The finite mass method

SIAM Journal on Numerical Analysis

Volumn 37, Issue 6, 2000, Pages 1768-1799

  Gauger, Christoph ^a   Leinen, Peter ^a   Yserentant, Harry ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Compressible fluids; Finite mass method; Gridless discretizations

Indexed keywords

EID: 0039637664     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999352564     Document Type: Article

References (14)

1. A.J. CHORIN AND J.E. MARSDEN, A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, New York, 1993.
2. R. COURANT AND K.O. FRIEDRICHS, Supersonic Flow and Shock Waves, Interscience Publishers, New York, 1948.
3. E. HAIRER, S.P. NØRSETT, AND G. WANNER, Solving Ordinary Differential Equations, 1. Nonstiff Problems, 2nd ed., Springer-Verlag, Berlin, 1993.
4. M. HOCHBRUCK AND C. LUBICH, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 34 (1997), pp. 1911-1925.
5. L.D. LANDAU AND E.M. LIFSCHITZ, Lehrbuch der Theoretischen Physik. Band I, Mechanik, Akademie-Verlag, Berlin, 1990.
6. L.D. LANDAU AND E.M. LIFSCHITZ, Lehrbuch der Theoretischen Physik. Band VI, Hydrodynamik, Akademie-Verlag, Berlin, 1991.
7. C. LUBICH, private communication, 1999.
8. J.J. MONAGHAN, Smoothed particle hydrodynamics, Ann. Rev. Astron. Astrophys., 30 (1992), pp. 543-574.
9. J.R. PASTA AND S. ULAM, Heuristic numerical work in some problems of hydrodynamics, Math. Tables Aids Comput., 13 (1959), pp. 1-12.
10. J. VON NEUMANN, Proposal and analysis of a new numerical method in the treatment of hydrodynamical shock problems, in Collected Works, Vol. 6, Pergamon Press, Oxford, 1963, pp. 351-379.
11. H. YSERENTANT, A particle model of compressible fluids, Numer. Math., 76 (1997), pp. 111-142.
12. H. YSERENTANT, Particles of variable size, Numer. Math., 82 (1999), pp. 143-159.
13. H. YSERENTANT, Entropy generation and shock resolution in the particle model of compressible fluids, Numer. Math., 82 (1999), pp. 161-177.
14. H. YSERENTANT, A convergence analysis for the finite mass method for flows in external force and velocity fields, SIAM J. Numer. Anal., submitted.