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  • 1
    ISSN: 0271-2091
    Keywords: Backward-facing step ; Flow stability ; Incompressible flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A detailed case study is made of one particular solution of the 2D incompressible Navier-Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high-order finite-element method solving the unsteady equations by time-marching; (2) a high-order finite-element method solving both the steady equations and the associated linear-stability problem; (3) a second-order finite difference method solving the unsteady equations in streamfunction form by time-marching; and (4) a spectral-element method solving the unsteady equations by time-marching. The unanimous conclusion is that the correct solution for flow over the backward-facing step at Re = 800 is steady - and it is stable, to both small and large perturbations.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 1988-11-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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  • 3
    Publication Date: 1990-09-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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  • 4
    Publication Date: 1989-09-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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  • 5
    Publication Date: 2011-08-24
    Description: An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: In: Numerical methods in laminar and turbulent flow; Proceedings of the 7th International Conference, Stanford Univ., CA, July 15-19, 1991. Vol. 7, pt. 2 (A93-34301 13-34); p. 1612-1622.
    Format: text
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  • 6
    Publication Date: 2004-12-03
    Description: The simulation of sound generation and propagation in three space dimensions with realistic aircraft components is a very large time dependent computation with fine details. Simulations in open domains with embedded objects require accurate and robust algorithms for propagation, for artificial inflow and outflow boundaries, and for the definition of geometrically complex objects. The development, implementation, and validation of methods for solving these demanding problems is being done to support the NASA pillar goals for reducing aircraft noise levels. Our goal is to provide algorithms which are sufficiently accurate and efficient to produce usable results rapidly enough to allow design engineers to study the effects on sound levels of design changes in propulsion systems, and in the integration of propulsion systems with airframes. There is a lack of design tools for these purposes at this time. Our technical approach to this problem combines the development of new, algorithms with the use of Mathematica and Unix utilities to automate the algorithm development, code implementation, and validation. We use explicit methods to ensure effective implementation by domain decomposition for SPMD parallel computing. There are several orders of magnitude difference in the computational efficiencies of the algorithms which we have considered. We currently have new artificial inflow and outflow boundary conditions that are stable, accurate, and unobtrusive, with implementations that match the accuracy and efficiency of the propagation methods. The artificial numerical boundary treatments have been proven to have solutions which converge to the full open domain problems, so that the error from the boundary treatments can be driven as low as is required. The purpose of this paper is to briefly present a method for developing highly accurate algorithms for computational aeroacoustics, the use of computer automation in this process, and a brief survey of the algorithms that have resulted from this work. A review of computational aeroacoustics has recently been given by Lele.
    Keywords: Acoustics
    Type: HPCCP/CAS Workshop Proceedings 1998; 9-14; NASA/CP-1999-208757
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  • 7
    Publication Date: 2011-08-19
    Description: The algorithm employed in the present incompressible two-dimensional calculations of an impulsively-started lid-driven cavity has its basis in the time-dependent stream-function equation. While a Crank-Nicholson differencing scheme is used for the diffusion terms, the Adams-Bashforth scheme is used for the convection terms. The periodic asymptotic solutions obtained for Reynolds numbers of 5000 and 10,000 are found to be precisely periodic; it is demonstrated that they have reached asymptotic states. The indicators of that achievement are discussed.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 90; 219-261
    Format: text
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  • 8
    Publication Date: 2011-08-19
    Description: The numerical scheme used by the present time-accurate FEM numerical method for incompressible Navier-Stokes equations, using primitive variables as the unknowns, is a Crank-Nicholson implicit treatment of all equation terms with central differencing for space derivatives. The introduction of a continuous auxilliary system in pseudo-time, with artificial compressibility, yields the incompressible solution at the advanced time level; time-accurate solutions are thereby obtained for two-dimensional fluid flows in a square cavity, in the cases of both an impulsively starting lid and an oscillating lid.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 79; 113-134
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  • 9
    Publication Date: 2011-08-19
    Description: Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 84; 207-241
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  • 10
    Publication Date: 2013-08-29
    Description: Acoustic problems have become extremely important in recent years because of research efforts such as the High Speed Civil Transport program. Computational aeroacoustics (CAA) requires a faithful representation of wave propagation over long distances, and needs algorithms that are accurate and boundary conditions that are unobtrusive. This paper applies a new finite difference method and boundary algorithm to the Linearized Euler Equations (LEE). The results demonstrate the ability of a new fourth order propagation algorithm to accurately simulate the genuinely multidimensional wave dynamics of acoustic propagation in two space dimensions with the LEE. The results also show the ability of a new outflow boundary condition and fourth order algorithm to pass the evolving solution from the computational domain with no perceptible degradation of the solution remaining within the domain.
    Keywords: ACOUSTICS
    Type: NASA. Langley Research Center, ICASE(LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA) p 255-259 (SEE N95-30133 10-71); NASA. Langley Resear
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