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  • 1
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    Partial implicitization (1973)
    In:  Other Sources
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    Publication Date: 2011-08-16
    Description: The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.
    Keywords: FLUID MECHANICS
    Type: Journal of Computational Physics; 13; Nov. 197
    Format: text
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  • 2
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    Solutions to divergence form equations using the method of partial implicitization (1976)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: Partial implicitization is well suited for use on vector-processing computers since the method is an explicit unconditionally stable numerical technique. So far equations cast in nondivergence form have been used, though equations cast in the divergence form would have inherently greater accuracy. Since the method of partial implicitization is applicable only to relaxing problems to their steady state and is not applicable to true transient problems, a simple mathematical manipulation can be carried out which will produce the desired partial implicitization solution to divergence form equations.
    Keywords: NUMERICAL ANALYSIS
    Type: Journal of Computational Physics; 21; July 197
    Format: text
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  • 3
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    Comparative study of the convergence rates of two numerical techniques (1978)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: The paper examines the applicability of the three-step Stetter (1968) method to the problem of hypersonic viscous flow over a blunt axisymmetric body used for planetary entry probes at zero angle of attack. The flow-field results using the two-step finite-difference MacCormack (1969) method are reported by Kumar and Graves (1977). Only the computational efficiency of Stetter's method is compared with that of MacCormack's in terms of the iterative time steps and computing time required for the steady-state solution. Advantages of Stetter's method over MacCormack's are established.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA Journal; 16; Nov. 197
    Format: text
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  • 4
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    Navier-Stokes solutions using Stetter's method (1978)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: Compressible Navier-Stokes equations for quasi-one-dimensional flow in a converging-diverging nozzle have been solved using Stetter's three-step predictor-corrector technique. Particular emphasis is given to the minimum iterative step feature for steady-state solutions. It is found that for the nonviscous-dominated case, Stetter's method attains the steady-state solution in the fewest steps when compared to four other currently used techniques.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA Journal; 16; Sept
    Format: text
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  • 5
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    Laminar and turbulent flows over a spherically blunted cone with massive surface blowing (1979)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: Numerical solutions are presented for the flow over a spherically blunted cone with massive surface blowing. Time-dependent viscous shock layer equations are used to describe the flowfield. The boundary conditions on the body surface include a prescribed blowing rate distribution. The governing equations are solved by a time-asymptotic finite-difference method. Results presented here are only for a perfect gas-type flow at zero angle of attack. Both laminar and turbulent flow solutions are obtained. It is found that the surface blowing smooths out the effect of the curvature discontinuity at the sphere-cone juncture point on the laminar flowfield and results in a negative pressure gradient over the body. The shock slope increases on the downstream portion of the body as the surface blowing rate is increased. The turbulent flow with surface blowing is found to redevelop a boundary-layer-like region near the surface. The effects of this boundary-layer-like region on the flowfield and heating rates are discussed.
    Keywords: AERODYNAMICS
    Type: AIAA Journal; 17; Dec. 197
    Format: text
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  • 6
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    Flowfield calculations past an entry probe with ablated nose shape (1980)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: The effects of ablated nose shapes on the flowfield solutions are studied, using a time-dependent finite-difference method developed by Kumar, et al. (1979). Solutions are obtained for the laminar flow of a radiating mixture of H-He in chemical equilibrium past a blunt axisymmetric body at zero angle of attack. The freestream conditions correspond to a point on a typical Jovian entry trajectory, and the initial probe shape is a 45-deg half-angle spherically blunted cone. It is found that as nose bluntness increases, the following occur: in the nose region, shock standoff distances and radiative heating rates increase substantially; surface pressure level increases, but convective heating rates decrease.
    Keywords: AERODYNAMICS
    Type: AIAA Journal; 18; June 198
    Format: text
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  • 7
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    User's guide for vectorized code EQUIL for calculating equilibrium chemistry on Control Data STAR-100 computer (1980)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: A vectorized code, EQUIL, was developed for calculating the equilibrium chemistry of a reacting gas mixture on the Control Data STAR-100 computer. The code provides species mole fractions, mass fractions, and thermodynamic and transport properties of the mixture for given temperature, pressure, and elemental mass fractions. The code is set up for the electrons H, He, C, O, N system of elements. In all, 24 chemical species are included.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: NASA-TM-80193 , L-13342
    Format: application/pdf
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  • 8
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    Viscous compressible flow about blunt bodies using a numerically generated orthogonal coordinate system (1980)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A numerical solution to the Navier-Stokes equations was obtained for blunt axisymmetric entry bodies of arbitrary shape in supersonic flow. These equations are solved on a finite difference mesh obtained from a simple numerical technique which generates orthogonal coordinates between arbitrary boundaries. The governing equations are solved in time dependent form using Stetter's improved stability three step predictor corrector method. For the present application, the metric coefficients were obtained numerically using fourth order accurate, finite difference relations and proved to be totally reliable for the highly stretched mesh used to resolve the thin viscous boundary layer. Solutions are obtained for a range of blunt body nose shapes including concavities.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-TM-81859
    Format: application/pdf
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  • 9
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    A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg (1973)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: 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.
    Keywords: FLUID MECHANICS
    Type: NASA-TM-X-2843 , L-8944
    Format: application/pdf
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  • 10
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    Viscous flow solutions with a cubic spline approximation (1975)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: A cubic spline approximation is used for the solution of several problems in fluid mechanics. This procedure provides a high degree of accuracy even with a nonuniform mesh, and leads to a more accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several typical integration schemes are presented. For two-dimensional flows a spline-alternating-direction-implicit (SADI) method is evaluated. The spline procedure is assessed and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computers and Fluids; 3; Mar. 197
    Format: text
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