An Upwind Finite Pointset Method (FPM) for Compressible Euler and Navier-Stokes Equations

  • Jörg Kuhnert
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 26)


A Lagrangian scheme for compressible fluid flows is presented. The method can be viewed as a generalized finite difference upwind scheme. The scheme is based on the classical Euler equations in fluid mechanics, which concerns mainly non viscous problems. However, it can easily be extended to viscous problems as well. For the approximation of the spatial derivatives in the Euler equations, a modified moving least squares (MLS) method is used.


Euler Equation Smooth Particle Hydrodynamic Upwind Scheme Move Little Square Lagrangian Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. Benz. Smoothed Particle Hydrodynamics: A review, NATO workshop, Les Arcs, France, page 269, 1989Google Scholar
  2. 2.
    W. Benz, Simulation of brittle solids using smooth particle hydrodynamics, Computer Physics Communications 87 (1995) 253–265zbMATHCrossRefGoogle Scholar
  3. 3.
    W. Benz, E. Asphaug, Impact simulations with fracture, ICARUS 107, 98–116 (1994)CrossRefGoogle Scholar
  4. 4.
    G.A. Dilts. Moving Least Squares Particle Hydrodynamics I, Consistency and Stability, Hydrodynamic Methods Group, Los Alamos National Laboratory, 1996Google Scholar
  5. 5.
    C. Hirsch. Numerical Computation of Internal and External Flows, John Wiley & Sons Ltd., 1988Google Scholar
  6. 6.
    J. Kuhnert. General Smoothed Particle Hydrodynamics, PhD thesis, University Kaiserslautern, Germany (1999)Google Scholar
  7. 7.
    J. Kuhnert, A. Trameçon, P. Ullrich. Advanced Fluid Structure Coupled Simulations applied to Out-of-position Cases, EUROPAM Conference Proceedings 2000, ESI group, Paris, FranceGoogle Scholar
  8. 8.
    J. Monaghan. Smoothed Particle Hydrodynamics, Annu. Rev. Astronom. Astrophys. 30, 543 (1992)CrossRefGoogle Scholar
  9. 9.
    J. Monaghan. Simulating free surface flows with SPH, J. Com. Phy., 109, 67–93 (1993)MathSciNetCrossRefGoogle Scholar
  10. 10.
    J. Monaghan. Simulating free surface flows with SPH, J. Com. Phy., 109, 67–93 (1993)MathSciNetCrossRefGoogle Scholar
  11. 11.
    J.P. Morris. An Overview of the Method of Smoothed Particle Hydrodynamics, Berichte der AGTM, 95–152, Fachbereich Mathematik, Universität Kaiseslautern, 1995Google Scholar
  12. 12.
    J.P. Morris, Analysis of smoothed particle hydrodynamics with applications, PhD Thesis, Monash University (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jörg Kuhnert
    • 1
  1. 1.Fraunhofer für Institut Techno- und WirtschaftmathematikKaiserslauternGermany

Personalised recommendations