface currents and charges induced by a driving function on and within a complex scattering object which may be perfectly conducting or a lossy dielectric. This is accomplished by modeling the object with cells within a three-dimensional, rectangular problem space, enforcing the appropriate boundary conditions and differencing Maxwell's equations in time. In the present version of the program, the driving function can be either the field radiated by a lightning strike or a direct lightning strike. The F-106 B aircraft is used as an example scattering object.

Application of the ASP3D Computer Program to Unsteady Aerodynamic and Aeroelastic Analyses

NASA Technical Reports Server (NTRS)

Batina, John T.

2006-01-01

A new computer program has been developed called ASP3D (Advanced Small Perturbation - 3D), which solves the small perturbation potential flow equation in an advanced form including mass-consistent surface and trailing wake boundary conditions, and entropy, vorticity, and viscous effects. The purpose of the program is for unsteady aerodynamic and aeroelastic analyses, especially in the nonlinear transonic flight regime. The program exploits the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The paper presents unsteady aerodynamic and aeroelastic applications of ASP3D to assess the time dependent capability and demonstrate various features of the code.

A computer program for the calculation of laminar and turbulent boundary layer flows

NASA Technical Reports Server (NTRS)

Dwyer, H. A.; Doss, E. D.; Goldman, A. L.

1972-01-01

The results are presented of a study to produce a computer program to calculate laminar and turbulent boundary layer flows. The program is capable of calculating the following types of flow: (1) incompressible or compressible, (2) two dimensional or axisymmetric, and (3) flows with significant transverse curvature. Also, the program can handle a large variety of boundary conditions, such as blowing or suction, arbitrary temperature distributions and arbitrary wall heat fluxes. The program has been specialized to the calculation of equilibrium air flows and all of the thermodynamic and transport properties used are for air. For the turbulent transport properties, the eddy viscosity approach has been used. Although the eddy viscosity models are semi-empirical, the model employed in the program has corrections for pressure gradients, suction and blowing and compressibility. The basic method of approach is to put the equations of motion into a finite difference form and then solve them by use of a digital computer. The program is written in FORTRAN 4 and requires small amounts of computer time on most scientific machines. For example, most laminar flows can be calculated in less than one minute of machine time, while turbulent flows usually require three or four minutes.

The orbifolder: A tool to study the low-energy effective theory of heterotic orbifolds

NASA Astrophysics Data System (ADS)

Nilles, H. P.; Ramos-Sánchez, S.; Vaudrevange, P. K. S.; Wingerter, A.

2012-06-01

The orbifolder is a program developed in C++ that computes and analyzes the low-energy effective theory of heterotic orbifold compactifications. The program includes routines to compute the massless spectrum, to identify the allowed couplings in the superpotential, to automatically generate large sets of orbifold models, to identify phenomenologically interesting models (e.g. MSSM-like models) and to analyze their vacuum configurations. Program summaryProgram title: orbifolder Catalogue identifier: AELR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 145 572 No. of bytes in distributed program, including test data, etc.: 930 517 Distribution format: tar.gz Programming language:C++ Computer: Personal computer Operating system: Tested on Linux (Fedora 15, Ubuntu 11, SuSE 11) Word size: 32 bits or 64 bits Classification: 11.1 External routines: Boost (http://www.boost.org/), GSL (http://www.gnu.org/software/gsl/) Nature of problem: Calculating the low-energy spectrum of heterotic orbifold compactifications. Solution method: Quadratic equations on a lattice; representation theory; polynomial algebra. Running time: Less than a second per model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Jih-Sheng

This paper introduces control system design based softwares, SIMNON and MATLAB/SIMULINK, for power electronics system simulation. A complete power electronics system typically consists of a rectifier bridge along with its smoothing capacitor, an inverter, and a motor. The system components, featuring discrete or continuous, linear or nonlinear, are modeled in mathematical equations. Inverter control methods,such as pulse-width-modulation and hysteresis current control, are expressed in either computer algorithms or digital circuits. After describing component models and control methods, computer programs are then developed for complete systems simulation. Simulation results are mainly used for studying system performances, such as input and outputmore » current harmonics, torque ripples, and speed responses. Key computer programs and simulation results are demonstrated for educational purposes.« less

Three-Dimensional Boundary-Layer program (BL3D) for swept subsonic or supersonic wings with application to laminar flow control

NASA Technical Reports Server (NTRS)

Iyer, Venkit

1993-01-01

The theory, formulation, and solution of three-dimensional, compressible attached laminar flows, applied to swept wings in subsonic or supersonic flow are discussed. Several new features and modifications to an earlier general procedure described in NASA CR 4269, Jan. 1990 are incorporated. Details of interfacing the boundary-layer computation with solution of the inviscid Euler equations are discussed. A description of the computer program, complete with user's manual and example cases, is also included. Comparison of solutions with Navier-Stokes computations with or without boundary-layer suction is given. Output of solution profiles and derivatives required in boundary-layer stability analysis is provided.

Random harmonic analysis program, L221 (TEV156). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Miller, R. D.; Graham, M. L.

1979-01-01

A digital computer program capable of calculating steady state solutions for linear second order differential equations due to sinusoidal forcing functions is described. The field of application of the program, the analysis of airplane response and loads due to continuous random air turbulence, is discussed. Optional capabilities including frequency dependent input matrices, feedback damping, gradual gust penetration, multiple excitation forcing functions, and a static elastic solution are described. Program usage and a description of the analysis used are presented.

Software Reviews.

ERIC Educational Resources Information Center

Teles, Elizabeth, Ed.; And Others

1990-01-01

Reviewed are two computer software packages for Macintosh microcomputers including "Phase Portraits," an exploratory graphics tool for studying first-order planar systems; and "MacMath," a set of programs for exploring differential equations, linear algebra, and other mathematical topics. Features, ease of use, cost, availability, and hardware…

Beam-plasma dielectric tensor with Mathematica

NASA Astrophysics Data System (ADS)

Bret, A.

2007-03-01

We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summaryTitle of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the dimensionless variables. Restrictions on the complexity of the problem: Temperature effects are limited to small, i.e. non-relativistic, temperatures. The kinetic counterpart of the present Mathematica will usually not compute the required integrals. Typical running time: About 1 minute on a Intel Centrino 1.5 GHz Laptop with 512 MB of RAM. Unusual features of the program: None.

Ground resonance analysis using a substructure modeling approach

NASA Technical Reports Server (NTRS)

Chen, S.-Y.; Berman, A.; Austin, E. E.

1984-01-01

A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented.

Ground resonance analysis using a substructure modeling approach

NASA Technical Reports Server (NTRS)

Chen, S. Y.; Austin, E. E.; Berman, A.

1985-01-01

A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented.

Transport methods and interactions for space radiations

NASA Technical Reports Server (NTRS)

Wilson, John W.; Townsend, Lawrence W.; Schimmerling, Walter S.; Khandelwal, Govind S.; Khan, Ferdous S.; Nealy, John E.; Cucinotta, Francis A.; Simonsen, Lisa C.; Shinn, Judy L.; Norbury, John W.

1991-01-01

A review of the program in space radiation protection at the Langley Research Center is given. The relevant Boltzmann equations are given with a discussion of approximation procedures for space applications. The interaction coefficients are related to solution of the many-body Schroedinger equation with nuclear and electromagnetic forces. Various solution techniques are discussed to obtain relevant interaction cross sections with extensive comparison with experiments. Solution techniques for the Boltzmann equations are discussed in detail. Transport computer code validation is discussed through analytical benchmarking, comparison with other codes, comparison with laboratory experiments and measurements in space. Applications to lunar and Mars missions are discussed.

Automated symbolic calculations in nonequilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Kröger, Martin; Hütter, Markus

2010-12-01

We cast the Jacobi identity for continuous fields into a local form which eliminates the need to perform any partial integration to the expense of performing variational derivatives. This allows us to test the Jacobi identity definitely and efficiently and to provide equations between different components defining a potential Poisson bracket. We provide a simple Mathematica TM notebook which allows to perform this task conveniently, and which offers some additional functionalities of use within the framework of nonequilibrium thermodynamics: reversible equations of change for fields, and the conservation of entropy during the reversible dynamics. Program summaryProgram title: Poissonbracket.nb Catalogue identifier: AEGW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 227 952 No. of bytes in distributed program, including test data, etc.: 268 918 Distribution format: tar.gz Programming language: Mathematica TM 7.0 Computer: Any computer running Mathematica TM 6.0 and later versions Operating system: Linux, MacOS, Windows RAM: 100 Mb Classification: 4.2, 5, 23 Nature of problem: Testing the Jacobi identity can be a very complex task depending on the structure of the Poisson bracket. The Mathematica TM notebook provided here solves this problem using a novel symbolic approach based on inherent properties of the variational derivative, highly suitable for the present tasks. As a by product, calculations performed with the Poisson bracket assume a compact form. Solution method: The problem is first cast into a form which eliminates the need to perform partial integration for arbitrary functionals at the expense of performing variational derivatives. The corresponding equations are conveniently obtained using the symbolic programming environment Mathematica TM. Running time: For the test cases and most typical cases in the literature, the running time is of the order of seconds or minutes, respectively.

Stability of mixing layers

NASA Technical Reports Server (NTRS)

Tam, Christopher; Krothapalli, A

1993-01-01

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Computing Interactions Of Free-Space Radiation With Matter

NASA Technical Reports Server (NTRS)

Wilson, J. W.; Cucinotta, F. A.; Shinn, J. L.; Townsend, L. W.; Badavi, F. F.; Tripathi, R. K.; Silberberg, R.; Tsao, C. H.; Badwar, G. D.

1995-01-01

High Charge and Energy Transport (HZETRN) computer program computationally efficient, user-friendly package of software adressing problem of transport of, and shielding against, radiation in free space. Designed as "black box" for design engineers not concerned with physics of underlying atomic and nuclear radiation processes in free-space environment, but rather primarily interested in obtaining fast and accurate dosimetric information for design and construction of modules and devices for use in free space. Computational efficiency achieved by unique algorithm based on deterministic approach to solution of Boltzmann equation rather than computationally intensive statistical Monte Carlo method. Written in FORTRAN.

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Grid generation in three dimensions by Poisson equations with control of cell size and skewness at boundary surfaces

NASA Technical Reports Server (NTRS)

Sorenson, R. L.; Steger, J. L.

1983-01-01

An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.

Implementation and Testing of Turbulence Models for the F18-HARV Simulation

NASA Technical Reports Server (NTRS)

Yeager, Jessie C.

1998-01-01

This report presents three methods of implementing the Dryden power spectral density model for atmospheric turbulence. Included are the equations which define the three methods and computer source code written in Advanced Continuous Simulation Language to implement the equations. Time-history plots and sample statistics of simulated turbulence results from executing the code in a test program are also presented. Power spectral densities were computed for sample sequences of turbulence and are plotted for comparison with the Dryden spectra. The three model implementations were installed in a nonlinear six-degree-of-freedom simulation of the High Alpha Research Vehicle airplane. Aircraft simulation responses to turbulence generated with the three implementations are presented as plots.

Applications of Parallel Process HiMAP for Large Scale Multidisciplinary Problems

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Potsdam, Mark; Rodriguez, David; Kwak, Dochay (Technical Monitor)

2000-01-01

HiMAP is a three level parallel middleware that can be interfaced to a large scale global design environment for code independent, multidisciplinary analysis using high fidelity equations. Aerospace technology needs are rapidly changing. Computational tools compatible with the requirements of national programs such as space transportation are needed. Conventional computation tools are inadequate for modern aerospace design needs. Advanced, modular computational tools are needed, such as those that incorporate the technology of massively parallel processors (MPP).

NASA Computational Fluid Dynamics Conference. Volume 1: Sessions 1-6

NASA Technical Reports Server (NTRS)

1989-01-01

Presentations given at the NASA Computational Fluid Dynamics (CFD) Conference held at the NASA Ames Research Center, Moffett Field, California, March 7-9, 1989 are given. Topics covered include research facility overviews of CFD research and applications, validation programs, direct simulation of compressible turbulence, turbulence modeling, advances in Runge-Kutta schemes for solving 3-D Navier-Stokes equations, grid generation and invicid flow computation around aircraft geometries, numerical simulation of rotorcraft, and viscous drag prediction for rotor blades.

Program manual for HILTOP, a heliocentric interplanetary low thrust trajectory optimization program. Part 1: User's guide

NASA Technical Reports Server (NTRS)

Mann, F. I.; Horsewood, J. L.

1974-01-01

A performance-analysis computer program, that was developed explicitly to generate optimum electric propulsion trajectory data for missions of interest in the exploration of the solar system is presented. The program was primarily designed to evaluate the performance capabilities of electric propulsion systems, and in the simulation of a wide variety of interplanetary missions. A numerical integration of the two-body, three-dimensional equations of motion and the Euler-Lagrange equations was used in the program. Transversality conditions which permit the rapid generation of converged maximum-payload trajectory data, and the optimization of numerous other performance indices for which no transversality conditions exist are included. The ability to simulate constrained optimum solutions, including trajectories having specified propulsion time and constant thrust cone angle, is also in the program. The program was designed to handle multiple-target missions with various types of encounters, such as rendezvous, stopover, orbital capture, and flyby. Performance requirements for a variety of launch vehicles can be determined.

Improvements to the adaptive maneuvering logic program

NASA Technical Reports Server (NTRS)

Burgin, George H.

1986-01-01

The Adaptive Maneuvering Logic (AML) computer program simulates close-in, one-on-one air-to-air combat between two fighter aircraft. Three important improvements are described. First, the previously available versions of AML were examined for their suitability as a baseline program. The selected program was then revised to eliminate some programming bugs which were uncovered over the years. A listing of this baseline program is included. Second, the equations governing the motion of the aircraft were completely revised. This resulted in a model with substantially higher fidelity than the original equations of motion provided. It also completely eliminated the over-the-top problem, which occurred in the older versions when the AML-driven aircraft attempted a vertical or near vertical loop. Third, the requirements for a versatile generic, yet realistic, aircraft model were studied and implemented in the program. The report contains detailed tables which make the generic aircraft to be either a modern, high performance aircraft, an older high performance aircraft, or a previous generation jet fighter.

Computation of transonic separated wing flows using an Euler/Navier-Stokes zonal approach

NASA Technical Reports Server (NTRS)

Kaynak, Uenver; Holst, Terry L.; Cantwell, Brian J.

1986-01-01

A computer program called Transonic Navier Stokes (TNS) has been developed which solves the Euler/Navier-Stokes equations around wings using a zonal grid approach. In the present zonal scheme, the physical domain of interest is divided into several subdomains called zones and the governing equations are solved interactively. The advantages of the Zonal Grid approach are as follows: (1) the grid for any subdomain can be generated easily; (2) grids can be, in a sense, adapted to the solution; (3) different equation sets can be used in different zones; and, (4) this approach allows for a convenient data base organization scheme. Using this code, separated flows on a NACA 0012 section wing and on the NASA Ames WING C have been computed. First, the effects of turbulence and artificial dissipation models incorporated into the code are assessed by comparing the TNS results with other CFD codes and experiments. Then a series of flow cases is described where data are available. The computed results, including cases with shock-induced separation, are in good agreement with experimental data. Finally, some futuristic cases are presented to demonstrate the abilities of the code for massively separated cases which do not have experimental data.

Sensitivity analysis of dynamic biological systems with time-delays.

PubMed

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2010-10-15

Mathematical modeling has been applied to the study and analysis of complex biological systems for a long time. Some processes in biological systems, such as the gene expression and feedback control in signal transduction networks, involve a time delay. These systems are represented as delay differential equation (DDE) models. Numerical sensitivity analysis of a DDE model by the direct method requires the solutions of model and sensitivity equations with time-delays. The major effort is the computation of Jacobian matrix when computing the solution of sensitivity equations. The computation of partial derivatives of complex equations either by the analytic method or by symbolic manipulation is time consuming, inconvenient, and prone to introduce human errors. To address this problem, an automatic approach to obtain the derivatives of complex functions efficiently and accurately is necessary. We have proposed an efficient algorithm with an adaptive step size control to compute the solution and dynamic sensitivities of biological systems described by ordinal differential equations (ODEs). The adaptive direct-decoupled algorithm is extended to solve the solution and dynamic sensitivities of time-delay systems describing by DDEs. To save the human effort and avoid the human errors in the computation of partial derivatives, an automatic differentiation technique is embedded in the extended algorithm to evaluate the Jacobian matrix. The extended algorithm is implemented and applied to two realistic models with time-delays: the cardiovascular control system and the TNF-α signal transduction network. The results show that the extended algorithm is a good tool for dynamic sensitivity analysis on DDE models with less user intervention. By comparing with direct-coupled methods in theory, the extended algorithm is efficient, accurate, and easy to use for end users without programming background to do dynamic sensitivity analysis on complex biological systems with time-delays.

A second-order closure analysis of turbulent diffusion flames. [combustion physics

NASA Technical Reports Server (NTRS)

Varma, A. K.; Fishburne, E. S.; Beddini, R. A.

1977-01-01

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

NASA Technical Reports Server (NTRS)

Korte, John J.; Kumar, Ajay; Singh, D. J.; White, J. A.

1992-01-01

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

Three-dimensional transonic potential flow about complex 3-dimensional configurations

NASA Technical Reports Server (NTRS)

Reyhner, T. A.

1984-01-01

An analysis has been developed and a computer code written to predict three-dimensional subsonic or transonic potential flow fields about lifting or nonlifting configurations. Possible condfigurations include inlets, nacelles, nacelles with ground planes, S-ducts, turboprop nacelles, wings, and wing-pylon-nacelle combinations. The solution of the full partial differential equation for compressible potential flow written in terms of a velocity potential is obtained using finite differences, line relaxation, and multigrid. The analysis uses either a cylindrical or Cartesian coordinate system. The computational mesh is not body fitted. The analysis has been programmed in FORTRAN for both the CDC CYBER 203 and the CRAY-1 computers. Comparisons of computed results with experimental measurement are presented. Descriptions of the program input and output formats are included.

Computer program for calculating and fitting thermodynamic functions

NASA Technical Reports Server (NTRS)

Mcbride, Bonnie J.; Gordon, Sanford

1992-01-01

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

TORO II: A finite element computer program for nonlinear quasi-static problems in electromagnetics: Part 1, Theoretical background

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gartling, D.K.

The theoretical and numerical background for the finite element computer program, TORO II, is presented in detail. TORO II is designed for the multi-dimensional analysis of nonlinear, electromagnetic field problems described by the quasi-static form of Maxwell`s equations. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in TORO II are also outlined. Instructions for the use of the code are documented in SAND96-0903; examples of problems analyzed with the code are also provided in the user`s manual. 24 refs., 8 figs.

A model of heat transfer in immersed man

NASA Technical Reports Server (NTRS)

Montgomery, L. D.

1974-01-01

An equation representing man's thermal balance under water is considered. The equation states that the body thermal loading from metabolic heat production and artificial heat input must be offset by respiratory and environmental heat exchange to maintain a constant body temperature. Critical body regions are affected by cold-water thermal stress. A model of the thermoregulatory system may be divided into the physical-controlled system and the dynamic controlling system. The thermal model is simulated by computer programs.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burge, S.W.

This report describes the theory and structure of the FORCE2 flow program. The manual describes the governing model equations, solution procedure and their implementation in the computer program. FORCE2 is an extension of an existing B&V multidimensional, two-phase flow program. FORCE2 was developed for application to fluid beds by flow implementing a gas-solids modeling technology derived, in part, during a joint government -- industry research program, ``Erosion of FBC Heat Transfer Tubes,`` coordinated by Argonne National Laboratory. The development of FORCE2 was sponsored by ASEA-Babcock, an industry participant in this program. This manual is the principal documentation for the programmore » theory and organization. Program usage and post-processing of code predictions with the FORCE2 post-processor are described in a companion report, FORCE2 -- A Multidimensional Flow Program for Fluid Beds, User`s Guide. This manual is segmented into sections to facilitate its usage. In section 2.0, the mass and momentum conservation principles, the basis for the code, are presented. In section 3.0, the constitutive relations used in modeling gas-solids hydrodynamics are given. The finite-difference model equations are derived in section 4.0 and the solution procedures described in sections 5.0 and 6.0. Finally, the implementation of the model equations and solution procedure in FORCE2 is described in section 7.0.« less

Computer code for predicting coolant flow and heat transfer in turbomachinery

NASA Technical Reports Server (NTRS)

Meitner, Peter L.

1990-01-01

A computer code was developed to analyze any turbomachinery coolant flow path geometry that consist of a single flow passage with a unique inlet and exit. Flow can be bled off for tip-cap impingement cooling, and a flow bypass can be specified in which coolant flow is taken off at one point in the flow channel and reintroduced at a point farther downstream in the same channel. The user may either choose the coolant flow rate or let the program determine the flow rate from specified inlet and exit conditions. The computer code integrates the 1-D momentum and energy equations along a defined flow path and calculates the coolant's flow rate, temperature, pressure, and velocity and the heat transfer coefficients along the passage. The equations account for area change, mass addition or subtraction, pumping, friction, and heat transfer.

Solving Equations of Multibody Dynamics

NASA Technical Reports Server (NTRS)

Jain, Abhinandan; Lim, Christopher

2007-01-01

Darts++ is a computer program for solving the equations of motion of a multibody system or of a multibody model of a dynamic system. It is intended especially for use in dynamical simulations performed in designing and analyzing, and developing software for the control of, complex mechanical systems. Darts++ is based on the Spatial-Operator- Algebra formulation for multibody dynamics. This software reads a description of a multibody system from a model data file, then constructs and implements an efficient algorithm that solves the dynamical equations of the system. The efficiency and, hence, the computational speed is sufficient to make Darts++ suitable for use in realtime closed-loop simulations. Darts++ features an object-oriented software architecture that enables reconfiguration of system topology at run time; in contrast, in related prior software, system topology is fixed during initialization. Darts++ provides an interface to scripting languages, including Tcl and Python, that enable the user to configure and interact with simulation objects at run time.

A computer program for simulating geohydrologic systems in three dimensions

USGS Publications Warehouse

Posson, D.R.; Hearne, G.A.; Tracy, J.V.; Frenzel, P.F.

1980-01-01

This document is directed toward individuals who wish to use a computer program to simulate ground-water flow in three dimensions. The strongly implicit procedure (SIP) numerical method is used to solve the set of simultaneous equations. New data processing techniques and program input and output options are emphasized. The quifer system to be modeled may be heterogeneous and anisotropic, and may include both artesian and water-table conditions. Systems which consist of well defined alternating layers of highly permeable and poorly permeable material may be represented by a sequence of equations for two dimensional flow in each of the highly permeable units. Boundaries where head or flux is user-specified may be irregularly shaped. The program also allows the user to represent streams as limited-source boundaries when the streamflow is small in relation to the hydraulic stress on the system. The data-processing techniques relating to ' cube ' input and output, to swapping of layers, to restarting of simulation, to free-format NAMELIST input, to the details of each sub-routine 's logic, and to the overlay program structure are discussed. The program is capable of processing large models that might overflow computer memories with conventional programs. Detailed instructions for selecting program options, for initializing the data arrays, for defining ' cube ' output lists and maps, and for plotting hydrographs of calculated and observed heads and/or drawdowns are provided. Output may be restricted to those nodes of particular interest, thereby reducing the volumes of printout for modelers, which may be critical when working at remote terminals. ' Cube ' input commands allow the modeler to set aquifer parameters and initialize the model with very few input records. Appendixes provide instructions to compile the program, definitions and cross-references for program variables, summary of the FLECS structured FORTRAN programming language, listings of the FLECS and FORTRAN source code, and samples of input and output for example simulations. (USGS)

A numerical code for the simulation of non-equilibrium chemically reacting flows on hybrid CPU-GPU clusters

NASA Astrophysics Data System (ADS)

Kudryavtsev, Alexey N.; Kashkovsky, Alexander V.; Borisov, Semyon P.; Shershnev, Anton A.

2017-10-01

In the present work a computer code RCFS for numerical simulation of chemically reacting compressible flows on hybrid CPU/GPU supercomputers is developed. It solves 3D unsteady Euler equations for multispecies chemically reacting flows in general curvilinear coordinates using shock-capturing TVD schemes. Time advancement is carried out using the explicit Runge-Kutta TVD schemes. Program implementation uses CUDA application programming interface to perform GPU computations. Data between GPUs is distributed via domain decomposition technique. The developed code is verified on the number of test cases including supersonic flow over a cylinder.

Thermophysical properties of Helium-4 from 0.8 to 1500 K with pressures to 2000 MPa

NASA Technical Reports Server (NTRS)

Arp, Vincent D.; Mccarty, Robert D.

1989-01-01

Tabular summary data of the thermophysical properties of fluid helium are given for temperatures from 0.8 to 1500 K, with pressures to 2000 MPa between 75 and 300 K, or to 100 MPa outside of this temperature band. Properties include density, specific heats, enthalpy, entropy, internal energy, sound velocity, expansivity, compressibility, thermal conductivity, and viscosity. The data are calculated from a computer program which is available from the National Institute of Standards and Technology. The computer program is based on carefully fitted state equations for both normal and superfluid helium.

Documentation of a numerical code for the simulation of variable density ground-water flow in three dimensions

USGS Publications Warehouse

Kuiper, L.K.

1985-01-01

A numerical code is documented for the simulation of variable density time dependent groundwater flow in three dimensions. The groundwater density, although variable with distance, is assumed to be constant in time. The Integrated Finite Difference grid elements in the code follow the geologic strata in the modeled area. If appropriate, the determination of hydraulic head in confining beds can be deleted to decrease computation time. The strongly implicit procedure (SIP), successive over-relaxation (SOR), and eight different preconditioned conjugate gradient (PCG) methods are used to solve the approximating equations. The use of the computer program that performs the calculations in the numerical code is emphasized. Detailed instructions are given for using the computer program, including input data formats. An example simulation and the Fortran listing of the program are included. (USGS)

Orbital Maneuvering Engine Feed System Coupled Stability Investigation, Computer User's Manual

NASA Technical Reports Server (NTRS)

Schuman, M. D.; Fertig, K. W.; Hunting, J. K.; Kahn, D. R.

1975-01-01

An operating manual for the feed system coupled stability model was given, in partial fulfillment of a program designed to develop, verify, and document a digital computer model that can be used to analyze and predict engine/feed system coupled instabilities in pressure-fed storable propellant propulsion systems over a frequency range of 10 to 1,000 Hz. The first section describes the analytical approach to modelling the feed system hydrodynamics, combustion dynamics, chamber dynamics, and overall engineering model structure, and presents the governing equations in each of the technical areas. This is followed by the program user's guide, which is a complete description of the structure and operation of the computerized model. Last, appendices provide an alphabetized FORTRAN symbol table, detailed program logic diagrams, computer code listings, and sample case input and output data listings.

BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures

NASA Astrophysics Data System (ADS)

Deslippe, Jack; Samsonidze, Georgy; Strubbe, David A.; Jain, Manish; Cohen, Marvin L.; Louie, Steven G.

2012-06-01

BerkeleyGW is a massively parallel computational package for electron excited-state properties that is based on the many-body perturbation theory employing the ab initio GW and GW plus Bethe-Salpeter equation methodology. It can be used in conjunction with many density-functional theory codes for ground-state properties, including PARATEC, PARSEC, Quantum ESPRESSO, SIESTA, and Octopus. The package can be used to compute the electronic and optical properties of a wide variety of material systems from bulk semiconductors and metals to nanostructured materials and molecules. The package scales to 10 000s of CPUs and can be used to study systems containing up to 100s of atoms. Program summaryProgram title: BerkeleyGW Catalogue identifier: AELG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Open source BSD License. See code for licensing details. No. of lines in distributed program, including test data, etc.: 576 540 No. of bytes in distributed program, including test data, etc.: 110 608 809 Distribution format: tar.gz Programming language: Fortran 90, C, C++, Python, Perl, BASH Computer: Linux/UNIX workstations or clusters Operating system: Tested on a variety of Linux distributions in parallel and serial as well as AIX and Mac OSX RAM: (50-2000) MB per CPU (Highly dependent on system size) Classification: 7.2, 7.3, 16.2, 18 External routines: BLAS, LAPACK, FFTW, ScaLAPACK (optional), MPI (optional). All available under open-source licenses. Nature of problem: The excited state properties of materials involve the addition or subtraction of electrons as well as the optical excitations of electron-hole pairs. The excited particles interact strongly with other electrons in a material system. This interaction affects the electronic energies, wavefunctions and lifetimes. It is well known that ground-state theories, such as standard methods based on density-functional theory, fail to correctly capture this physics. Solution method: We construct and solve the Dyson's equation for the quasiparticle energies and wavefunctions within the GW approximation for the electron self-energy. We additionally construct and solve the Bethe-Salpeter equation for the correlated electron-hole (exciton) wavefunctions and excitation energies. Restrictions: The material size is limited in practice by the computational resources available. Materials with up to 500 atoms per periodic cell can be studied on large HPCs. Additional comments: The distribution file for this program is approximately 110 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: 1-1000 minutes (depending greatly on system size and processor number).

Multithreaded transactions in scientific computing. The Growth06_v2 program

NASA Astrophysics Data System (ADS)

Daniluk, Andrzej

2009-07-01

Writing a concurrent program can be more difficult than writing a sequential program. Programmer needs to think about synchronization, race conditions and shared variables. Transactions help reduce the inconvenience of using threads. A transaction is an abstraction, which allows programmers to group a sequence of actions on the program into a logical, higher-level computation unit. This paper presents a new version of the GROWTHGr and GROWTH06 programs. New version program summaryProgram title: GROWTH06_v2 Catalogue identifier: ADVL_v2_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVL_v2_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 65 255 No. of bytes in distributed program, including test data, etc.: 865 985 Distribution format: tar.gz Programming language: Object Pascal Computer: Pentium-based PC Operating system: Windows 9x, XP, NT, Vista RAM: more than 1 MB Classification: 4.3, 7.2, 6.2, 8, 14 Catalogue identifier of previous version: ADVL_v2_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 678 Does the new version supersede the previous version?: Yes Nature of problem: The programs compute the RHEED intensities during the growth of thin epitaxial structures prepared using the molecular beam epitaxy (MBE). The computations are based on the use of kinematical diffraction theory. Solution method: Epitaxial growth of thin films is modelled by a set of non-linear differential equations [1]. The Runge-Kutta method with adaptive stepsize control was used for solving initial value problem for non-linear differential equations [2]. Reasons for new version: According to the users' suggestions functionality of the program has been improved. Moreover, new use cases have been added which make the handling of the program easier and more efficient than the previous ones [3]. Summary of revisions:The design pattern (See Fig. 2 of Ref. [3]) has been modified according to the scheme shown on Fig. 1. A graphical user interface (GUI) for the program has been reconstructed. Fig. 2 presents a hybrid diagram of a GUI that shows how onscreen objects connect to use cases. The program has been compiled with English/USA regional and language options. Note: The figures mentioned above are contained in the program distribution file. Unusual features: The program is distributed in the form of source project GROWTH06_v2.dpr with associated files, and should be compiled using Borland Delphi compilers versions 6 or latter (including Borland Developer Studio 2006 and Code Gear compilers for Delphi). Additional comments: Two figures are included in the program distribution file. These are captioned Static classes model for Transaction design pattern. A model of a window that shows how onscreen objects connect to use cases. Running time: The typical running time is machine and user-parameters dependent. References: [1] A. Daniluk, Comput. Phys. Comm. 170 (2005) 265. [2] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in Pascal: The Art of Scientific Computing, first ed., Cambridge University Press, 1989. [3] M. Brzuszek, A. Daniluk, Comput. Phys. Comm. 175 (2006) 678.

Relativity and the TRS-80.

ERIC Educational Resources Information Center

Levin, Sidney

1984-01-01

Presents the listing (TRS-80) for a computer program which derives the relativistic equation (employing as a model the concept of a moving clock which emits photons at regular intervals) and calculates transformations of time, mass, and length with increasing velocities (Einstein-Lorentz transformations). (JN)

Earth-moon system: Dynamics and parameter estimation

NASA Technical Reports Server (NTRS)

Breedlove, W. J., Jr.

1975-01-01

A theoretical development of the equations of motion governing the earth-moon system is presented. The earth and moon were treated as finite rigid bodies and a mutual potential was utilized. The sun and remaining planets were treated as particles. Relativistic, non-rigid, and dissipative effects were not included. The translational and rotational motion of the earth and moon were derived in a fully coupled set of equations. Euler parameters were used to model the rotational motions. The mathematical model is intended for use with data analysis software to estimate physical parameters of the earth-moon system using primarily LURE type data. Two program listings are included. Program ANEAMO computes the translational/rotational motion of the earth and moon from analytical solutions. Program RIGEM numerically integrates the fully coupled motions as described above.

Loci-STREAM Version 0.9

NASA Technical Reports Server (NTRS)

Wright, Jeffrey; Thakur, Siddharth

2006-01-01

Loci-STREAM is an evolving computational fluid dynamics (CFD) software tool for simulating possibly chemically reacting, possibly unsteady flows in diverse settings, including rocket engines, turbomachines, oil refineries, etc. Loci-STREAM implements a pressure- based flow-solving algorithm that utilizes unstructured grids. (The benefit of low memory usage by pressure-based algorithms is well recognized by experts in the field.) The algorithm is robust for flows at all speeds from zero to hypersonic. The flexibility of arbitrary polyhedral grids enables accurate, efficient simulation of flows in complex geometries, including those of plume-impingement problems. The present version - Loci-STREAM version 0.9 - includes an interface with the Portable, Extensible Toolkit for Scientific Computation (PETSc) library for access to enhanced linear-equation-solving programs therein that accelerate convergence toward a solution. The name "Loci" reflects the creation of this software within the Loci computational framework, which was developed at Mississippi State University for the primary purpose of simplifying the writing of complex multidisciplinary application programs to run in distributed-memory computing environments including clusters of personal computers. Loci has been designed to relieve application programmers of the details of programming for distributed-memory computers.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 3: Design philosophy and programming details

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular Finite-Element, digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water-flow. The modular structure of MODFE places the computationally independent tasks that are performed routinely by digital-computer programs simulating ground-water flow into separate subroutines, which are executed from the main program by control statements. Each subroutine consists of complete sets of computations, or modules, which are identified by comment statements, and can be modified by the user without affecting unrelated computations elsewhere in the program. Simulation capabilities can be added or modified by either adding or modifying subroutines that perform specific computational tasks, and the modular-program structure allows the user to create versions of MODFE that contain only the simulation capabilities that pertain to the ground-water problem of interest. MODFE is written in a Fortran programming language that makes it virtually device independent and compatible with desk-top personal computers and large mainframes. MODFE uses computer storage and execution time efficiently by taking advantage of symmetry and sparseness within the coefficient matrices of the finite-element equations. Parts of the matrix coefficients are computed and stored as single-subscripted variables, which are assembled into a complete coefficient just prior to solution. Computer storage is reused during simulation to decrease storage requirements. Descriptions of subroutines that execute the computational steps of the modular-program structure are given in tables that cross reference the subroutines with particular versions of MODFE. Programming details of linear and nonlinear hydrologic terms are provided. Structure diagrams for the main programs show the order in which subroutines are executed for each version and illustrate some of the linear and nonlinear versions of MODFE that are possible. Computational aspects of changing stresses and boundary conditions with time and of mass-balance and error terms are given for each hydrologic feature. Program variables are listed and defined according to their occurrence in the main programs and in subroutines. Listings of the main programs and subroutines are given.

Rotman Lens Sidewall Design and Optimization with Hybrid Hardware/Software Based Programming

DTIC Science & Technology

2015-01-09

conventional MoM and stored in memory. The components of Zfar are computed as needed through a fast matrix vector multiplication ( MVM ), which...V vector. Iterative methods, e.g. BiCGSTAB, are employed for solving the linear equation. The matrix-vector multiplications ( MVMs ), which dominate...most of the computation in the solving phase, consists of calculating near and far MVMs . The far MVM comprises aggregation, translation, and

COST FUNCTION STUDIES FOR POWER REACTORS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heestand, J.; Wos, L.T.

1961-11-01

A function to evaluate the cost of electricity produced by a nuclear power reactor was developed. The basic equation, revenue = capital charges + profit + operating expenses, was expanded in terms of various cost parameters to enable analysis of multiregion nuclear reactors with uranium and/or plutonium for fuel. A corresponding IBM 704 computer program, which will compute either the price of electricity or the value of plutonium, is presented in detail. (auth)

Development and verification of real-time, hybrid computer simulation of F100-PW-100(3) turbofan engine

NASA Technical Reports Server (NTRS)

Szuch, J. R.; Seldner, K.; Cwynar, D. S.

1977-01-01

A real time, hybrid computer simulation of a turbofan engine is described. Controls research programs involving that engine are supported by the simulation. The real time simulation is shown to match the steady state and transient performance of the engine over a wide range of flight conditions and power settings. The simulation equations, FORTRAN listing, and analog patching diagrams are included.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David Michael

1997-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. The formulation uses the principle of virtual work. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are then derived after the application of several simplifying assumptions. These equations are then modified to allow the reference surface of the plate to be located at a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described as well. The terms of the plate stiffness matrix using both Classical Plate Theory (CPT) and first-order Shear-Deformation Plate Theory (SDPT) are presented. The necessary steps to include the effects of in-plane transverse and in-plane shear loads in the in-plane stability equations are also outlined. Numerical results are presented using the newly implemented capability. Comparisons of results for several example problems with different loading states are made. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPF are also made. Results comparing the computational effort required by the new analysis to that of the analysis currently in the VICONOPT program are presented. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

Computer model of two-dimensional solute transport and dispersion in ground water

USGS Publications Warehouse

Konikow, Leonard F.; Bredehoeft, J.D.

1978-01-01

This report presents a model that simulates solute transport in flowing ground water. The model is both general and flexible in that it can be applied to a wide range of problem types. It is applicable to one- or two-dimensional problems involving steady-state or transient flow. The model computes changes in concentration over time caused by the processes of convective transport, hydrodynamic dispersion, and mixing (or dilution) from fluid sources. The model assumes that the solute is non-reactive and that gradients of fluid density, viscosity, and temperature do not affect the velocity distribution. However, the aquifer may be heterogeneous and (or) anisotropic. The model couples the ground-water flow equation with the solute-transport equation. The digital computer program uses an alternating-direction implicit procedure to solve a finite-difference approximation to the ground-water flow equation, and it uses the method of characteristics to solve the solute-transport equation. The latter uses a particle- tracking procedure to represent convective transport and a two-step explicit procedure to solve a finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. This explicit procedure has several stability criteria, but the consequent time-step limitations are automatically determined by the program. The report includes a listing of the computer program, which is written in FORTRAN IV and contains about 2,000 lines. The model is based on a rectangular, block-centered, finite difference grid. It allows the specification of any number of injection or withdrawal wells and of spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, and initial heads and concentrations. The program also permits the designation of up to five nodes as observation points, for which a summary table of head and concentration versus time is printed at the end of the calculations. The data input formats for the model require three data cards and from seven to nine data sets to describe the aquifer properties, boundaries, and stresses. The accuracy of the model was evaluated for two idealized problems for which analytical solutions could be obtained. In the case of one-dimensional flow the agreement was nearly exact, but in the case of plane radial flow a small amount of numerical dispersion occurred. An analysis of several test problems indicates that the error in the mass balance will be generally less than 10 percent. The test problems demonstrated that the accuracy and precision of the numerical solution is sensitive to the initial number of particles placed in each cell and to the size of the time increment, as determined by the stability criteria. Mass balance errors are commonly the greatest during the first several time increments, but tend to decrease and stabilize with time.

SUMMARY OF EQUATIONS FOR EFFECT OF SHIP ATTITUDE AND SHIP MOTION ON PRIMARY COOLANT SYSTEM FLOW RATES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stevens, H.E. Jr.

1960-02-16

SYNFAR, the buckling, reflector saviags, flux, and reactivity segments of the pilot code, was assembled, checked out, and placed in production status. A reduction of 50% in the computation time required for SYNFAR was achieved through incorporation of a convergence acceleration technique. Modification of SYNFAR to perrait computation of dynamic flux and reactivity was raade and the option was prepared for checkout. Retails of the APWRC Error and Exit Diagnosis package and the APWRC Library Tape System are given. The latter was checked out except for the simultaneous tape shifting fuaction. Digitalization of basic cross section data was completed formore » fifteen materials. The portion of the Cross Section Data Program which converts the punched card data to magnetic tape form, interpolating as necessary to obtain data at 1001 energy levels, was completed and checked out. The Breit-Wigner Analysis Program, used with the Cross Section Data Program, was checked out. A listing of the Fortran source program, containing definitions of terms used, fiow diagrams, input data forms, and a sample caloulation is contained. The theory and equations developed to compute the scattering parametera, mu and xi , also used by the Croas Section Data Program, were developed. Checkout of the corresponding program, XIMU, was started. Theory and equations for computing an inelastic scattering matrix, for use with the Cross Section Data Program, were developed and a FORTRAN program for evaluating them was started. An aralysis of the results of the experimental program was started using SYNFAR. Multiplication factors for the two cores studied, Nos. 453 and 454, agreed with the experimental value of 1.00 within 0.6%. The experimental program on Core 454 was completed. Experiments performed were determination of temperature coefficient (--8.9 x 10/sup -5/ DELTA k/k per degree centigrade at 35 deg C), per cent fiasions by subcadmium neutrons (18%), intracell thermal flux measurements, and buckling measuremerts. Core 453 was assembled. The cold clean critical mass for this core was 17.5 kg of U/sup 235/ with 134.63 grams of natural boron in the core. A complete series of clean core experiments was performed on this core. Core 452 was also assembled. The critical mass for this core was 14.4 kg of U/sup 235/ with 83.14 grams of natural boron in the core. The critical experiment control rods were calibrated. Material and dimensional specifications of the homogeneous fuel elements were prepared. A number of saruple blocks containing powdered stainless steel and lucite was pressed. Improvements in the process are being made in an attempt to minimize dimensioral variations from block to block. (See also MND-E-2119.) (auth)« less

Decay of super-heavy particles: user guide of the SHdecay program

NASA Astrophysics Data System (ADS)

Barbot, C.

2004-02-01

I give here a detailed user guide for the C++ program SHdecay, which has been developed for computing the final spectra of stable particles (protons, photons, LSPs, electrons, neutrinos of the three species and their antiparticles) arising from the decay of a super-heavy X particle. It allows to compute in great detail the complete decay cascade for any given decay mode into particles of the Minimal Supersymmetric Standard Model (MSSM). In particular, it takes into account all interactions of the MSSM during the perturbative cascade (including not only QCD, but also the electroweak and 3rd generation Yukawa interactions), and includes a detailed treatment of the SUSY decay cascade (for a given set of parameters) and of the non-perturbative hadronization process. All these features allow us to ensure energy conservation over the whole cascade up to a numerical accuracy of a few per mille. Yet, this program also allows to restrict the computation to QCD or SUSY-QCD frameworks. I detail the input and output files, describe the role of each part of the program, and include some advice for using it best. Program summaryTitle of program: SHdecay Catalogue identifier:ADSL Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSL Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer and operating system: Program tested on PC running Linux KDE and Suse 8.1 Programming language used: C with STL C++ library and using the standard gnu g++ compiler No. lines in distributed program: 14 955 No. of bytes in distributed program, including test data, etc.: 624 487 Distribution format: tar gzip file Keywords: Super-heavy particles, fragmentation functions, DGLAP equations, supersymmetry, MSSM, UHECR Nature of physical problem: Obtaining the energy spectra of the final stable decay products (protons, photons, electrons, the three species of neutrinos and the LSPs) of a decaying super-heavy X particle, within the framework of the Minimal Supersymmetric Standard Model (MSSM). It can be done numerically by solving the full set of DGLAP equations in the MSSM for the perturbative evolution of the fragmentation functions Dp2p1( x, Q) of any particle p1 into any other p2 ( x is the energy fraction carried by the particle p2 and Q its virtuality), and by treating properly the different decay cascades of all unstable particles and the final hadronization of quarks and gluons. In order to obtain proper results at very low values of x (up to x˜10 -13), NLO color coherence effects have been included by using the Modified Leading Log Approximation (MLLA). Method of solution: the DGLAP equations are solved by a four order Runge-Kutta method with a fixed step. Typical running time: Around 35 hours for the first run, but the most time consuming sub-programs can be run only once for most applications.

TACT1- TRANSIENT THERMAL ANALYSIS OF A COOLED TURBINE BLADE OR VANE EQUIPPED WITH A COOLANT INSERT

NASA Technical Reports Server (NTRS)

Gaugler, R. E.

1994-01-01

As turbine-engine core operating conditions become more severe, designers must develop more effective means of cooling blades and vanes. In order to design reliable, cooled turbine blades, advanced transient thermal calculation techniques are required. The TACT1 computer program was developed to perform transient and steady-state heat-transfer and coolant-flow analyses for cooled blades, given the outside hot-gas boundary condition, the coolant inlet conditions, the geometry of the blade shell, and the cooling configuration. TACT1 can analyze turbine blades, or vanes, equipped with a central coolant-plenum insert from which coolant-air impinges on the inner surface of the blade shell. Coolant-side heat-transfer coefficients are calculated with the heat transfer mode at each station being user specified as either impingement with crossflow, forced convection channel flow, or forced convection over pin fins. A limited capability to handle film cooling is also available in the program. The TACT1 program solves for the blade temperature distribution using a transient energy equation for each node. The nodal energy balances are linearized, one-dimensional, heat-conduction equations which are applied at the wall-outer-surface node, at the junction of the cladding and the metal node, and at the wall-inner-surface node. At the mid-metal node a linear, three-dimensional, heat-conduction equation is used. Similarly, the coolant pressure distribution is determined by solving the set of transfer momentum equations for the one-dimensional flow between adjacent fluid nodes. In the coolant channel, energy and momentum equations for one-dimensional compressible flow, including friction and heat transfer, are used for the elemental channel length between two coolant nodes. The TACT1 program first obtains a steady-state solution using iterative calculations to obtain convergence of stable temperatures, pressures, coolant-flow split, and overall coolant mass balance. Transient calculations are based on the steady-state solutions obtained. Input to the TACT1 program includes a geometrical description of the blade and insert, the nodal spacing to be used, and the boundary conditions describing the outside hot-gas and the coolant-inlet conditions. The program output includes the value of nodal temperatures and pressures at each iteration. The final solution output includes the temperature at each coolant node, and the coolant flow rates and Reynolds numbers. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 computer with a central memory requirement of approximately 480K of 8 bit bytes. The TACT1 program was developed in 1978.

Airline return-on-investment model for technology evaluation. [computer program to measure economic value of advanced technology applied to passenger aircraft

NASA Technical Reports Server (NTRS)

1974-01-01

This report presents the derivation, description, and operating instructions for a computer program (TEKVAL) which measures the economic value of advanced technology features applied to long range commercial passenger aircraft. The program consists of three modules; and airplane sizing routine, a direct operating cost routine, and an airline return-on-investment routine. These modules are linked such that they may be operated sequentially or individually, with one routine generating the input for the next or with the option of externally specifying the input for either of the economic routines. A very simple airplane sizing technique was previously developed, based on the Brequet range equation. For this program, that sizing technique has been greatly expanded and combined with the formerly separate DOC and ROI programs to produce TEKVAL.

Predicting chemical degradation during storage from two successive concentration ratios: Theoretical investigation.

PubMed

Peleg, Micha; Normand, Mark D

2015-09-01

When a vitamin's, pigment's or other food component's chemical degradation follows a known fixed order kinetics, and its rate constant's temperature-dependence follows a two parameter model, then, at least theoretically, it is possible to extract these two parameters from two successive experimental concentration ratios determined during the food's non-isothermal storage. This requires numerical solution of two simultaneous equations, themselves the numerical solutions of two differential rate equations, with a program especially developed for the purpose. Once calculated, these parameters can be used to reconstruct the entire degradation curve for the particular temperature history and predict the degradation curves for other temperature histories. The concept and computation method were tested with simulated degradation under rising and/or falling oscillating temperature conditions, employing the exponential model to characterize the rate constant's temperature-dependence. In computer simulations, the method's predictions were robust against minor errors in the two concentration ratios. The program to do the calculations was posted as freeware on the Internet. The temperature profile can be entered as an algebraic expression that can include 'If' statements, or as an imported digitized time-temperature data file, to be converted into an Interpolating Function by the program. The numerical solution of the two simultaneous equations requires close initial guesses of the exponential model's parameters. Programs were devised to obtain these initial values by matching the two experimental concentration ratios with a generated degradation curve whose parameters can be varied manually with sliders on the screen. These programs too were made available as freeware on the Internet and were tested with published data on vitamin A. Copyright © 2015 Elsevier Ltd. All rights reserved.

MPPhys—A many-particle simulation package for computational physics education

NASA Astrophysics Data System (ADS)

Müller, Thomas

2014-03-01

In a first course to classical mechanics elementary physical processes like elastic two-body collisions, the mass-spring model, or the gravitational two-body problem are discussed in detail. The continuation to many-body systems, however, is deferred to graduate courses although the underlying equations of motion are essentially the same and although there is a strong motivation for high-school students in particular because of the use of particle systems in computer games. The missing link between the simple and the more complex problem is a basic introduction to solve the equations of motion numerically which could be illustrated, however, by means of the Euler method. The many-particle physics simulation package MPPhys offers a platform to experiment with simple particle simulations. The aim is to give a principle idea how to implement many-particle simulations and how simulation and visualization can be combined for interactive visual explorations. Catalogue identifier: AERR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERR_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 111327 No. of bytes in distributed program, including test data, etc.: 608411 Distribution format: tar.gz Programming language: C++, OpenGL, GLSL, OpenCL. Computer: Linux and Windows platforms with OpenGL support. Operating system: Linux and Windows. RAM: Source Code 4.5 MB Complete package 242 MB Classification: 14, 16.9. External routines: OpenGL, OpenCL Nature of problem: Integrate N-body simulations, mass-spring models Solution method: Numerical integration of N-body-simulations, 3D-Rendering via OpenGL. Running time: Problem dependent

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Predation.

ERIC Educational Resources Information Center

Spain, James D.; Soldan, Theodore

1983-01-01

Describes two computer simulations of the predator-prey interaction in which students explore theories and mathematical equations involved in this biological process. The programs (for Apple II), designed for college level ecology, may be used in lecture/demonstrations or as a basis for laboratory assignments. A list of student objectives is…

An integral-equation solution for TE radiation and scattering from conducting cylinders

NASA Technical Reports Server (NTRS)

Richmond, J. H.

1973-01-01

The piecewise-sinusoidal reaction technique is applied to low frequency radiation and scattering from noncircular cylinders with perfect or imperfect conductivity. This report presents the theory, computer programs and numerical results for these two-dimensional problems with the TE polarization.

Computing Flows Using Chimera and Unstructured Grids

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Zheng, Yao

2006-01-01

DRAGONFLOW is a computer program that solves the Navier-Stokes equations of flows in complexly shaped three-dimensional regions discretized by use of a direct replacement of arbitrary grid overlapping by nonstructured (DRAGON) grid. A DRAGON grid (see figure) is a combination of a chimera grid (a composite of structured subgrids) and a collection of unstructured subgrids. DRAGONFLOW incorporates modified versions of two prior Navier-Stokes-equation-solving programs: OVERFLOW, which is designed to solve on chimera grids; and USM3D, which is used to solve on unstructured grids. A master module controls the invocation of individual modules in the libraries. At each time step of a simulated flow, DRAGONFLOW is invoked on the chimera portion of the DRAGON grid in alternation with USM3D, which is invoked on the unstructured subgrids of the DRAGON grid. The USM3D and OVERFLOW modules then immediately exchange their solutions and other data. As a result, USM3D and OVERFLOW are coupled seamlessly.

Prediction and verification of creep behavior in metallic materials and components for the space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Davis, J. W.; Cramer, B. A.

1976-01-01

A method of analysis was developed for predicting permanent cyclic creep deflections in stiffened panel structures. This method uses creep equations based on cyclic tensile creep tests and a computer program to predict panel deflections as a function of mission cycle. Four materials were investigated - a titanium alloy (Ti-6Al-4V), a cobalt alloy (L605), and two nickel alloys (Rene'41 and TDNiCr). Steady-state and cyclic creep response data were obtained by testing tensile specimens fabricated from thin gage sheet (0.025 and 0.63 cm nominal). Steady-state and cyclic creep equations were developed which describe creep as a function of time, temperature and load. Tests were also performed on subsize (6.35 x 30.5 cm) rib and corrugation stiffened panels. These tests were used to correlate creep responses between elemental specimens and panels. The panel response was analyzed by use of a specially written computer program.

Development of automatic and manual flight director landing systems for the XV-15 tilt rotor aircraft in helicopter mode

NASA Technical Reports Server (NTRS)

Hofmann, L. G.; Hoh, R. H.; Jewell, W. F.; Teper, G. L.; Patel, P. D.

1978-01-01

The objective of this effort is to determine IFR approach path and touchdown dispersions for manual and automatic XV-15 tilt rotor landings, and to develop missed approach criteria. Only helicopter mode XV-15 operation is considered. The analysis and design sections develop the automatic and flight director guidance equations for decelerating curved and straight-in approaches into a typical VTOL landing site equipped with an MLS navigation aid. These system designs satisfy all known pilot-centered, guidance and control requirements for this flying task. Performance data, obtained from nonstationary covariance propagation dispersion analysis for the system, are used to develop the approach monitoring criteria. The autoland and flight director guidance equations are programmed for the VSTOLAND 1819B digital computer. The system design dispersion data developed through analysis and the 1819B digital computer program are verified and refined using the fixed-base, man-in-the-loop XV-15 VSTOLAND simulation.

CAS2D: FORTRAN program for nonrotating blade-to-blade, steady, potential transonic cascade flows

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

An exact, full-potential-equation (FPE) model for the steady, irrotational, homentropic and homoenergetic flow of a compressible, homocompositional, inviscid fluid through two dimensional planar cascades of airfoils was derived, together with its appropriate boundary conditions. A computer program, CAS2D, was developed that numerically solves an artificially time-dependent form of the actual FPE. The governing equation was discretized by using type-dependent, rotated finite differencing and the finite area technique. The flow field was discretized by providing a boundary-fitted, nonuniform computational mesh. The mesh was generated by using a sequence of conforming mapping, nonorthogonal coordinate stretching, and local, isoparametric, bilinear mapping functions. The discretized form of the FPE was solved iteratively by using successive line overrelaxation. The possible isentropic shocks were correctly captured by adding explicitly an artificial viscosity in a conservative form. In addition, a three-level consecutive, mesh refinement feature makes CAS2D a reliable and fast algorithm for the analysis of transonic, two dimensional cascade flows.

CrasyDSE: A framework for solving Dyson-Schwinger equations.

PubMed

Huber, Markus Q; Mitter, Mario

2012-11-01

Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quantum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automating parts of the calculations will certainly be helpful in future investigations. In this article we present a framework for such an automation based on a C++ code that can deal with a large number of Green functions. Since also the creation of the expressions for the integrals of the Dyson-Schwinger equations needs to be automated, we defer this task to a Mathematica notebook. We illustrate the complete workflow with an example from Yang-Mills theory coupled to a fundamental scalar field that has been investigated recently. As a second example we calculate the propagators of pure Yang-Mills theory. Our code can serve as a basis for many further investigations where the equations are too complicated to tackle by hand. It also can easily be combined with DoFun , a program for the derivation of Dyson-Schwinger equations. Program title : CrasyDSE Catalogue identifier : AEMY _v1_0 Program summary URL : http://cpc.cs.qub.ac.uk/summaries/AEMY_v1_0.html Program obtainable from : CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions : Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc. : 49030 No. of bytes in distributed program, including test data, etc. : 303958 Distribution format : tar.gz Programming language : Mathematica 8 and higher, C++ . Computer : All on which Mathematica and C++ are available. Operating system : All on which Mathematica and C++ are available (Windows, Unix, Mac OS). Classification : 11.1, 11.4, 11.5, 11.6. Nature of problem : Solve (large) systems of Dyson-Schwinger equations numerically. Solution method : Create C++ functions in Mathematica to be used for the numeric code in C++ . This code uses structures to handle large numbers of Green functions. Unusual features : Provides a tool to convert Mathematica expressions into C++ expressions including conversion of function names. Running time : Depending on the complexity of the investigated system solving the equations numerically can take seconds on a desktop PC to hours on a cluster.

HELAC-PHEGAS: A generator for all parton level processes

NASA Astrophysics Data System (ADS)

Cafarella, Alessandro; Papadopoulos, Costas G.; Worek, Malgorzata

2009-10-01

The updated version of the HELAC-PHEGAS event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations using color connection representation. Phase-space generation is based on a multichannel approach, including optimization. HELAC-PHEGAS generates parton level events with all necessary information, in the most recent Les Houches Accord format, for the study of any process within the Standard Model in hadron and lepton colliders. New version program summaryProgram title: HELAC-PHEGAS Catalogue identifier: ADMS_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADMS_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 35 986 No. of bytes in distributed program, including test data, etc.: 380 214 Distribution format: tar.gz Programming language: Fortran Computer: All Operating system: Linux Classification: 11.1, 11.2 External routines: Optionally Les Houches Accord (LHA) PDF Interface library ( http://projects.hepforge.org/lhapdf/) Catalogue identifier of previous version: ADMS_v1_0 Journal reference of previous version: Comput. Phys. Comm. 132 (2000) 306 Does the new version supersede the previous version?: Yes, partly Nature of problem: One of the most striking features of final states in current and future colliders is the large number of events with several jets. Being able to predict their features is essential. To achieve this, the calculations need to describe as accurately as possible the full matrix elements for the underlying hard processes. Even at leading order, perturbation theory based on Feynman graphs runs into computational problems, since the number of graphs contributing to the amplitude grows as n!. Solution method: Recursive algorithms based on Dyson-Schwinger equations have been developed recently in order to overcome the computational obstacles. The calculation of the amplitude, using Dyson-Schwinger recursive equations, results in a computational cost growing asymptotically as 3 n, where n is the number of particles involved in the process. Off-shell subamplitudes are introduced, for which a recursion relation has been obtained allowing to express an n-particle amplitude in terms of subamplitudes, with 1-, 2-, … up to (n-1) particles. The color connection representation is used in order to treat amplitudes involving colored particles. In the present version HELAC-PHEGAS can be used to efficiently obtain helicity amplitudes, total cross sections, parton-level event samples in LHA format, for arbitrary multiparticle processes in the Standard Model in leptonic, pp¯ and pp collisions. Reasons for new version: Substantial improvements, major functionality upgrade. Summary of revisions: Color connection representation, efficient integration over PDF via the PARNI algorithm, interface to LHAPDF, parton level events generated in the most recent LHA format, k reweighting for Parton Shower matching, numerical predictions for amplitudes for arbitrary processes for phase-space points provided by the user, new user interface and the possibility to run over computer clusters. Running time: Depending on the process studied. Usually from seconds to hours. References:A. Kanaki, C.G. Papadopoulos, Comput. Phys. Comm. 132 (2000) 306. C.G. Papadopoulos, Comput. Phys. Comm. 137 (2001) 247. URL: http://www.cern.ch/helac-phegas.

The method of complex characteristics for design of transonic blade sections

NASA Technical Reports Server (NTRS)

Bledsoe, M. R.

1986-01-01

A variety of computational methods were developed to obtain shockless or near shockless flow past two-dimensional airfoils. The approach used was the method of complex characteristics, which determines smooth solutions to the transonic flow equations based on an input speed distribution. General results from fluid mechanics are presented. An account of the method of complex characteristics is given including a description of the particular spaces and coordinates, conformal transformations, and numerical procedures that are used. The operation of the computer program COMPRES is presented along with examples of blade sections designed with the code. A user manual is included with a glossary to provide additional information which may be helpful. The computer program in Fortran, including numerous comment cards is listed.

An explicit mixed numerical method for mesoscale model

NASA Technical Reports Server (NTRS)

Hsu, H.-M.

1981-01-01

A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.

Transonic flow analysis for rotors. Part 3: Three-dimensional, quasi-steady, Euler calculation

NASA Technical Reports Server (NTRS)

Chang, I-Chung

1990-01-01

A new method is presented for calculating the quasi-steady transonic flow over a lifting or non-lifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with published experimental data.

Unsteady transonic flow analysis for low aspect ratio, pointed wings.

NASA Technical Reports Server (NTRS)

Kimble, K. R.; Ruo, S. Y.; Wu, J. M.; Liu, D. Y.

1973-01-01

Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flow field. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms.

Analytical approach to peel stresses in bonded composite stiffened panels

NASA Technical Reports Server (NTRS)

Barkey, Derek A.; Madan, Ram C.; Sutton, Jason O.

1987-01-01

A closed-form solution was obtained for the stresses and displacements of two bonded beams. A system of two fourth-order and two second-order differential equations with the associated boundary equations was determined using a variational work approach. A FORTRAN computer program was devised to solve for the eigenvalues and eigenvectors of this system and to calculate the coefficients from the boundary conditions. The results were then compared with NASTRAN finite-element solutions and shown to agree closely.

Numerical analysis and FORTRAN program for the computation of the turbulent wakes of turbomachinery rotor blades, isolated airfoils and cascade of airfoils. Final Report - Ph.D. Thesis Mar. 1980

NASA Technical Reports Server (NTRS)

Hah, C.; Lakshminarayana, B.

1982-01-01

Turbulent wakes of turbomachinery rotor blades, isolated airfoils, and a cascade of airfoils were investigated both numerically and experimentally. Low subsonic and incompressible wake flows were examined. A finite difference procedure was employed in the numerical analysis utilizing the continuity, momentum, and turbulence closure equations in the rotating, curvilinear, and nonorthogonal coordinate system. A nonorthogonal curvilinear coordinate system was developed to improve the accuracy and efficiency of the numerical calculation. Three turbulence models were employed to obtain closure of the governing equations. The first model was comprised to transport equations for the turbulent kinetic energy and the rate of energy dissipation, and the second and third models were comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, respectively. The second model handles the convection and diffusion terms in the Reynolds stress transport equation collectively, while the third model handles them individually. The numerical results demonstrate that the second and third models provide accurate predictions, but the computer time and memory storage can be considerably saved with the second model.

Rapid Aeroelastic Analysis of Blade Flutter in Turbomachines

NASA Technical Reports Server (NTRS)

Trudell, J. J.; Mehmed, O.; Stefko, G. L.; Bakhle, M. A.; Reddy, T. S. R.; Montgomery, M.; Verdon, J.

2006-01-01

The LINFLUX-AE computer code predicts flutter and forced responses of blades and vanes in turbomachines under subsonic, transonic, and supersonic flow conditions. The code solves the Euler equations of unsteady flow in a blade passage under the assumption that the blades vibrate harmonically at small amplitudes. The steady-state nonlinear Euler equations are solved by a separate program, then equations for unsteady flow components are obtained through linearization around the steady-state solution. A structural-dynamics analysis (see figure) is performed to determine the frequencies and mode shapes of blade vibrations, a preprocessor interpolates mode shapes from the structural-dynamics mesh onto the LINFLUX computational-fluid-dynamics mesh, and an interface code is used to convert the steady-state flow solution to a form required by LINFLUX. Then LINFLUX solves the linearized equations in the frequency domain to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. A post-processor uses the unsteady pressures to calculate generalized aerodynamic forces, response amplitudes, and eigenvalues (which determine the flutter frequency and damping). In comparison with the TURBO-AE aeroelastic-analysis code, which solves the equations in the time domain, LINFLUX-AE is 6 to 7 times faster.

Computer program for analysis of coupled-cavity traveling wave tubes

NASA Technical Reports Server (NTRS)

Connolly, D. J.; Omalley, T. A.

1977-01-01

A flexible, accurate, large signal computer program was developed for the design of coupled cavity traveling wave tubes. The program is written in FORTRAN IV for an IBM 360/67 time sharing system. The beam is described by a disk model and the slow wave structure by a sequence of cavities, or cells. The computational approach is arranged so that each cavity may have geometrical or electrical parameters different from those of its neighbors. This allows the program user to simulate a tube of almost arbitrary complexity. Input and output couplers, severs, complicated velocity tapers, and other features peculiar to one or a few cavities may be modeled by a correct choice of input data. The beam-wave interaction is handled by an approach in which the radio frequency fields are expanded in solutions to the transverse magnetic wave equation. All significant space harmonics are retained. The program was used to perform a design study of the traveling-wave tube developed for the Communications Technology Satellite. Good agreement was obtained between the predictions of the program and the measured performance of the flight tube.

Computer prediction of three-dimensional potential flow fields in which aircraft propellers operate. M.S. Thesis

NASA Technical Reports Server (NTRS)

Jumper, S. J.

1982-01-01

A computer program was developed to calculate the three dimensional, steady, incompressible, inviscid, irrotational flow field at the propeller plane (propeller removed) located upstream of an arbitrary airframe geometry. The program uses a horseshoe vortex of known strength to model the wing. All other airframe surfaces are modeled by a network source panels of unknown strength which is exposed to a uniform free stream and the wing-induced velocity field. By satisfying boundary conditions on each panel (the Neumann problem), relaxed boundary conditions being used on certain panels to simulate inlet inflow, the source strengths are determined. From the known source and wing vortex strengths, the resulting velocity fields on the airframe surface and at the propeller plane are obtained. All program equations are derived in detail, and a brief description of the program structure is presented. A user's manual which fully documents the program is cited. Computer predictions of the flow on the surface of a sphere and at a propeller plane upstream of the sphere are compared with the exact mathematical solutions. Agreement is good, and correct program operation is verified.

ADPAC v1.0: User's Manual

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Heidegger, Nathan J.; Delaney, Robert A.

1999-01-01

The overall objective of this study was to evaluate the effects of turbulence models in a 3-D numerical analysis on the wake prediction capability. The current version of the computer code resulting from this study is referred to as ADPAC v7 (Advanced Ducted Propfan Analysis Codes -Version 7). This report is intended to serve as a computer program user's manual for the ADPAC code used and modified under Task 15 of NASA Contract NAS3-27394. The ADPAC program is based on a flexible multiple-block and discretization scheme permitting coupled 2-D/3-D mesh block solutions with application to a wide variety of geometries. Aerodynamic calculations are based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. Steady flow predictions are accelerated by a multigrid procedure. Turbulence models now available in the ADPAC code are: a simple mixing-length model, the algebraic Baldwin-Lomax model with user defined coefficients, the one-equation Spalart-Allmaras model, and a two-equation k-R model. The consolidated ADPAC code is capable of executing in either a serial or parallel computing mode from a single source code.

Multiple regression technique for Pth degree polynominals with and without linear cross products

NASA Technical Reports Server (NTRS)

Davis, J. W.

1973-01-01

A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent analysis. To implement this technique, separate computer programs were developed for the case without linear cross products and for the case incorporating such cross products which evaluate the various constants in the model regression equation. In addition, the significance of the estimated regression equation is considered and the standard deviation, the F statistic, the maximum absolute percent error, and the average of the absolute values of the percent of error evaluated. The computer programs and their manner of utilization are described. Sample problems are included to illustrate the use and capability of the technique which show the output formats and typical plots comparing computer results to each set of input data.

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, E. F.

1974-01-01

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Langtangen, Hans Petter; Wells, Garth N.

2011-09-01

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model.

Magnetic dipole moment determination by near-field analysis

NASA Technical Reports Server (NTRS)

Eichhorn, W. L.

1972-01-01

A method for determining the magnetic moment of a spacecraft from magnetic field data taken in a limited region of space close to the spacecraft. The spacecraft's magnetic field equations are derived from first principles. With measurements of this field restricted to certain points in space, the near-field equations for the spacecraft are derived. These equations are solved for the dipole moment by a least squares procedure. A method by which one can estimate the magnitude of the error in the calculations is also presented. This technique was thoroughly tested on a computer. The test program is described and evaluated, and partial results are presented.

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

NASA automatic system for computer program documentation, volume 2

NASA Technical Reports Server (NTRS)

Simmons, D. B.

1972-01-01

The DYNASOR 2 program is used for the dynamic nonlinear analysis of shells of revolution. The equations of motion of the shell are solved using Houbolt's numerical procedure. The displacements and stress resultants are determined for both symmetrical and asymmetrical loading conditions. Asymmetrical dynamic buckling can be investigated. Solutions can be obtained for highly nonlinear problems utilizing as many as five of the harmonics generated by SAMMSOR program. A restart capability allows the user to restart the program at a specified time. For Vol. 1, see N73-22129.

Combustion of hydrogen injected into a supersonic airstream (the SHIP computer program)

NASA Technical Reports Server (NTRS)

Markatos, N. C.; Spalding, D. B.; Tatchell, D. G.

1977-01-01

The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. The computer time required for a given case is approximately 1 minute on a CDC 7600 machine. A discussion of the assumption of parabolic flow in the injection region is given which suggests that improvement in calculation in this region could be obtained by use of the partially parabolic procedure of Pratap and Spalding. It is concluded that the technique described herein provides the basis for an efficient and reliable means for predicting the effects of hydrogen injection into supersonic airstreams and of its subsequent combustion.

A Digital Program for Calculating the Interaction Between Flexible Structures, Unsteady Aerodynamics and Active Controls

NASA Technical Reports Server (NTRS)

Peele, E. L.; Adams, W. M., Jr.

1979-01-01

A computer program, ISAC, is described which calculates the stability and response of a flexible airplane equipped with active controls. The equations of motion relative to a fixed inertial coordinate system are formulated in terms of the airplane's rigid body motion and its unrestrained normal vibration modes. Unsteady aerodynamic forces are derived from a doublet lattice lifting surface theory. The theoretical basis for the program is briefly explained together with a description of input data and output results.

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. User's manual

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

The TranAir computer program calculates transonic flow about arbitrary configurations at subsonic, transonic, and supersonic freestream Mach numbers. TranAir solves the nonlinear full potential equations subject to a variety of boundary conditions modeling wakes, inlets, exhausts, porous walls, and impermeable surfaces. Regions with different total temperature and pressure can be represented. The user's manual describes how to run the TranAir program and its graphical support programs.

GEOSURF: a computer program for modeling adsorption on mineral surfaces from aqueous solution

NASA Astrophysics Data System (ADS)

Sahai, Nita; Sverjensky, Dimitri A.

1998-11-01

A new program, GEOSURF, has been developed for calculating aqueous and surface speciation consistent with the triple-layer model of surface complexation. GEOSURF is an extension of the original programs MINEQL, MICROQL and HYDRAQL. We present, here, the basic algorithm of GEOSURF along with a description of the new features implemented. GEOSURF is linked to internally consistent data bases for surface species (SURFK.DAT) and for aqueous species (AQSOL.DAT). SURFK.DAT contains properties of minerals such as site densities, and equilibrium constants for adsorption of aqueous protons and electrolyte ions on a variety of oxides and hydroxides. The Helgeson, Kirkham and Flowers version of the extended Debye-Huckel Equation for 1:1 electrolytes is implemented for calculating aqueous activity coefficients. This permits the calculation of speciation at ionic strengths greater than 0.5 M. The activity of water is computed explicitly from the osmotic coefficient of the solution, and the total amount of electrolyte cation (or anion) is adjusted to satisfy the electroneutrality condition. Finally, the use of standard symbols for chemical species rather than species identification numbers is included to facilitate use of the program. One of the main limitations of GEOSURF is that aqueous and surface speciation can only be calculated at fixed pH and at fixed concentration of total adsorbate. Thus, the program cannot perform reaction-path calculations: it cannot determine whether or not a solution is over- or under-saturated with respect to one or more solid phases. To check the proper running of GEOSURF, we have compared results generated by GEOSURF with those from two other programs, HYDRAQL and EQ3. The Davies equation and the "bdot" equation, respectively, are used in the latter two programs for calculating aqueous activity coefficients. An example of the model fit to experimental data for rutile in 0.001 M-2.0 M NaNO 3 is included.

Finding higher symmetries of differential equations using the MAPLE package DESOLVII

NASA Astrophysics Data System (ADS)

Vu, K. T.; Jefferson, G. F.; Carminati, J.

2012-04-01

We present and describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade of DESOLV. DESOLVII now includes new routines allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary and partial differential equations. Catalogue identifier: ADYZ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYZ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 858 No. of bytes in distributed program, including test data, etc.: 112 515 Distribution format: tar.gz Programming language: MAPLE internal language Computer: PCs and workstations Operating system: Linux, Windows XP and Windows 7 RAM: Depends on the type of problem and the complexity of the system (small ≈ MB, large ≈ GB) Classification: 4.3, 5 Catalogue identifier of previous version: ADYZ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 682 Does the new version supersede the previous version?: Yes Nature of problem: There are a number of approaches one may use to find solutions to systems of differential equations. These include numerical, perturbative, and algebraic methods. Unfortunately, approximate or numerical solution methods may be inappropriate in many cases or even impossible due to the nature of the system and hence exact methods are important. In their own right, exact solutions are valuable not only as a yardstick for approximate/numerical solutions but also as a means of elucidating the physical meaning of fundamental quantities in systems. One particular method of finding special exact solutions is afforded by the work of Sophus Lie and the use of continuous transformation groups. The power of Lie's group theoretic method lies in its ability to unify a number of ad hoc integration methods through the use of symmetries, that is, continuous groups of transformations which leave the differential system “unchanged”. These symmetry groups may then be used to find special solutions. Solutions found in this manner are called similarity or invariant solutions. The method of finding symmetry transformations initially requires the generation of a large overdetermined system of linear, homogeneous, coupled PDEs. The integration of this system is usually reasonably straightforward requiring the (often elementary) integration of equations by splitting the system according to dependency on different orders and degrees of the dependent variable/s. Unfortunately, in the case of contact and Lie-Bäcklund symmetries, the integration of the determining system becomes increasingly more difficult as the order of the symmetry is increased. This is because the symmetry generating functions become dependent on higher orders of the derivatives of the dependent variables and this diminishes the overall resulting “separable” differential conditions derived from the main determining system. Furthermore, typical determining systems consist of tens to hundreds of equations and this, combined with standard mechanical solution methods, makes the process well suited to automation using computer algebra systems. The new MAPLE package DESOLVII, which is a major upgrade of DESOLV, now includes routines allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary and partial differential equations. In addition, significant improvements have been implemented to the algorithm for PDE solution. Finally, we have made some improvements in the overall automated process so as to improve user friendliness by reducing user intervention where possible. Solution method: See “Nature of problem” above. Reasons for new version: New and improved functionality. New functionality - can now compute generalised symmetries. Much improved efficiency (speed and memory use) of existing routines. Restrictions: Sufficient memory may be required for complex systems. Running time: Depends on the type of problem and the complexity of the system (small ≈ seconds, large ≈ hours).

Thermohydrodynamic Analysis of Cryogenic Liquid Turbulent Flow Fluid Film Bearings

NASA Technical Reports Server (NTRS)

SanAndres, Luis

1996-01-01

Computational programs developed for the thermal analysis of tilting and flexure-pad hybrid bearings, and the unsteady flow and transient response of a point mass rotor supported on fluid film bearings are described. The motion of a cryogenic liquid on the thin film annular region of a fluid film bearing is described by a set of mass and momentum conservation, and energy transport equations for the turbulent bulk-flow velocities and pressure, and accompanied by thermophysical state equations for evaluation of the fluid material properties. Zeroth-order equations describe the fluid flow field for a journal static equilibrium position, while first-order (linear) equations govern the fluid flow for small amplitude-journal center translational motions. Solution to the zeroth-order flow field equations provides the bearing flow rate, load capacity, drag torque and temperature rise. Solution to the first-order equations determines the rotordynamic force coefficients due to journal radial motions.

Computational strategies in the dynamic simulation of constrained flexible MBS

NASA Technical Reports Server (NTRS)

Amirouche, F. M. L.; Xie, M.

1993-01-01

This research focuses on the computational dynamics of flexible constrained multibody systems. At first a recursive mapping formulation of the kinematical expressions in a minimum dimension as well as the matrix representation of the equations of motion are presented. The method employs Kane's equation, FEM, and concepts of continuum mechanics. The generalized active forces are extended to include the effects of high temperature conditions, such as creep, thermal stress, and elastic-plastic deformation. The time variant constraint relations for rolling/contact conditions between two flexible bodies are also studied. The constraints for validation of MBS simulation of gear meshing contact using a modified Timoshenko beam theory are also presented. The last part deals with minimization of vibration/deformation of the elastic beam in multibody systems making use of time variant boundary conditions. The above methodologies and computational procedures developed are being implemented in a program called DYAMUS.

Computer program /P1-GAS/ calculates the P-0 and P-1 transfer matrices for neutron moderation in a monatomic gas

NASA Technical Reports Server (NTRS)

Collier, G.; Gibson, G.

1968-01-01

FORTRAN 4 program /P1-GAS/ calculates the P-O and P-1 transfer matrices for neutron moderation in a monatomic gas. The equations used are based on the conditions that there is isotropic scattering in the center-of-mass coordinate system, the scattering cross section is constant, and the target nuclear velocities satisfy a Maxwellian distribution.

Attitude dynamic of spin-stabilized satellites with flexible appendages

NASA Technical Reports Server (NTRS)

Renard, M. L.

1973-01-01

Equations of motion and computer programs have been developed for analyzing the motion of a spin-stabilized spacecraft having long, flexible appendages. Stability charts were derived, or can be redrawn with the desired accuracy for any particular set of design parameters. Simulation graphs of variables of interest are readily obtainable on line using program FLEXAT. Finally, applications to actual satellites, such as UK-4 and IMP-1 have been considered.

An Investigation of the Reacting and Non-Reacting Flow Characteristics of Solid Fuel Ramjets.

DTIC Science & Technology

1980-09-01

which was run on the IBM-360 computer at the Naval 23 Postgraduate School. Programs for Texas Instruments TI - 59 programmable calculator were utilized...Pc’ F P A e 12 = g(y+l) F + PA e-TT 2(R F (9) lil Equations 7, 8, and 9 were solved for each run by software programs written for the TI - 59 programmable calculator . The

Adjustment technique without explicit formation of normal equations /conjugate gradient method/

NASA Technical Reports Server (NTRS)

Saxena, N. K.

1974-01-01

For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

Effects of Turbulence Model on Prediction of Hot-Gas Lateral Jet Interaction in a Supersonic Crossflow

DTIC Science & Technology

2015-07-01

performance computing time from the US Department of Defense (DOD) High Performance Computing Modernization program at the US Army Research Laboratory...Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time ...dimensional, compressible, Reynolds-averaged Navier-Stokes (RANS) equations are solved using a finite volume method. A point-implicit time - integration