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Mehmet Ersoy

  1. Compressible primitive equation: formal derivation and stability of weak solutions.

    Втр, 06/15/2010 - 15:01 — SomNambul
    Authors: Mehmet Ersoy, Timack Ngom, Mamadou Sy
    Subjects: Classical Analysis and ODEs
    Abstract

    We 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.

  2. A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms.

    Втр, 11/24/2009 - 16:01 — SomNambul
    Authors: Christian Bourdarias, Mehmet Ersoy, Stéphane Gerbi
    Subjects: Analysis of PDEs
    Abstract

    We 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.

  3. Air entrainment in transient flows in closed water pipes: a two-layer approach.

    Пнд, 10/05/2009 - 20:24 — SomNambul
    Authors: Christian Bourdarias, Mehmet Ersoy, Stéphane Gerbi
    Subjects: Analysis of PDEs
    Abstract

    In 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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