Mehmet Ersoy
Compressible primitive equation: formal derivation and stability of weak solutions.
Tue, 06/15/2010 - 15:01 — SomNambulAuthors: Mehmet Ersoy, Timack Ngom, Mamadou Sy
Subjects: Classical Analysis and ODEs
AbstractWe present a formal derivation of a simplified version of Compressible
Primitive Equations (CPEs) for atmosphere modeling. They are obtained from
$3$-D compressible Navier-Stokes equations with an \emph{anisotropic viscous
stress tensor} where viscosity depends on the density. We then study the
stability of the weak solutions of this model by using an intermediate model,
called model problem, which is more simple and practical, to achieve the main
result.A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms.
Tue, 11/24/2009 - 16:01 — SomNambulAuthors: Christian Bourdarias, Mehmet Ersoy, Stéphane Gerbi
Subjects: Analysis of PDEs
AbstractWe present a numerical kinetic scheme for an unsteady mixed pressurised and
free surface model. This model has a source term depending on both the space
variable and the unknown, U, of the system. The source term is composed by a
topography, a section variation, a curvature (also called corrective) and a
friction term. Using the Finite Volume and Kinetic (FVK) framework, we propose
an approximation of the source terms following the principle of interfacial
upwind with a kinetic interpretation: the source term is not treated as a
volumic term, but included in the numerical fluxes.Air entrainment in transient flows in closed water pipes: a two-layer approach.
Mon, 10/05/2009 - 20:24 — SomNambulAuthors: Christian Bourdarias, Mehmet Ersoy, Stéphane Gerbi
Subjects: Analysis of PDEs
AbstractIn this paper, we first construct a model for transient free surface flows
that takes into account the air entrainment by a sytem of 4 partial
differential equations. We derive it by taking averaged values of gas and fluid
velocities on the cross surface flow in the Euler equations (incompressible for
the fluid and compressible for the gas). Then, we propose a mathematical
kinetic interpretation of this system to finally construct a well-balanced
kinetic scheme having the properties of conserving the still water steady state
and possesing an energy.
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