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  • 1
    Publication Date: 2019-06-28
    Description: A previously developed upwind/relaxation algorithm for solving the unsteady, compressible, thin-layer Navier-Stokes equations is presently modified so that the downstream influence of the subsonic part of the boundary layer in an otherwise supersonic flow is suppressed by restricting the streamwise pressure gradient. A 'parabolized' solution is then efficiently obtained by marching downstream and iterating locally in each crossflow plane until achieving convergence. This parabolized solution is an excellent final one for problems without large adverse streamwise pressure gradients.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA PAPER 87-1113
    Format: text
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  • 2
    Publication Date: 2019-06-28
    Description: The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TP-2829 , L-16416 , NAS 1.60:2829
    Format: application/pdf
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  • 3
    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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  • 4
    Publication Date: 2019-07-12
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA Journal (ISSN 0001-1452); 27; 1165
    Format: text
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