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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 76 (1997), S. 111-142 
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991): 76N99, 76M25, 65M12, 65M99
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. Fluid mechanics describes the motion of mass in space under the influence of internal and external forces. The particle model presented in this article is based on this fact. The fluid is subdivided into a finite number of small mass packets, the particles. These mass packets have a finite extension and share all properties with the fluid, except for the restriction that they cannot get deformed and can perform only rigid body motions. The forces acting upon the particles are identical to those acting on a part of a fluid. The exact conservation of mass and, for the case of adiabatic flows, also of entropy is automatically guaranteed by the approach. When the particle size tends to zero, the mean local displacement of the particles converges in the weak sense. In the inviscid case, the resulting flows can be regarded as solutions of the Euler equations.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 82 (1999), S. 143-159 
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991):76N99, 76M25, 65M99
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract. A problem of all particle methods is that they produce large vacuum regions when they are applied to a free gas flow, for example. With the approach recently proposed by the author [Numer. Math. (1997) 76: 111–142], this difficulty can be avoided. One can let the particles adapt their size to the local state of the fluid. How, is described in the present article. The diameter as an additional degree of freedom strongly improves the performance of the numerical methods based on this particle model.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 82 (1999), S. 161-177 
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991):76N99, 76M25, 65M99
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract. The examination of the particle model of compressible fluids that has been developed by the author [Numer. Math. (1997) 76: 111–142] and that has recently been extended to particles of variable size [Numer. Math. (1999) 82: 143–159], is continued. It is shown that, in the limit of particle sizes tending to zero, both the mass density and the mass flux density and the entropy density and the entropy flux density converge in the weak sense and satisfy the corresponding conservation laws. To incorporate entropy generation in shocks, a new kind of viscous force is introduced.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Numerical algorithms 21 (1999), S. 387-392 
    ISSN: 1572-9265
    Schlagwort(e): multigrid methods ; domains of complicated shape ; 65N55 ; 65N30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract It is shown that, with homogeneous Dirichlet boundary conditions, the condition number of finite element discretization matrices remains uniformly bounded independent of the size of the boundary elements provided that the size of the elements increases with their distance to the boundary. This fact allows the construction of simple multigrid methods of optimal complexity for domains of nearly arbitrary shape.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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