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  • 1
    Electronic Resource
    Electronic Resource
    An effective multigrid method for high-speed flows (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 8 (1992), S. 671-681 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the use of a multigrid method with central differencing to solve the Navier-Stokes equations for high-speed flows. The time-dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time-stepping and variable-coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for two-dimensional laminar flow over a circular cylinder and a 15-degree compression ramp.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630080913
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    Paper (German National Licenses)
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  • 2
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    Efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations (1990)
    In:  Other Sources
    Details
    Publication Date: 2011-08-19
    Keywords: AERODYNAMICS
    Type: AIAA Journal (ISSN 0001-1452); 28; 1464-147
    Format: text
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  • 3
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    Multigrid schemes for viscous hypersonic flows (1993)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving two different hypersonic flow problems. Some new multigrid schemes, based on semicoarsening strategies, are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6).
    Keywords: AERODYNAMICS
    Type: The Sixth Copper Mountain Conference on Multigrid Methods, Part 2; p 481-495
    Format: application/pdf
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  • 4
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    Upwind relaxation algorithms for Euler/Navier-Stokes equations (1986)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.
    Keywords: AERODYNAMICS
    Type: Langley Symposium on Aerodynamics, Volume 1; p 89-107
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  • 5
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    A multistage time-stepping scheme for the thin-layer Navier-Stokes equations (1986)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: A finite-volume scheme for numerical integration of the Euler equations was extended to allow solution of the thin-layer Navier-Stokes equations in two and three dimensions. The extended algorithm, which is based on a class of four-stage Runge-Kutta time-stepping schemes, was made numerically efficient through the following convergence acceleration technique: (1) local time stepping, (2) enthalpy damping, and (3) residual smoothing. Also, the high degree of vectorization possible with the algorithm has yielded an efficient program for vector processors. The scheme was evaluated by solving laminar and turbulent flows. Numerical results have compared well with either theoretical or other numerical solutions and/or experimental data.
    Keywords: AERODYNAMICS
    Type: Langley Symposium on Aerodynamics, Volume 1; p 109-135
    Format: application/pdf
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  • 6
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    An effective multigrid method for high-speed flows (1991)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for 2-D laminar flow over a circular cylinder and a 15 deg compression ramp.
    Keywords: AERODYNAMICS
    Type: NASA-CR-187602 , NAS 1.26:187602 , ICASE-91-56 , AD-A240568
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  • 7
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    Multigrid for hypersonic viscous two- and three-dimensional flows (1991)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.
    Keywords: AERODYNAMICS
    Type: NASA-CR-187603 , NAS 1.26:187603 , ICASE-91-57 , AD-A240707
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  • 8
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    Pseudo-time algorithms for the Navier-Stokes equations (1986)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.
    Keywords: AERODYNAMICS
    Type: NASA-CR-178127 , ICASE-86-37 , NAS 1.26:178127
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  • 9
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    A comparison of two central difference schemes for solving the Navier-Stokes equations (1990)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Five viscous transonic airfoil cases were computed by two significantly different computational fluid dynamics codes: An explicit finite-volume algorithm with multigrid, and an implicit finite-difference approximate-factorization method with Eigenvector diagonalization. Both methods are described in detail, and their performance on the test cases is compared. The codes utilized the same grids, turbulence model, and computer to provide the truest test of the algorithms. The two approaches produce very similar results, which, for attached flows, also agree well with experimental results; however, the explicit code is considerably faster.
    Keywords: AERODYNAMICS
    Type: NASA-TM-102815 , A-90141 , NAS 1.15:102815
    Format: application/pdf
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  • 10
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    Progress with multigrid schemes for hypersonic flow problems (1991)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.
    Keywords: AERODYNAMICS
    Type: NASA-CR-189579 , ICASE-91-89 , NAS 1.26:189579 , AD-A244822
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