Category: Geometry And Topology
By Gaston Darboux
Excerpt from Leçons sur les Systèmes Orthogonaux Et les Coordonnées Curvilignes
Dans les Leçons sur l. a. théorie des surfaces, j avais déjà fait connaître, d'une manière incidente, différentes professional priétés des systèmes triples orthogonaux et des coordon nées curvilignes; mais j'avais réservé le développement régulier et systématique des théories qui se rattachent à ce beau sujet pour le nouveau Traité dont je begin aujourd'hui los angeles publication.
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By ZhiJunt S., GuangWei Y., JingYan Y.
A brand new Lagrangian cell-centered scheme for two-dimensional compressible flows in planar geometry is proposed through Maire et al. the most new characteristic of the set of rules is that the vertex velocities and the numerical puxes throughout the phone interfaces are all evaluated in a coherent demeanour opposite to straightforward techniques. during this paper the strategy brought by means of Maire et al. is prolonged for the equations of Lagrangian gasoline dynamics in cylindrical symmetry. diverse schemes are proposed, whose distinction is that one makes use of quantity weighting and the opposite zone weighting within the discretization of the momentum equation. within the either schemes the conservation of overall power is ensured, and the nodal solver is followed which has an analogous formula as that during Cartesian coordinates. the quantity weighting scheme preserves the momentum conservation and the area-weighting scheme preserves round symmetry. The numerical examples display our theoretical concerns and the robustness of the recent technique.