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  • 1
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    An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension) (1994)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.
    Keywords: NUMERICAL ANALYSIS
    Type: AD-280296 , NASA-CR-194902 , NAS 1.26:194902 , ICASE-94-24
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 2
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    An accuracy assessment of Cartesian-mesh approaches for the Euler equations (1995)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-111200 , NAS 1.15:111200 , NIPS-96-07173 , (ISSN 0021-9991)
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 3
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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
    Format: application/pdf
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    NASA TECHNICAL REPORTS
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