Walid Kheriji

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In this paper, we analyze the stability and consistency of a time-implicit scheme and a pressure correction scheme, based on staggered space discretizations, for the compressible barotropic Euler equations. We first show that the solutions to these schemes satisfy a discrete kinetic energy and a discrete elastic potential balance equations. Integrating(More)
We present in this paper a class of schemes for the numerical simulation of compressible flows. In order to ensure the stability of the discretizations in a wide range of Mach numbers and introduce sufficient decoupling for the numerical resolution, we choose to implement and study pressure correction schemes on staggered meshes. The implicit version of the(More)
We present in this paper a class of schemes for the solution of the barotropic NavierStokes equations. These schemes work on general meshes, preserve the stability properties of the continuous problem, irrespectively of the space and time steps, and boil down, when the Mach number vanishes, to discretizations which are standard (and stable) in the(More)
In this paper, we propose implicit and pressure correction schemes for the Euler equations, based on staggered space discretizations, namely the MAC finite volume scheme or the low-order (Rannacher-Turek or Crouzeix-Raviart) finite elements. Both schemes rely on the discretization of the internal energy balance equation, which offers two main advantages:(More)
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For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for(More)
We assess in this paper the capability of a pressure correction scheme to compute shock solutions of the homogeneous model for barotropic two-phase flows. This scheme is designed to inherit the stability properties of the continuous problem: the unknowns (in particular the density and the dispersed phase mass fraction y) are kept within their physical(More)
Abstract. In reservoir simulations, nearwell regions usually require finer space and time scales compared with the remaining of the reservoir domain. We present a domain decomposition algorithm for a two phase Darcy flow model coupling nearwell regions locally refined in space and time with a coarser reservoir discretization. The algorithm is based on an(More)
We propose a discretization for the MAC scheme of the viscous dissipation term τ (u) : ∇u (where τ (u) stands for the shear stress tensor associated to the velocity field u), which is suitable for the approximation of this term in a conservation equation for a scalar variable. This discretization enjoys the property that the integral over the computational(More)
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