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  • 11
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    Time dependent viscous incompressible Navier-Stokes equations (1989)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: Information on time dependent incompressible Navier-Stokes equations is given in viewgraph form. Information is given on streamfunction equations for unsteady incompressible flow, the streamfunction algorithm for unsteady incompressible flow, and a multigrid solver for the laminar implicit equations.
    Keywords: AERODYNAMICS
    Type: NASA, Ames Research Center, NASA Computational Fluid Dynamics Conference. Volume 1: Sessions 1-6; p 255-270
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  • 12
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    An efficient and robust algorithm for time dependent viscous incompressible Navier-Stokes equations (1992)
    In:  CASI
    Details
    Publication Date: 2013-08-29
    Description: A recently developed finite difference algorithm is presented for steady incompressible Navier-Stokes calculations. The algorithm is extremely robust with respect to Reynolds number, and has been used to directly compute incompressible flows with smoothly resolved streamfunction, kinetic energy and vorticity contours for Reynolds numbers as high as Re = 100,000 without requiring any subscale modelling. The algorithm is second order accurate in both time and space, with Crank-Nicolson differencing for the diffusion terms, with a lagged second order Adams-Basforth differencing for the convection terms, and with central differencing for all space derivatives. The algorithm is extremely efficient with respect to both computing time and physical memory. Solutions are shown for cavity and channel flows at various Reynolds numbers.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computational Fluid Dynamics; p 133-141
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  • 13
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    An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case (1995)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-106928 , E-9649 , NAS 1.15:106928
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  • 14
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    A Low Order and a High Order Solution for a Converging-Diverging Nozzle Problem (2000)
    In:  CASI
    Details
    Publication Date: 2017-10-02
    Description: The Computational Aeroacoustics Workshops on Benchmark problems are conducted in order to generate solutions with a variety of methods for problems that are chosen both to be representative of significant and relevant acoustic phenomena. It is generally recognized that CAA applications require the resolution in time and in space of solution details over a significantly broader range of scales than typical computational fluid dynamics applications. These requirements are forcing the development of new methodologies for CAA applications. This paper presents numerical results from a third and a seventh order algorithm for the propagation of an acoustic signal through a converging-diverging nozzle. These two algorithms are members of a new family of high accuracy methods that have the same order accuracy in both space and time, and are an extension of previous work for linearized Euler equations to fully nonlinear time dependent problems. The simulations are all with the fully nonlinear quasi-1D Euler equations for the total solution, which includes both the fluid dynamics and the acoustics. The acoustic solution is obtained from the time dependent nonlinear solution by subtracting the steady solution.
    Keywords: Acoustics
    Type: Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems; 265-271; NASA/CP-2000-209790
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  • 15
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    High Order And High Resolution Methods For a Model CAA Problem (2004)
    In:  CASI
    Details
    Publication Date: 2018-06-06
    Description: The initial value problem for the first order linear wave equation in one space dimension is treated for two cases with specified initial data and grid, and data from solutions at t = 400 and t = 800 are presented, as prescribed for Problem 1 in Category 1. Results are shown from computations with a sequence of recently developed high order and high resolution methods which combine Hermite interpolation, Cauchy-Kowaleskya recursion for time derivatives, and Taylor series time advancement. These methods have the same order of accuracy in time as in space. Results are shown from methods that range from third to nineteenth order. The stated problems with the prescribed coarse grid can be simulated with errors that are at the level of machine accuracy if the method is sufficiently high order. In addition, the growth of the maximum absolute error out to t = 100,000 is given for simulations with the stated problem data.
    Keywords: Numerical Analysis
    Type: Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems; 417-422; NASA/CP-2004-212954
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  • 16
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    Hopf bifurcation in the driven cavity (1989)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two. The algorithm is based on the time dependent streamfunction equation, with a Crank-Nicolson differencing scheme for the diffusion terms, and with an Adams-Bashforth scheme for the convection terms. A multigrid method is used to solve the linear implicit equations at each time step. Periodic asymptotic solutions have been found for Re = 10000 and for Re = 5000. The Re = 5000 results are validated by grid refinement calculations. The solutions are shown to be precisely periodic, and care is taken to demonstrate that asymptotic states were reached. A discussion is included about the indicators that are used to show that an asymptotic state was reached, and to show that the asymptotic state is indeed periodic.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-TM-102334 , E-4957-1 , ICOMP-89-21 , NAS 1.15:102334
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  • 17
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    Computational Methods for Jet Noise Simulation (2003)
    In:  Other Sources
    Details
    Publication Date: 2019-07-18
    Description: The purpose of our project is to develop, analyze, and test novel numerical technologies central to the long term goal of direct simulations of subsonic jet noise. Our current focus is on two issues: accurate, near-field domain truncations and high-order, single-step discretizations of the governing equations. The Direct Numerical Simulation (DNS) of jet noise poses a number of extreme challenges to computational technique. In particular, the problem involves multiple temporal and spatial scales as well as flow instabilities and is posed on an unbounded spatial domain. Moreover, the basic phenomenon of interest, the radiation of acoustic waves to the far field, involves only a minuscule fraction of the total energy. The best current simulations of jet noise are at low Reynolds number. It is likely that an increase of one to two orders of magnitude will be necessary to reach a regime where the separation between the energy-containing and dissipation scales is sufficient to make the radiated noise essentially independent of the Reynolds number. Such an increase in resolution cannot be obtained in the near future solely through increases in computing power. Therefore, new numerical methodologies of maximal efficiency and accuracy are required.
    Keywords: Fluid Mechanics and Thermodynamics
    Type: HBCUs/OMUs Research Conference Agenda and Abstracts; 28; NASA/TM-2003-212207
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  • 18
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    An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries (2000)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (〉15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.
    Keywords: Acoustics
    Type: NASA/TM-2000-210378 , E-12433 , AIAA Paper 2000-2006 , NAS 1.15:210378 , Aeroacoustics; Jun 12, 2000 - Jun 14, 2000; Lahaina, HI; United States
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  • 19
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    Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment (2017)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].
    Keywords: Aeronautics (General); Acoustics
    Type: GRC-E-DAA-TN42274 , AIAA Aviation 2017; Jun 05, 2017 - Jun 09, 2017; Denver, CO; United States
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  • 20
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    Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment (2017)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].
    Keywords: Acoustics; Aeronautics (General)
    Type: GRC-E-DAA-TN43110 , 2017 AIAA Aviation and Aeronautics Forum; Jun 05, 2017 - Jun 09, 2017; Denver, CO; United States
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