Multidimensional upwinding and implicit newton acceleration for the 3D euler equations on tetrahedral meshes

  • A. Bonfiglioli
  • T. Barth
  • H. Deconinck
Algorithms Euler
Part of the Lecture Notes in Physics book series (LNP, volume 490)


Matrix distribution schemes, originally developed and tested in two dimensions, have been extended to three dimensions. Preliminary numerical evidence shows great promise for these methods, but addition work is still needed to improve robustness near stagnation points and discontinuities.


Computational Fluid Dynamics Euler Equation Stagnation Point Supersonic Flow Tetrahedral Mesh 
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  1. [1]
    H. Deconinck and G. Degrez. Multidimensional Upwinding and Implicit Newton Acceleration for the 3D Euler Equations on Tetrahedral Meshes. In 15th International Conference on Numerical Methods in Fluid Dynamics, Monterey, USA, June 1996.Google Scholar
  2. [2]
    H. Deconinck, R. Struijs, G. Bourgois, and P.L. Roe. Compact advection schemes on unstructured grids. In VKI LS 1993-04, Computational Fluid Dynamics, 1993.Google Scholar
  3. [3]
    E. van der Weide and H. Deconinck. Positive Matrix Distribution Schemes for Hyperbolic Systems, with application to the Euler Equations. In Computational Fluid Dynamics’ 96, Proc. of 3d ECCOMAS CFD Conference, pp. 747–753. J. Wiley, 1996.Google Scholar
  4. [4]
    H. Deconinck, P.L. Roe, and R. Struijs. A Multi-dimensional Generalization of Roe's Flux Difference Splitter for the Euler Equations. Journal of Computers and Fluids, 22(2/3):215–222, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    P.L. Roe. Multidimensional upwinding: motivation and concepts. In VKI LS 1994-05, Computational Fluid Dynamics, 1994.Google Scholar
  6. [6]
    B. van Leer, W.-T. Lee, and P. Roe. Characteristic Time-Stepping or Local Preconditioning of the Euler equations. In AIAA 10th Computational Fluid Dynamics Conference, 1991. AIAA-91-1552-CP.Google Scholar
  7. [7]
    A. Bonfiglioli and H. Deconinck. Multidimensional Upwind Schemes for the 3D Euler Equations on unstructured tetrahedral meshes. In Notes on Numerical Fluid Dynamics, (eds. H. Deconinck and B. Koren eds.). Vieweg, to be published 1996.Google Scholar
  8. [8]
    H. Paillère, H. Deconinck, and P.L. Roe. Conservative upwind residual-distribution schemes based on the steady characteristics of the Euler equations. 1995. 12th AIAA CFD Conference, San Diego, Paper 95–1700.Google Scholar
  9. [9]
    L.M. Mesaros and P.L. Roe. Multidimensional Fluctuation Splitting Schemes Based on Decomposition Methods. 1995. 12th AIAA CFD Conference, San Diego, Paper 95–1699.Google Scholar
  10. [10]
    V. Schmitt and F. Charpin. Pressure Distributions on the ONERA M6-Wing at Transonic Mach Numbers. Technical Report 138, AGARD, 1979.Google Scholar
  11. [11]
    T. J. Barth. Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations. In VKI LS 1994-05, Computational Fluid Dynamics, 1994.Google Scholar
  12. [12]
    T. J. Barth and S. W. Linton. An Unstructured Mesh Newton Solver for Compressible Fluid Flow and Its Parallel Implementation. 1995. AIAA-95-0221.Google Scholar
  13. [13]
    T. J. Barth. Analysis of Implicit Local Linearization Techniques for TVD and Upwind Algorithms. 1987. AIAA 87-0595.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • A. Bonfiglioli
    • 1
    • 2
  • T. Barth
    • 3
  • H. Deconinck
    • 3
  1. 1.von Karman Institute for Fluid DynamicsBelgium
  2. 2.Dipartimento di Ingegneria e Fisica dell’ AmbienteUniversità della BasilicataPotenzaItaly
  3. 3.NASA Ames RC M.S. T27B-1 Moffett Field

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