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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)
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)
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)
In this paper, we propose implicit and semi-implicit schemes for the barotropic Euler equations (and the shallow water equations) and the full Euler equations, based on staggered finite volume discretizations, namely the MAC finite volume scheme for rectangular meshes, and, for general mixed triangular and quadragular meshes, a construction of fluxes based(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)
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