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  • 1985-1989  (9)
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  • 1
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    Experiments with implicit upwind methods for the Euler equations (1985)
    Elsevier
    Details
    Publication Date: 1985-06-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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    PAPER CURRENT
  • 2
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    An implicit flux-split algorithm for the compressible Navier-Stokes equations (1987)
    In:  Other Sources
    Details
    Publication Date: 2011-08-19
    Description: An implicit upwind scheme for the compressible Navier-Stokes equations is described and applied to the internal flow in a dual-throat nozzle. The method is second-order accurate spatially and naturally dissipative. A spatially-split approximate factorization method is used to obtain efficient steady-state solutions on the NASA Langley VPS-32 (CYBER 205) supercomputer.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Format: text
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    NASA TECHNICAL REPORTS
  • 3
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    Choice of implicit and explicit operators for the upwind differencing method (1988)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust: it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA PAPER 88-0624
    Format: text
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    NASA TECHNICAL REPORTS
  • 4
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    A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: A scheme of solving the two-dimensional Euler equations is developed. The scheme is genuinely two-dimensional. At each iteration, the data are locally decomposed into four variables, allowing convection in appropriate directions. This is done via a cell-vertex scheme with a downwind-weighted distribution step. The scheme is conservative and third-order accurate in space. The derivation and stability analysis of the scheme for the convection equation, and the derivation of the extension to the Euler equations are given. Preconditioning techniques based on local values of the convection speeds are discussed. The scheme for the Euler equations is applied to two channel-flow problems. It is shown to converge rapidly to a solution that agrees well with that of a third-order upwind solver.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 89-0095
    Format: text
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    NASA TECHNICAL REPORTS
  • 5
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    A comparison of numerical flux formulas for the Euler and Navier-Stokes equations (1987)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA PAPER 87-1104
    Format: text
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    NASA TECHNICAL REPORTS
  • 6
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    Sonic-point capturing (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: A prototype scheme that produces perfectly smooth transonic solutions to nozzle-flow problems is derived and tested. The basic upwind scheme is described as well as satisfying the entropy condition, treatment of the source term, and numerical verification. The analysis yielded a numerical flux function for use near a sonic point, which is based on a full model of a transonic expansion wave, and a matched treatment for the source term.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 89-1945 , AIAA Computational Fluid Dynamics Conference; Jun 13, 1989 - Jun 15, 1989; Buffalo, NY; United States
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    NASA TECHNICAL REPORTS
  • 7
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    A detailed analysis of inviscid flux splitting algorithms for real gases with equilibrium or finite-rate chemistry (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: The extension of the known flux-vector and flux-difference splittings to real gases via rigorous mathematical procedures is demonstrated. Formulations of both equilibrium and finite-rate chemistry for real-gas flows are described, with emphasis on derivations of finite-rate chemistry. Split-flux formulas from other authors are examined. A second-order upwind-based TVD scheme is adopted to eliminate oscillations and to obtain a sharp representation of discontinuities.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Conference on Numerical Methods in Fluid Dynamics; Jun 27, 1988 - Jul 01, 1988; Williamsburg, VA; United States
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    NASA TECHNICAL REPORTS
  • 8
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    Splitting of inviscid fluxes for real gases (1988)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Flux-vector and flux-difference splittings for the inviscid terms of the compressible flow equations are derived under the assumption of a general equation of state for a real gas in equilibrium. No necessary assumptions, approximations or auxiliary quantities are introduced. The formulas derived include several particular cases known for ideal gases and readily apply to curvilinear coordinates. Applications of the formulas in a TVD algorithm to one-dimensional shock-tube and nozzle problems show their quality and robustness.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 88-3526 , AIAA, ASME, SIAM, and APS, National Fluid Dynamics Congress; Jul 25, 1988 - Jul 28, 1988; Cincinnati, OH; United States
    Format: text
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    NASA TECHNICAL REPORTS
  • 9
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    Design of optimally smoothing multi-stage schemes for the Euler equations (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator. The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step. The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. The analysis is extended to the Euler equations in one space-dimension by use of 'characteristic time-stepping', which preconditions the equations, removing stiffness due to variations among characteristic speeds. Convergence rates independent of the number of cells in the finest grid are achieved for transonic flow with and without a shock. Characteristic time-stepping is shown to be preferable to local time-stepping, although use of the optimally damping schemes appears to enhance the performance of local time-stepping. The extension of the analysis to the two-dimensional Euler equations is hampered by the lack of a model for characteristic time-stepping in two dimensions. Some results for local time-stepping are presented.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 89-1933 , AIAA Computational Fluid Dynamics Conference; Jun 13, 1989 - Jun 15, 1989; Buffalo, NY; United States
    Format: text
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    NASA TECHNICAL REPORTS
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