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Solving the Vlasov equation in complex geometries

J. Abiteboul, G. Latu, V. Grandgirard, A. Ratnani, E. Sonnendrücker, A. Strugarek (2011)

ESAIM: Proceedings

This paper introduces an isoparametric analysis to solve the Vlasov equation with a semi-Lagrangian scheme. A Vlasov-Poisson problem modeling a heavy ion beam in an axisymmetric configuration is considered. Numerical experiments are conducted on computational meshes targeting different geometries. The impact of the computational grid on the accuracy and the computational cost are shown. The use of analytical mapping or Bézier patches does not induce...

Some application of the implicit function theorem to the stationary Navier-Stokes equations

Konstanty Holly (1991)

Annales Polonici Mathematici

We prove that - in the case of typical external forces - the set of stationary solutions of the Navier-Stokes equations is the limit of the (full) sequence of sets of solutions of the appropriate Galerkin equations, in the sense of the Hausdorff metric (for every inner approximation of the space of velocities). Then the uniqueness of the N-S equations is equivalent to the uniqueness of almost every of these Galerkin equations.

Some inverse and control problems for fluids

Enrique Fernández-Cara, Thierry Horsin, Henry Kasumba (2013)

Annales mathématiques Blaise Pascal

This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.

Some methodical remarks concerning the flow around arbitrary profiles

Ilja Černý (1982)

Aplikace matematiky

Two well known definitions of the flow of a plane vector field around the boundary of a region Ω are compared. The definition (appropriately arranged) based on the constantness of the stream function on every profile is not only invariant under conformal mappings but more general than the definition based on the vanishing of the normal component of the field on ∂ Ω .

Some properties of forced, dissipative large-scale circulations in a barotropic, non-divergent rotating atmosphere

Laura Gardini, Renzo Lupini, Carlo Pellacani (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Viene studiata la stabilità dell’atmosfera in un pianeta ruotante, forzata da un agente esterno ed in presenza di dissipazione. Lo studio vien condotto nelle ipotesi barotropiche e riguarda, per l’effetto delle approssimazioni adottate, solamente quei fenomeni caratterizzati da grandi scale spaziali. In particolare viene studiata la stabilità dei flussi zonali che caratterizzano la circolazione dei maggiori pianeti del sistema solare; ne vengono determinate, servendosi della approssimazione di Galerkin,...

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