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  • 1
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    Characteristic time-stepping or local preconditioning of the Euler equations (1991)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: A derivation is presented of a local preconditioning matrix for multidimensional Euler equations, that reduces the spread of the characteristic speeds to the lowest attainable value. Numerical experiments with this preconditioning matrix are applied to an explicit upwind discretization of the two-dimensional Euler equations, showing that this matrix significantly increases the rate of convergence to a steady solution. It is predicted that local preconditioning will also simplify convergence-acceleration boundary procedures such as the Karni (1991) procedure for the far field and the Mazaheri and Roe (1991) procedure for a solid wall.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 91-1552 , AIAA Computational Fluid Dynamics Conference; Jun 24, 1991 - Jun 27, 1991; Honolulu, HI; United States
    Format: text
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    NASA TECHNICAL REPORTS
  • 2
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    Sonic-point capturing (1989)
    In:  Other Sources
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    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
  • 3
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    Design of optimally smoothing multistage schemes for the Euler equations (1992)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: A recently derived local preconditioning of the Euler equations is shown to be useful in developing multistage schemes suited for multigrid use. The effect of the preconditioning matrix on the spatial Euler operator is to equalize the characteristic speeds. When applied to the discretized Euler equations, the preconditioning has the effect of strongly clustering the operator's eigenvalues in the complex plane. This makes possible the development of explicit marching schemes that effectively damp most high-frequency Fourier modes, as desired in multigrid applications. The technique is the same as developed earlier for scalar convection schemes: placement of the zeros of the amplification factor of the multistage scheme in locations where eigenvalues corresponding to high-frequency modes abound.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Communications in Applied Numerical Methods (ISSN 0748-8025); 8; 10; p. 761-769.
    Format: text
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    NASA TECHNICAL REPORTS
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