Numerical Control Machine Data Manual
Numerical Control Machine Data Manual provides programmers with specific information for various types and sizes of numerical control machine tools and auxiliary equipment.
Mackey, R. T., Sr.↗
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Numerical inversion of finite Toeplitz matrices and vector Toeplitz matrices
Numerical technique increases the efficiencies of the numerical methods involving Toeplitz matrices by reducing the number of multiplications required by an N-order Toeplitz matrix from N-cubed to N-squared multiplications. Some efficient algorithms are given.
Bareiss, E. H.↗
Numerical solutions of differential equations
Various numerical methods for solving differential equations were analyzed and refined in an effort to develop a method which was adaptable to a large class of problems. The prime capabilities of the method included accuracy, numerical stability, and economic use of computer time. In multistep processes the corrector was changed at each step.
Wesson, J. R.↗
Numerical integration in a rigid-body trajectory program
Comparison of fourth order Runge-Kutta numerical integration technique with two numerical integration formulas in mathematical models used for computing rigid body trajectories
Moore, J. E.↗
A numerical method for computing three dimensional viscous supersonic flow fields about slender bodies
A numerical method is presented for the calculation of steady, three-dimensional, viscous, compressible flow fields about slender bodies at angle of attack and at supersonic speeds. Approximations are introduced in modeling the flow in the longitudinal direction. Accordingly, the flow fields calculated with the program were computed with a model that permits viscous crossflow together with inviscid axial flow. An analysis of the errors introduced by such a treatment is presented. Numerical calculations were made and compared with experimental results for an ogive-cylinder and an airplane fuselage configuration. Generally, good agreement with experiment was obtained. However, boundary layer separation and body vortex positions differed from experimental locations on the ogive-cylinder, and the shock induced by the fuselage canopy was predicted at a slightly different location.
Walitt, L.↗
Flow field analysis of aircraft configurations using a numerical solution to the three-dimensional unified supersonic/hypersonic small disturbance equations, part 1
The unified small disturbance equations are numerically solved using the well-known Lax-Wendroff finite difference technique. The method allows complete determination of the inviscid flow field and surface properties as long as the flow remains supersonic. Shock waves and other discontinuities are accounted for implicity in the numerical method. This technique was programed for general application to the three-dimensional case. The validity of the method is demonstrated by calculations on cones, axisymmetric bodies, lifting bodies, delta wings, and a conical wing/body combination. Part 1 contains the discussion of problem development and results of the study. Part 2 contains flow charts, subroutine descriptions, and a listing of the computer program.
Gunness, R. C., Jr.↗
Numerical solution of flowfields behind rectangular wings
The numerical solution of flow fields behind rectangular wings is described. Subjects discussed are: (1) evaluation of various differencing methods applied to the hyperbolic partial differential equations encountered in gas dynamics, (2) application of the numerical differencing techniques to the wedge flow, two dimensional shock reflection for the three dimensional finite thickness wing at zero degrees angle of attack, and (3) calculation of preliminary results for wedge flows using optimum differencing methods.
Anderson, D.↗
A direct numerical method for predicting concentration profiles in a turbulent boundary layer over a flat plate
A numerical solution of the turbulent mass transport equation utilizing the concept of eddy diffusivity is presented as an efficient method of investigating turbulent mass transport in boundary layer type flows. A FORTRAN computer program is used to study the two-dimensional diffusion of ammonia, from a line source on the surface, into a turbulent boundary layer over a flat plate. The results of the numerical solution are compared with experimental data to verify the results of the solution. Several other solutions to diffusion problems are presented to illustrate the versatility of the computer program and to provide some insight into the problem of mass diffusion as a whole.
Dow, J. W.↗
Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner
Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.
Carter, J. E.↗
Some three-body numerical solutions for low-thrust orbiter missions.
A ?velocity at the sphere of influence' method and an asymptotic matching method of patching together two-body low thrust solutions are compared to a number of three-body numerical results for outer planet orbiter missions. The two patching methods compare well with the numerical three-body results and do not depend on any particular choice for the size of the sphere of influence. The results apply, in a strict sense, only to the operational mode used-high-thrust terminal retro into orbit. Low-thrust spirals are not considered in the three-body analysis. The terminal low-thrust phase of thrusting is almost entirely reverse to the velocity vector during the planet centered phase of the trajectory. This may lead to important simplifications for low-thrust guidance and navigation procedures.
Mackay, J. S.↗
Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.
Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.
Lancaster, J. E.↗
A numerical algorithm suggested by problems of transport in periodic media - The matrix case.
Extension of Allen and Wing's (1970) previous work on problems of transport in periodic media to the matrix case. A method in the form of a complete set of equations is presented that may be used without any further analytical work by investigators interested in computing solutions to problems of the type the method is designed to handle. All the formulas have been checked out numerically, and their effectiveness is demonstrated by numerical examples.
Allen, R. C., Jr.↗
Tests of a procedure for inserting satellite radiance measurements into a numerical circulation model.
Description of experiments designed to test the sensitivity of a new method for retrieving vertical temperature profiles from satellite radiance measurements to the initial guess of temperature distribution. Emphasis is placed on initial guesses of the kind that would be provided by a numerical model of the atmospheric circulation, with the objective of developing a procedure for direct use of satellite radiation measurements as input to a numerical forecasting scheme.
Hogan, J. S.↗
A Numerical Analysis of the Transient Response of an Ablation System Including Effects of Thermal Nonequilibrium, Mass Transfer and Chemical Kinetics
The differential equations governing the transient response of a one-dimensional ablative thermal protection system undergoing stagnation ablation are derived. These equations are for thermal nonequilibrium effects between the pyrolysis gases and the char layer and kinetically controlled chemical reactions and mass transfer between the pyrolysis gases and the char layer. The boundary conditions are written for the particular case of stagnation heating with surface removal by oxidation or sublimation and pyrolysis of the uncharred layer occurring in a plane. The governing equations and boundary conditions are solved numerically using the modified implicit method (Crank-Nicolson method). Numerical results are compared with exact solutions for a number of simplified cases. The comparison is favorable in each instance.
Clark, R. K.↗
A field investigation and numerical simulation of coastal fog
A field investigation of the microphysical and micrometeorological features of fogs occurring near Los Angeles and Vandenberg, California was conducted. Observations of wind speed and direction, temperature, dew point, vertical wind velocity, dew deposition, drop-size distribution, liquid water content, and haze and cloud nucleus concentration were obtained. These observations were initiated in late evening prior to fog formation and continued until the time of dissipation in both advection and radiation fogs. Data were also acquired in one valley fog and several dense haze situations. The behavior of these parameters prior to and during fog are discussed in detail. A two-dimensional numerical model was developed to investigate the formation and dissipation of advection fogs under the influence of horizontal variations in surface temperature. The model predicts the evolution of potential temperature, water vapor content, and liquid water content in a vertical plane as determined by vertical turbulent transfer and horizontal advection. Results are discussed from preliminary numerical experiments on the formation of warm-air advection fog and dissipation by natural and artificial heating from the surface.
Mack, E. J.↗
A method for direct numerical integration of the Boltzmann equation
The principal difficulties in numerical solution of the Boltzmann equation are considered. The study is aimed at formulating a numerical solution in such a manner that it contains a minimum amount of excess information at the distribution function level. It is pointed out that the accurate calculation of the distribution function at each point in phase space requires a tremendous number of operations, due to the necessity of solving five-fold quadratures in the collision integral. This results in the operational memory of the digital computer being insufficient to store all the data on the distribution functions at the necessary points in phase space. An algorithm is constructed involving successive iterations of the Boltzmann equation which does not require storage of each step of the new distribution function.
Cheremisin, F. G.↗
A numerical solution for thermoacoustic convection of fluids in low gravity
A finite difference numerical technique for solving the differential equations which describe thermal convection of compressible fluids in low gravity are reported. Results of one-dimensional calculations are presented, and comparisons are made to previous solutions. The primary result presented is a one-dimensional radial model of the Apollo 14 heat flow and convection demonstration flight experiment. The numerical calculations show that thermally induced convective motion in a confined fluid can have significant effects on heat transfer in a low gravity environment.
Spradley, L. W.↗
Numerical studies of unsteady two dimensional subsonic flows using the ICE method
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.
Wieber, P. R.↗