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  • 1
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    Splitting of inviscid fluxes for real gases (1988)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    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: NUMERICAL ANALYSIS
    Type: NASA-TM-100856 , ICOMP-88-7 , E-4059 , NAS 1.15:100856
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 2
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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
  • 3
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    Choice of implicit and explicit operators for the upwind differencing method (1988)
    In:  CASI
    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 on 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: NASA-TM-100857 , ICOMP-88-8 , E-4061 , NAS 1.15:100857
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    NASA TECHNICAL REPORTS
  • 4
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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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  • 5
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    A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations (1989)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The solution of the two-dimensional Euler equations is based on the two-dimensional linear convection equation and the Euler-equation decomposition developed by Hirsch et al. 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: NUMERICAL ANALYSIS
    Type: NASA-TM-102029 , E-4772 , NAS 1.15:102029 , ICOMP-89-13 , AIAA PAPER 89-0095 , Aerospace Sciences Meeting; Jan 09, 1989 - Jan 12, 1989; Reno, NV; United States
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