Realization of the Finite Mass Method

  • Peter Leinen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2330)


The finite mass method, a new Lagrangian method for the numerical simulation of gas flow, is presented. The finite mass method is founded on a discretization of mass, not of space. Mass is subdivided into small mass packets. These mass packets move under the influence of internal and external forces. The right-hand sides of the differential equations governing the motion of the particles are integrals which cannot be evaluated exactly. A Lagrangian discretization of these integrals will be presented that maintains the invariance and conservation properties of the method. An efficient way to implement and parallelize the method is discussed.


Mass Density Smooth Particle Hydrodynamic Quadrature Rule Smooth Particle Hydrodynamic Quadrature Point 
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.


  1. 1.
    Gauger, Chr., Leinen, P., Yserentant, H.: The finite mass method. SIAM J. Numer. Anal., 37 (2000), 1768–1799zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Hilbert, D.: Über die stetige Abbildung einer Linie auf ein Flächenstück. Math. Annalen, 38 (1891), 459–460.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Sagan, H.: Space-filling curves. Springer, 1994Google Scholar
  4. 4.
    Monaghan, J.J.: Smoothed particle hydrodynamics. Ann. Rev. Astron. Astrophys., 30 (1992), 543–574.CrossRefGoogle Scholar
  5. 5.
    Yserentant, H.: A particle model of compressible fluids. Numer. Math., 76 (1997), 111–142.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Yserentant, H.: Particles of variable size. Numer. Math., 82 (1999), 143–159.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Yserentant, H.: Entropy generation and shock resolution in the particle model of compressible fluids. Numer. Math., 82 (1999), 161–177.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Zumbusch, G.: On the quality of space-filling curve induced partitions. Z. Angew. Math. Mech., 81, (2001), 25–28zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Peter Leinen
    • 1
  1. 1.Mathematisches InstitutUniversität TübingenGermany

Personalised recommendations