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  • 1
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    An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations - High Reynolds number flows (1991)
    In:  Other Sources
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    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.
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  • 2
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    Hopf bifurcation in the driven cavity (1990)
    In:  Other Sources
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    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
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  • 3
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    Unsteady solution of incompressible Navier-Stokes equations (1988)
    In:  Other Sources
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    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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  • 4
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    Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms (1989)
    In:  Other Sources
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    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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  • 5
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    An efficient and robust algorithm for time dependent viscous incompressible Navier-Stokes equations (1992)
    In:  CASI
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    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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  • 6
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    Hopf bifurcation in the driven cavity (1989)
    In:  CASI
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    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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  • 7
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    An efficient and robust algorithm for two dimensional time dependent incompressible Navier-Stokes equations: High Reynolds number flows (1991)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    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: NASA-TM-104424 , E-6257 , NAS 1.15:104424 , International Conference on Numerical Methods in Laminar and Turbulent Flow; Jul 15, 1991 - Jul 19, 1991; Stanford, CA; United States
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  • 8
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    An unsteady time asymptotic flow in the square driven cavity (1990)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: Summary details of an aperiodic time asymptotic numerical solution for the square drive cavity at Re = 10000 are presented. The data presented is for 6100 less than t less than or equal to 7100, and is representative of the data that characterizes the aperiodic asymptotic state.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-TM-103141 , E-5493 , NAS 1.15:103141 , IMACS 1st International Conference on Computational Physics; Jun 11, 1990 - Jun 15, 1990; Boulder, CO; United States
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